40521228-8866-H1-Physics-2010-JC-Prelims-With-Ans

1

This paper consists of 15 printed pages

Anglo-Chinese Junior College Physics Preliminary Examination Higher 1

PHYSICS Paper 1 Multiple Choice Additional Materials: Multiple Choice Answer Sheet

8866/0131 Aug 2010

1 hour

READ THESE INSTRUCTIONS FIRST Write in soft pencil. Do not use staples, paper clips, highlighters, glue or correction fluid. Write your Name and Index number in the answer sheet provided. There are 30 questions in this section. Answer all questions. For each question there are four possible answers A, B, C and D. Choose the one you consider correct and circle your choice in soft pencil on the separate Answer Sheet. Read the instructions on the Answer sheet very carefully. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this Question Paper.

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2010 H1 8866 Prelim Exam P1

Data speed of light in free space, c = 3.00 × 108 m s−1 elementary charge, e = 1.60 × 10−19 C the Planck constant, h = 6.63 × 10−34 J s unified atomic mass constant, u = 1.66 × 10−27 kg rest mass of electron, me = 9.11 × 10−31 kg rest mass of proton, mp = 1.67 × 10−27 kg acceleration of free fall, g = 9.81 m s−2 Formulae uniformly accelerated motion, s = ut + 2

1 at 2

v 2 = u 2 + 2as work done on/by a gas, W = p ΔV hydrostatic pressure, p = ρ g h resistors in series, R = R1 + R2 + … resistors in parallel, 1/R = 1/R1 + 1/R2 + …

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2010ACJC8866P1 [Turn over

1 Which of the following pairs consists of two base SI units

A kilogram, newton B hertz, kelvin C ampere, mol D coulomb, second

2 The specific heat capacity of a liquid, c, can be determined by measuring the change in

temperature, θ f - θ i, of the liquid of mass m when heat H is supplied to it. The value of c is then calculated using the formula

( )f i

Hcm θ θ

=

The values measured are H = ( 9.6 ± 0.6) kJ m = (200.0 ± 0.5) g θ f = (40.0 ± 0.2) °C θ i = (20.0 ± 0.1) °C What is the percentage uncertainty in the value of c?

A 8.0 % B 7.0 % C 6.6 % D 6.5 % 3 A car is travelling at a velocity of 24 m s-1 due west initially. At a later time, it is seen

travelling at a velocity of 10 m s-1 due south. Given that the direction North N, points vertically upwards, which of the following vector

R represents the change in velocity of the car?

A B C D

R

N

R

N

R

N

R

N

4


4 Which displacement-time graph best represents the motion of a falling sphere until it begins to travel with terminal velocity?

A B

C D

5 A particle moves along a straight line. A variable K, of the particle's motion is plotted

against time as shown in Fig 5.

Fig 5

At any time, the slope of the graph is the acceleration of the particle. What is the variable K?

A the displacement of the particle B the distance travelled by the particle C the speed of the particle D the velocity of the particle

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2010 H1 8866 Prelim Exam P1 [Turn over

6 Newton's third law concerns the forces of interaction between two bodies. Which of the following statements relating to the third law is not correct?

A The two forces are equal and opposite so the bodies are in equilibrium. B The two forces are always in opposite directions. C The two forces are at all times equal in magnitude. D The two forces must act on different bodies.

7 A block of mass 0.60 kg is on a rough horizontal surface in Fig 7. A constant force of

12 N is applied to the block and it accelerates at 4.0 m s–2.

Fig 7

What is the magnitude of the frictional force acting on the block?

A 2.4 N B 9.6 N C 14 N D 16 N 8 In a particular crash test, a car of mass 1 500 kg collides with a wall, as shown in Fig 8.

The initial and final velocities of the car are shown. If the collision lasts for 0.150 s, find the impulse caused by the collision on the car.

Fig 8

A 18600 Ns to the right B 26400 Ns to the right C 18600 Ns to the left D 26400 Ns to the left

− 15 m s−1 + 2.6 m s−1

4.0 m s−2

12 N

block

horizontal surface

6


9 Two equal masses travel towards each other on a frictionless air track at speeds of 60 cm s–1 and 30 cm s–1. They stick together on impact.

What is the speed of the masses after impact?

A 15 cm s–1 B 20 cm s–1 C 30 cm s–1 D 45 cm s–1

10 A canopy roof, hinged to a vertical wall at one end and secured by a steel rod at the

other end as shown below, is in equilibrium.

The weight of the canopy roof is W, the force exerted by the rod on the roof is F and the reaction by the wall on the roof is R.

Which vector triangle represents the forces acting on the canopy roof?

A B

C D

R

F

WW

F

R

W

F

R

Steel Rod

Canopy roof

F

W

R

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11 A traditional Chinese physician is measuring the mass of herbs with his weighing scale.

The scale consists of a uniform 40 g rod, a 100 g counterweight and an 80 g pan. The rod is 30 cm long, the pan is placed at one end of the rod and the whole system is supported by a string 8 cm away from the pan as shown below.

The counterweight is located at 14 cm from the other end of the rod when the system is

in equilibrium. What is the mass of the herbs resting on the pan?

A 20 g B 55 g C 100 g D 135 g

String support

Pan

Rod Counterweight

14 cm 8 cm

8


12 A person of weight 500 N does a bungee jump using an elastic rope of unstretched length 40 m and having a spring constant k equal to 50 N m-1. During the initial fall there is a transfer of energy from gravitational potential energy to kinetic energy and elastic potential energy. The person falls through a distance of 80 m before beginning to move upwards.

Which set of graphs correctly represent the variation of the three energies?

A B

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60 70 80 90 100

Distance of fall / m

Ener

gy /

kJ

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60 70 80 90 100


Ener

gy /

kJ

C D

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60 70 80 90 100


Ene

rgy

/ kJ

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60 70 80 90 100


Ener

gy /

kJ

13 On braking, 400kJ of heat were produced when a vehicle of mass 1200kg was brought

to rest on a level road. The speed of the vehicle just before the brakes were applied was

A 12.4 m s-1 B 25.8 m s-1 C 124 m s-1 D 258 m s-1

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14 A bird reaches a high speed by falling from the nest before swooping away. What is the

minimum distance it must fall to achieve a speed of 10 m s−1.

A 3.80 m B 4.90 m C 5.10 m D 5.75 m

15 The diagram shows the profile of a transverse wave at a particular instant. The wave is

traveling to the right. The frequency of the wave is 12.5 Hz.

At the instant shown the displacement is zero at the point P. What is the shortest time to elapse before the displacement is zero at point Q?

A 0.01 s B 0.02 s C 0.03 s D 0.07 s

16 A sound wave of frequency 400 Hz is traveling in a gas at a speed of 320 m s-1. What is the phase difference between two points 0.1 m apart in the direction of travel?

A rad4π

B rad2π

C rad5

2π D rad

54π

PQ

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17 Fig 17 shows a trace produced by a sound wave on a cathode-ray oscilloscope. The timebase is set at 4 ms cm-1.

Fig 17

What is the frequency of the sound wave? A 5 Hz B 10 Hz C 20 Hz D 50 Hz

18 Two coherent monochromatic waves of equal amplitude are brought together to form

an interference pattern on a screen. Which of the following graphs could represent the variation of intensity with position (x) across the pattern of fringes?

1 cm

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19 Continuous water waves are diffracted through a gap in a barrier in a ripple tank. Which change will cause the diffraction of the waves to decrease?

A increasing the wavelength of the waves

B Increasing the width of the gap

C reducing the frequency of the waves

D reducing the width of the gap

20 In a Young’s double slit experiment which one of the following will increase the fringe

separation?

A Increasing the slit separation

B Placing the apparatus in a medium of higher refractive index

C Using light of lower frequency

D Decreasing the distance between the slit and the screen

21 Which one of the following statements must be true about two wave-trains of

monochromatic light arriving at a point on a screen if the wave-trains are coherent?

A They interfere constructively

B Their path difference is always in integral multiples of the wavelength.

C They are in phase

D They have a constant phase difference

12


22 A cylindrical wire 4.0 m long has a resistance of 31 Ω and is made of metal of resistivity 1.0 × 10–6 Ω m.

What is the radius of cross-section of the wire?

A 1.0 × 10–8 m B 2.0 × 10–8 m C 6.4 × 10–8 m D 2.0 × 10–4 m

23 Which of the following expression is used to define resistance?

A 2( )

Powercurrent

B ( )( )resistivity lengthArea

C differencepotentialcurrent

D 2( )( )

energytime current

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24 In the circuit below, the battery has negligible internal resistance. Three identical lamps L, M and N, having identical resistances are connected as shown.

The filament of lamp N breaks. Which one of the following shows the subsequent

changes to the brightness of lamp L and lamp M?

Lamp L Lamp M A stays the same Decreases B increases stays the same C increases Decreases D decreases Increases

25 Which diagram shows a potential divider circuit that can vary the voltage across the

lamp?

26 A compass is placed above a wire. The compass needle is seen to point toward the north. When a current is made to flow through the wire, the needle deflects to point along the northwest direction. The orientation of the wire and direction of the current are

orientation of wire direction of current

A north-south south to north

B north-south north to south

C east-west west to east

D east-west east to west

14


27

A current balance is used to measure the magnetic flux density B of a electromagnet. The length PQ of of a current balance is inserted inside a large electromagnet. The direction of the magnetic field is as shown in Fig 27. Length of PQ is L. PQ and RS are d1 and d2 respectively from the pivot. A load of mass m is placed along the RS length. Take acceleration due to gravity to be g.

The direction and magnitude of the current along length PQ are

Fig 27

direction magnitude

A from P to Q 1

2

dLBdm

B from P to Q 1

2

dLBdgm

C from Q to P 1

2

dLBdm

D from Q to P 1

2

dLBdgm

28 An electron moves in the negative x direction, through a uniform magnetic field in the negative y direction. The magnetic force on the electron is:

A in the positive z direction B in the negative z direction C in the positive y direction D in the negative x direction

P

Q R

S

B

15


29 When a parallel beam of white light passes through a cool vapour, dark lines appear in the spectrum of the emergent light. This is principally because energy is absorbed and

A Is not re-radiated at all B Is re-radiated as infra-red C Is re-radiated as ultra-violet D Is re-radiated uniformly in all directions

30 How would the maximum kinetic energy EK of the photoelectrons and the number of

photoelectrons emitted per second n be affected by using a more intense source of the same wavelength?

EK n

A unchanged increased

B unchanged unchanged

C increased increased

D increased unchanged

This paper consists of 19 printed pages

Anglo-Chinese Junior College Physics Preliminary Examination Higher 1

CANDIDATE NAME CLASS

CENTRE NUMBER S INDEX

NUMBER

PHYSICS Paper 2 Structured questions Candidates answer on the Question Paper No additional Materials are required

8866/0220 Aug 2010

2 hours

READ THESE INSTRUCTIONS FIRST Write your Name and Index number in the spaces provided at the boxes above and on all the work you hand in. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Section A Answer all questions. Section B Answer any two questions. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.

For examiners’ use only

Section A

1 / 6

2 / 7

3 / 8

4 / 7

5 / 12

Section B

6 / 20

7 / 20

8 / 20

Total / 80

2


Data speed of light in free space, c = 3.00 × 108 m s−1 elementary charge, e = 1.60 × 10−19 C the Planck constant, h = 6.63 × 10−34 J s unified atomic mass constant, u = 1.66 × 10−27 kg rest mass of electron, me = 9.11 × 10−31 kg rest mass of proton, mp = 1.67 × 10−27 kg acceleration of free fall, g = 9.81 m s−2 Formulae uniformly accelerated motion, s = ut + 2

1 at 2

v 2 = u 2 + 2as work done on/by a gas, W = p ΔV hydrostatic pressure, p = ρ g h resistors in series, R = R1 + R2 + … resistors in parallel, 1/R = 1/R1 + 1/R2 + …

3


For Examiner’s

Use Section A

Answer all the questions in the spaces provided.

1 (a) Give reasoned estimates of the following quantities. In each case, give your answer in an SI unit.

(i) The density of a mobile phone.

density = unit [2]

(ii) The current in the power cord connecting a 400 litre refrigerator to the power supply in Singapore.

current = unit [2]

(b) A student is measuring the diameter of a metal sphere, of similar size to a marble, using a vernier caliper.

(i) Suggest one possible source of systematic error that may arise.

[1]

(ii) Suggest one possible source of random error that may arise.

[1]

4


For Examiner’s

Use 2 A waiter holds a tray horizontally in one hand between fingers and thumb as shown in Fig 2.

Fig 2

(a) (i) State the conditions for the tray to be in equilibrium.

[2] (a) (ii) If the mass of the tray is 0.12 Kg, calculate the magnitudes of forces P

and Q. P = ....................... N Q = ……………….. N [3] (b) The waiter places a glass on the tray. Explain if it is possible for the force, P to

have the same value as in part (a) after the glass is added.

[2]

5


For Examiner’s

Use 3 (a) A copper wire S is stretched over two supports X and Y as shown in Fig 3.1. A permanent magnet is positioned at the central region of the wire. The signal generator provides an alternating current as shown in Fig 3.2 where the direction and magnitude of the current changes periodically.

(i) Explain why the wire in Fig 3.1 will vibrates when the signal generator is operating.

[2]

(ii) Stationary waves with one or more loops, similar to the one shown are set up only when the signal generator is set to certain frequencies.

Explain why stationary waves occur and only at certain frequencies.

[3]

Fig 3.1

Fig 3.2

c

urre

nt

6


For Examiner’s

Use (b) The wave with three loops is produced when signal generator is set to 60 Hz.

(i) Deduce the frequency which results in the formation of only one loop.

Frequency = …………….. Hz [2]

(ii) Draw a diagram to show that what would be observed when the signal generator is set to 100 Hz.

[1] 4 (a) Fig 4 shows the variation of the photocurrent I with the potential of the anode

with respect to the cathode V, in the photoelectric experiment.

Suggest possible reasons for the following observations as seen from Fig 4.

(i) no photocurrent is detected for values of V lower than − Vs

(ii) increasing photocurrent for values of V between − Vs and 0 V.

(iii) saturation current was not achieved immediately when V became greater

than 0 V.

[3]

I/nA

- Vs V/V 0 V1

Fig 4

7


For Examiner’s

Use (b) An orbiting satellite can become charged by the photoelectric effect when sunlight ejects electrons from its outer surface. Satellites must be designed to minimise such charging. Suppose a satellite is coated with platinum, a metal with a very large work function of 5.32 eV.

(i) Determine the longest wavelength of incident sunlight that can eject an

electron from platinum. λ = ……………… m [2]

(ii) The incident photon has a particle like nature. Determine the momentum of the photon.

momentum = ……………… Ns [2]

8


For Examiner’s

Use 5 Hydroelectricity Three Gorges Dam is a hydroelectric river dam that spans the Yangtze River located in the Yiling District of Yichang, at the Hubei province, China. It is the world's largest electricity-generating plant of any kind.

The dam body was completed in 2006. Except for a ship lift, all of the originally planned components of the project were completed on October 30, 2008 when the 26th generator was brought into commercial operation. Currently, it contains 26 completed generators in the shore power plant, each with a capacity of 700 MW. Six additional generators in the underground power plant are being installed and are not expected to become fully operational until around 2011. The completed dam will possess 32 main generators with 2 smaller generators (50 MW each) to power the plant itself. The project produces hydroelectricity, increases the river's navigation capacity, and reduces the potential for floods downstream by providing flood storage space. From completion until September 2009 the dam has generated 348.4 TWh of electricity, covering more than one third of its project cost.

9


For Examiner’s

Use

Maximum Installed Capacity

Current Installed Capacity Limit

Actual Power Output in 2008 (MW)

Maximum Possible Power Output at 18 300 MW capacity

Maximum Possible Power Output at 22 500 MW capacity

Average Actual Flow Rate

Maximum Plant Intake with 32 Main Generators

Maximum Plant Intake with 26 Main Generators

Flow

rate

/ m

3 s-1

10


For Examiner’s

Use (a) (i) Considering the maximum electric generating capacity of the generators, calculate the average power of each of the new generators that will be installed in 2011.

Average Power = …………… W [2] (ii) When all the generators are up in 2011, calculate the time required to

generate 100 TWh of electricity. Time = …………… days [2] (b) Considering conservation of energy, estimate the maximum water level

trapped behind the dam in July. You may assume that density of water = 1000 kg m-3. Maximum water level = …………… m [3] (c) From the graphs, suggest whether a higher flow rate necessarily leads to

larger amount of energy being generated. [2]

11


For Examiner’s

Use

(d) Referring to the temperature charts above, account for the low flow rate and

power output in January. (e) State one advantage of hydroelectricity over the burning of coal and state

another alternative source of energy that have the same advantage.

[1]

[2]

12


For Examiner’s

Use Section B

Answer two the questions for this section.

6 (a) Distinguish between elastic and inelastic collisions.

(b) A rope of length L is attached to a support at point C. A person of mass m1 sits on

a ledge at position A holding the other end of the rope so that it is horizontal and taut, as shown in Fig. 6. The person then drops off the ledge and swings down on the rope toward position B on a lower ledge where an object of mass m2 is at rest. At position B the person grabs hold of the object and simultaneously lets go of the rope. The person and object then land together in the lake at point D, which is a vertical distance L below position B.

Fig. 6

Assuming air resistance and the mass of the rope are negligible,

(i) show that the speed v1 of the person just before the collision with the object is given by v1 = gL2

[2]

(ii) deduce an expression for the speed v2 of the person and object just after the

collision in terms of m1, m2, L, and the acceleration of free fall g. State any assumption made,

Assumption:

Expression for v2 is [3]

[2]

13


For Examiner’s

Use (iii) hence deduce the expression for the time of flight T, and the horizontal

displacement, xo of the person from position B until he lands in the water at point D, assuming that the direction of v2 is horizontal,

Expression for T is

Expression for xo is [5] (iv) if air resistance is not negligible, state and explain how the horizontal

displacement x1, of the person from position B until he lands in the water would be affected,

[3]

(c) (i) State Newton’s second law of motion,

[2]

(ii) Referring to part (b), if the acceleration of the person just before the collision with the object at B is vertically upwards and directed from B to C, and

has a magnitude given by L

21v

,

1. draw a free body diagram of the person just before the collision with

the object at B. [1]

14


For Examiner’s

Use 2. hence determine the tension in the rope just before the collision of the person with the object.

tension = N [2] 7 (a) Fig 7.1 (a) shows the position of the particles of in a medium when they are at

equilibrium while Fig 7.1(b) shows their positions when in the presence of a travelling longitudinal sinusoidal wave.

(i) Deduce the magnitude of the displacement of particle 2 (see Fig 7.1(a)

and (b)) when the wave is passing through it?

[1] (ii) Draw the displacement-position graph of the particles in the wave at the

instant shown. Displacement to the right is taken as positive.

[2]

(b) A satellite passing the planet Jupiter communicates with its controller on Earth

using microwave transmitter with output power 24.0 W and wavelength 79 600 mμ . Jupiter is 588 x 109 m from the earth at the time when the communication takes place.

(i) State whether microwave is longitudinal or transverse.

[1] (ii) Calculate the time taken for a signal to travel from the satellite to the

Earth.

time taken = s [2]

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9

Displacement / cm

Position / cm

Fig 7.1 (a) Fig 7.1 (b)

15


For Examiner’s

Use Assuming that the power transmitted by the satellite is radiated uniformly in all directions,

(iii) calculate the intensity of the microwave received on earth

intensity received = [3]

(iv) calculate the power received on the Earth by a dish aerial of effective area 250 m2.

power received = W [1] (c) Fig 7.2 shows a Young’s double slit experiment. The monochromatic light from

S1 and S2 produces on the screen bright and dark parallel bands called fringes.

Fig 7.2

(i) Explain the term diffraction with reference to the above experiment.

[1] (ii) Explain the formation of the bright and dark fringes.

[5]

S1

S2

Screen

S

Light source

16


For Examiner’s

Use (iii) Given that the slit separation between S1 and S2 is 140 mμ , the wavelength of light is 600 nm and the distance between the screen to the double slits is 0.700 m, determine the distance between second and third bright fringes.

Distance = ………….. m [2]

(d) Two identical sources S1 and S2, dipping in phase into water in a ripple tank

generate the wavefronts as shown in Fig 7.3. Deduce and label on Fig 7.3, all the actual positions of the bright fringes (BF) and dark fringes (DF) that are formed on the screen.

Fig 7.3 [2]

Screen

S1

S2

17


For Examiner’s

Use 8 (a) (i) Define potential difference and the volt.

potential difference

volt [3]

(ii) Define resistance and the ohm of a conductor.

resistance

ohm [2]

(b) A filament lamp operates normally at a potential difference (p.d.) of 6.0 V. The variation with p.d. V, of the current I, in the lamp is shown in Fig 8.1.

Fig 8.1

18


For Examiner’s

Use Use Fig 8.1 to determine, for this lamp, (i) the resistance when it is operating at a p.d. of 6.0 V,

resistance of lamp = Ω

(ii) the change in resistance when the p.d increases from 6.0 V to

8.0 V. Hence explain the I -V characteristics of a filament lamp.

change in resistance = Ω

[6]

(c) The lamp is connected into the circuit of Fig 8.2.

Fig 8.2

R is a fixed resistor of resistance 200 Ω. The battery has e.m.f. E and negligible internal resistance. (i) On Fig 8.1, draw a line to show the variation with p.d. V of the current I in

the resistor R. [2] (ii) Assuming the filament lamp operates normally find the e.m.f. of the

battery.

e.m.f. = Ω [2]

(d) Fig 8.3 shows the variation with temperature (measures in degrees Celsius,

0C) of the resistance of a thermistor.

19


For Examiner’s

Use

Fig 8.3

(i) If the resistance of the thermistor could be read to 204 ± 2 Ω, determine its temperature to an appropriate number of decimal places

with its uncertainty.

temperature = 0C [2]

(ii) Suppose the resistor in Fig 8.2 is replaced by a thermistor with characteristics shown in Fig 8.3,

1. State and explain what will be observed in the filament lamp in the circuit when the temperature in the surrounding area decreases.

2. Suggest and explain a probable application for this circuit

[3]

H1 P1

H1 P2

3 (a) (i) When an alternating current passes through the wire placed in a perpendicular

magnetic field acting, an alternating force acts

at right angles to the wire. Hence the wire vibrates . (a) (ii) For a given length of the wire, the resonance only occurs at integral

multiples of half a wavelength

The copper wire would therefore only resonates when the signal generator

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20

C A B D D A B B A D B A B C C A D A B C

Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30 Q31 Q32 Q33 Q34 Q35 Q36 Q37 Q38 Q39 Q40

D D C C C B D B D A

1(a)(i) =××= hlbV 90 cm3, (accept values from 50 cm3 to 150 cm3) m = 150 g, (accept values from 80 g to 200 g)

==

Vm

ρ ∴ 1.7 g cm-3 (accept values from 0.5 g cm-3 to 4 g cm-3); accept

corresponding values if alternative units are used (e.g. kg m-3)

1(a)(ii) V = 230 V (accept values from 220 V to 240 V) and

P = 500 W (accept values from 200 W to 900 W)

VP

I = ∴ = 2.27 A (accept values from 0.8 A to 4 A)

1(b)(i) - zero error

- parallax error where observer is always looking from one side

1(b)(ii) - the object is not perfectly spherical

- parallax error where observer is looking from either side inconsistently - inability to place the vernier caliper exactly at the centre line of the

sphere every time a measurement is taken

2ai The resultant force acting on the tray is zero in all direction [or P+W=Q]. The resultant torque acting on the tray about any axes is zero.

ii W=0.12 x 9.81 = 1.18N Taking moments around P

Q x 0.1=W x 0.25

Q =2.9 N P =2.9N-1.2N

P =1.7 N

iii If the glass is place at where Q acts, resultant moment remains at zero, the increased in value Note :if placed to right side of Q, P will decrease, left side of Q P will increase

Hence possible

is set to frequency = integral multiples of 2cL

,

(that is corresponding to the fundamental frequencies and other resonance frequencies of the vibrating wire.)

In each case, the transverse wave traveling along the wire is reflected at the fixed points x and y, which act as nodes, thus producing a stationary wave since the incident and reflected waves superimposed and have the same frequency, speed and approximately the same amplitude.

(b) (i)

Three loops are produced when the signal generator is at 60 Hz. L – length of stretched wire 3 loops L = 3λ/2 = 3/2 (V/60) ⇒ v = 40 L

1 loop L = λ/2 = ½ (V/f) ∴ f = ½ (v/L) = ½ (40) = 20 Hz

Therefore a single loop would be formed when the signal generator is set at 20 Hz

(b)(ii) At 100 Hz five loops (of stationary waves) will be formed 4(a)(i) Vs is (stopping potential). Electrons with max KE cannot reach the anode/cannot be

collected.

(ii) (Electrons are emitted with a range of KE), hence when anode is make less negative with respect to cathode, some electrons may be able to reach the anode

(iii) Saturation not achieved immediately once V is +ve because the electrons are scattered randomly in different directions. (Hence with higher V, the path of more electrons may be altered so that it is able to reach the anode due to the increased in the magnitude of the electric force.)

(Saturation current is achieved at V1 when all emitted electrons are collected.) 4(b)(i) φ = 5.32 x 1.6 x 10-19 = 8.51 x 10-19 J hc/λ = 8.51 x 10-19 J λ= 2.34 x 10-7 m (ii) pr =h/λ

pr =2.83 x 10-27 N s

5ai) Current power stations: 700 MW X 26 + 50 MW X 2 = 18300 MW Total Power: 22500 MW

Hence, remaining 6 power stations = 22500 MW - 18300 MW= 4200 MW

Each of the 6 power stations provides 700 MW.

5aii) Total time needed = 100, 000, 000 M / 22500 M= 4444 hours Total time needed in days= 185 days.

5bi) Energy = mgh Power = (dm/dt) gh= (dV/dt) ρgh In July, Power = 14000 MW, h =14000000000/(1000*9.81*30000) h=47.6 m.

5c High water flow did not result in higher power output, Water may be released regularly at low heights to reduce risk of flooding during the

rainy seasons.

5d In temperate china, low temperatures result in freezing occurring, leaving little amount of liquids to flow through the dam and little amount of energies to be generated

5e There is lesser carbon dioxide emission, thus it does not result in build up of greenhouse gases in the future. Another technique is geothermal power stations.(Allow any alternative) (A1 follows advantage given)

6(a) In elastic collision total kinetic energy is conserved , in inelastic collision total kinetic energy is not conserved

In both types of collisions, linear momentum and total energy are conserved (b) (i)

By conservation of energy, and taking the zero of potential to be at the height of B or Loss in GPE = gain in KE

a is const since no air resistance

Lmm gv

21

12

11 =

v2 = 2gL

⇒ v1 = gL2

(ii) m1 v1= ( m1 + m2) v2

v2 = 121

1 v) ( mm

m+

= Lmm

m2g

) ( 21

1

+

Assumption is there is no net external force acting and there is conservation of linear momentum,

(iii) To find time taken T to fall from B to D, consider the vertical motion

and apply x = ut + 21

g t2 ⇒ L = 21

g T2

⇒ T = gL2

(iv) xBD = v2 T = ( L

mmm 2g

) ( 21

1

+) (

gL2

) = ) (

2

21

1

mmLm

+

Hence x = xBD + L =

) (2

21

1

mmLm

+ + L

=

) ()3(

21

21

mmLmm

++

(v) x1 will be shorter than xBD Reasons:

1. When there is air resistance, the retarding effect of air resistance is such that the net acceleration of the ball downwards due to the weight of the ball and the opposing effect of air resistance is less than that due to gravity alone.

2. At B the speed v2 will be smaller as some gravitational potential energy at A has been lost to do work against air resistance

(c)(i) It states that the rate of change of momentum of a body is directly

proportional to the net external force acting on it

and it takes place in the direction of the net external force. (ii) 1 Show correct free body diagram 2

T – m1g = m1L

21v

T = m1

L

21v

+ m1g

7(a)i) Displacement = 0.5 cm ii)

(b)i) Transverse ii)

9

8

tan

588 103 10

dis cetimespeed

=

×=

×

1960 s= iii)

24

PIAPrπ

=

=

9 2

244 (588 10 )π

=×

24 25.52 10 Wm− −= × iv) P = I A

= 5.52 x 10-24 x 250 m2

= 1.38 x 10-21 W

= 2m1g + m1g = 3 m1g

(c)i) Diffraction is the spreading of the waves when it reaches the slit whose size is

comparable to that of the wavelength of the wave. ii) Both waves starts in phase since from same source Light diffracts on passing through slit S1 and S2. When the two waves meet, interference occurs. On the screen, when the 2 waves meet in phase, they will interfere constructively to

form bright fringes. When the 2 waves meet and are out of phase byπ , they will interfere destructively to

form dark fringes. Alternative:

If students uses path difference award MAX 1 mark for the last 2 B1 mark if first B1 mark not awarded.

(iii)

9

6

600 10 0.7140 10

Dyd

λ

−

−

=

× ×=

×

33.0 10 m−= × (d)

BF (n=0)

BF (n=1)

BF (n=2)

BF (n=1)

BF (n=2)

DF (n=2)

DF (n=1)

DF (n=1)

DF (n=2)S1

S2

8(a)(i) The electric potential difference between two points in a circuit or across a conductor is defined as the rate of transformation of electrical energy

to other forms of energy per unit current passing through the two points. (V = P/I)

OR The electric potential difference between two points in a circuit is the amount of electrical energy transformed

per unit charge to some other forms of energy when the charge passes from one point to the other. (V = W/Q)

The volt is defined as potential difference between two points on a conductor carrying a current of one ampere when the power dissipated is one watt. (1 V = 1 W A−1)

OR The volt is defined as the potential difference between two points in a circuit where one joule of electrical energy is converted to other forms of energy when one coulomb of charge passes from one point to the other. (1 V = 1 J C−1)

(ii) The resistance R of a conductor is defined as the ratio where V is the potential

difference across the conductor and I is the current flowing through the conductor. i.e. R = V/I

The ohm is defined as the electrical resistance between two points of a conductor through which a steady current of one ampere (1A) flows when a constant potential difference of one volt (1V) is maintained across it. 1 Ω = 1 V A−1

8(b)(i) Resistance R = V/I R6 = 6.0/(40 x 10-3) =150 Ω

(ii) R8 = 8.0/(50 x 10-3) = 160 Ω R8 – R6 = 160 – 150 = 10 Ω As I and V increases, rate of atomic vibration increases Number of free electrons remains the same, hence resistance increases 8(c) (i) pd across resistor VR = I R

= (40 x 10−3)(200) = 8.0 V Show in Fig 8.1, straight line from (0,0) to (40 mA, 8.0 V)

(ii) Emf of battery ε = 6.0 + 8.0 = 14.0 V 8(d)(i) At R = (204 ± 2) Ω

Students knows that uncertainty is ± 0.2 0C θ = (15.0 ± 0.2) 0C

(ii)1. Temp decreases ⇒ Rthermistor increases Vbattery constant ⇒ current decreases/total R ↑ ⇒ ILamp decreases (dimmer)

(ii)2. Temp sensor with lamp as indicator (intensity of light calibrated vs temp), etc

1

Name: ……………………….…………………. HT group: …………...

CATHOLIC JUNIOR COLLEGE JC2 PRELIMINARY EXAM 2010

PHYSICS Higher 1 Paper 1 Multiple Choice

1 hour

Additional materials : Multiple Choice Answer Sheet READ THESE INSTRUCTIONS FIRST Write in soft pencil. Do not use staples, paper clips, highlighters, glue or correction fluid. Write your name, IC Number and HT group on the Answer Sheet in the spaces provided. There are thirty questions on this paper. Answer all questions. For each question there are four possible answers A, B , C and D. Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet. Read the instructions on the Answer Sheet very carefully. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet.

This question paper consists of 12 printed pages.

DATA: acceleration of free fall, g = 9.81 m s-2 Speed of light in free space c = 3.00 × 108 m s-1 Elementary charge e = 1.6 × 10-19 C The Planck Constant h = 6.63 × 10-34 J s Unified atomic mass constant u = 1.66 × 10-27 kg Rest mass of electron me = 9.11 × 10-31 kg Rest mass of proton mp = 1.67 × 10-27 kg FORMULAE: uniformly accelerated motion, s = u t +

21 a t2

v2 = u2 + 2 a s Work done on/by a gas W = pΔV Hydrostatic pressure p = ρgh Resistors in series R = R1 + R2 + … Resistors in parallel

R1

= ++21

11RR …

2

3

1. The power loss P through a resistor is found by measuring the potential difference V across the

resistor and the current I through it. The equation is given by P = VI. The voltmeter has a 4% uncertainty and the ammeter reading has a 3% uncertainty. What is the uncertainty in the power calculated?

A 3 % B 4 % C 7 % D 12 %

2. A student made a series of measurements of the diameter d, of a wire using four micrometer screw gauges A, B, C and D. The table shows the measurements taken. If the actual diameter of the wire was 1.49 mm, which micrometer screw gauge produced a set of readings that could be described as accurate but not precise?

micrometer screw gauge Readings d/ mm

A 1.49 1.46 1.52 1.50 B 1.48 1.58 1.51 1.40 C 1.35 1.37 1.42 1.42 D 1.32 1.37 1.41 1.50

3. An Olympic athlete competes in a sprint race.

What is the best estimate of his mean kinetic energy during the race?

A 4 x 102 J B 4 x 103 J C 4 x 104 J D 4 x 105 J 4. A man stands on the edge of a cliff. He throws a stone upwards with a velocity of 19.6 m s-1 at

time t = 0. The stone reaches the top of the trajectory after 2.00 s and then falls towards the bottom of the cliff. Air resistance is negligible. Which row shows the correct velocity v and acceleration a of the stone at different times?

t /s v / m s-1 a / m s-2 A 2.00 0 0 B 1.00 9.81 9.81 C 5.00 -29.4 -9.81 D 3.00 9.81 -9.81

5. The sketch graph below describes the motion of a ball rebounding from a horizontal surface after

being released from a point above the surface.

The quantity represented on the y-axis is the ball’s A Velocity C Acceleration B Kinetic energy D Displacement 6. Two objects, X and Y, were dropped from rest from a tall tower on a wind-free day. In the graph

below are plotted their squared velocities as a function of their height above the ground.

From the information given in the graph and knowledge of the properties of bodies falling under the influence of gravity, it is possible to say that the two objects

A experienced unequal viscous drag B had different masses C hit the ground at the same time D were not dropped simultaneously

4

7. A proton (mass 1 u) travelling with velocity +0.100 c collides elastically head-on with a helium

nucleus (mass 4 u) travelling with velocity -0.050 c.

What are the velocities of each particle after the collision? proton Helium nucleus A +0.140 c +0.010 c B -0.140 c +0.010 c C +0.233 c -0.083 c D -0.233 c +0.083 c 8. Which of the following pairs of forces is an action-reaction pair?

A Weight of a floating object in water and the force acting by water on it. B The force a ladder leaning on a smooth wall exerts on the rough floor and the normal

reaction from the floor C The force a ladder leaning on a smooth wall exerts on the wall and the normal reaction force

from the wall D Weight of a parachutist and the pull of the parachute on him when he is moving with

terminal velocity 9. A 100 N weight is supported by two weightless wires A and B as shown below. What can you

conclude about the tensions in these wires?

A the tensions are equal to 50 N each B the tensions are equal but greater than 50 N each C the tensions are equal but less than 50 N each D the tensions are equal to 100 N each

A B

θ

θ

5

10. The given diagram shows a column of dry air trapped by mercury in a narrow test tube.

Which graph best shows how the length l of the air column varies with the angle θ of the tube to

the vertical? A

C

B

D

11. A right-angle rule hangs at rest from a peg P as shown below. It is made from a metal sheet of

uniform density. One arm is L cm long while the other is 2L cm long.

The angle θ at which it will hang is A 8o B 14o C 42o D 76o

6

12. A spring fixed at one end, has a mass attached to the other end. The mass bounces up and down.

It is shown in the diagram at three positions X, Y and Z.

Which line gives the kinetic, gravitational potential and elastic potential energies? Kinetic energy Gravitational potential energy Elastic potential energy

A zero at X maximum at X maximum at X B maximum at Y zero at Z maximum at Y C zero at Z zero at Z zero at X D maximum at Y maximum at X maximum at Z 13. A space vehicle of mass m re-enters the Earth’s atmosphere at an angle θ to the horizontal.

Because of air resistance, the vehicle travels at a constant speed v. The heat shield of the vehicle dissipates heat at a rate P, so that the mean temperature of the vehicle remains constant. Taking g as the relevant value of the acceleration of free fall, which expression is equal to P.

A mgv B mgv sinθ C 2

21 mv

D θ22 sin

21 mgv

14. A mechanical wave of frequency 300 Hz travels along a railway line at 6 km s-1. Two points on

the rail which are 250 cm apart are out of phase by

A 0 rad B π rad C π / 2 rad D π / 4 rad 15. A boy blows gently across the top of a piece of glass tubing the low end of which is closed by his

finger so that the tube gives its fundamental note of frequency, f. While blowing, he removes his finger from the lower end. The note he then hears will have a frequency of approximately

A ¼ f B ½ f C 2 f D 4 f

7

16. A point source emits 50.0 W of sound. A small microphone of area 0.85 cm2 detects the sound

at 4.0 m from the source. What is the power detected by the microphone? A 1.6 × 10-5 W B 2.1 × 10-5 W C 2.1 × 10-1 W D 2.5 × 10-1 W 17. When a two-slit arrangement was set up to produce a superposition pattern on a screen using a

monochromatic source of green light, the fringes were found to be too close together for accurate observation. It would be possible to increase the separation of the fringes by

A replacing the light source with a monochromatic source of red light B increasing the distance between the source and the slits C decreasing the distance between the slits and the screen D increasing the distance between the two slits 18. Two loudspeakers L1 and L2, driven by a common oscillator and amplifier, are set up as shown.

As the frequency of the oscillator increases from zero, the detector at D recorded a series of maximum and minimum signals. At what frequency is the first maximum observed? (Speed of sound = 330 m s-1)

A 165 Hz B 330 Hz C 495 Hz D 660 Hz

D

9 m

40 mL1

L2

19. Two wires P and Q, each of the same length and the same material, are connected in parallel to

a battery. The diameter of P is half that of Q. What fraction of the total current passes through P?

A 0.20 B 0.25 C 0.33 D 0.50

8

20. The diagram shows three resistors of resistances 2 Ω, 20 Ω and 3 Ω connected in series. A

potential difference of 20 V is maintained across them. Point Q is earthed.

Which of the following gives the potentials at points P, Q, R and S?

Potential at P Q R S A 20 V 18.4 V 2.4 V 0 V B 1.6 V 0 V 16 V 18.4 V C 20 V 16 V - 6 V - 20 V D 1.6 V 0 V - 16 V - 18.4 V

9

21. A battery of e.m.f. E and internal resistance r delivers a current I through a variable resistance R.

R is set at two different values and the corresponding currents I are measured using an ammeter of negligible resistance.

R/Ω I/A 1.0 3.0 2.0 2.0

What is the value of e.m.f E?

A 3.0 V B 3.5 V C 4.0 V D 6.0 V

I

A

R

r E

2 Ω 20 Ω 3 Ω

20 V

SRQP

22. An electric heater can be represented as two resistors of resistances R1 and R2 and two

switches S1 and S2. The resistance R2 is greater than that of R1.

Which switches must be closed so that the heater produces the maximum possible power and the minimum non-zero power?

maximum possible power minimum non-zero power A S1 and S2 S2 B S1 and S2 S1 C S1 S2 D S2 S1

10

23. A bar magnet is to be placed in a non-uniform magnetic field as shown.

Which line of the table describes the subsequent motion of the magnet?

rotation movement A anticlockwise to the left B anticlockwise to the right C clockwise to the left D clockwise to the right

S

N

S1

R1

R2

S2

24. A straight wire PQ carrying a constant current I is placed at right angles to a uniform magnetic

field, as shown by the dotted line in the diagram.

The wire is then rotated through an angle θ about an axis perpendicular to the plane of the

diagram. Which graph shows how the magnitude of the magnetic force F on the wire varies with θ in the range 0o to 90o?

25. A positively-charged particle enters a uniform magnetic field.

Which diagram represents the path of the particle in the magnetic field?

A B C D

26. Monochromatic light is incident on a clean metal surface of work function φ. The Planck constant is h

and the speed of light is c. What is the threshold wavelength for the emission of electrons from the metal surface?

A

B

C

D

11

27. Which of the following statements about photoelectric emissions is correct? A The velocity of the emitted electrons is directly proportional to the intensity of the incident

radiation. B The number of electrons emitted per second does not depend on the intensity of the

incident radiation. C For any given type of metal, there is a maximum wavelength of radiation above which no

emission of electrons occurs. D No emission of electrons occurs at very low intensity of illumination. 28. The de Broglie wavelength of a rifle bullet of mass 0.02 kg which is moving at a speed of 300 m

s-1 is

A 7.3 x 10-36 m B 1.8 x 10-35 m C 1.1 x 10-34 m D 9.9 x 10-33 m

29. Which of the following statements is true?

A A beam of electrons directed at a vessel of cold gas can cause the formation of either an absorption or emission line spectrum.

B A beam of white light directed at a vessel of cold gas can cause the formation of either an absorption or emission line spectrum.

C A beam of electrons directed at a vessel of cold gas can only cause the formation of an absorption line spectrum.

D A beam of electrons directed at a vessel of cold gas can only cause the formation of an emission line spectrum.

30. A laser emits light of power P. The light consists of photons of frequency f. The Planck constant is h and the speed of light is c. How many of these photons are contained in a one metre length of the laser beam?

A

cP

B

hfP

C

hfPc

D

chfP

End of Paper 1

12

1

Name: ……………………….…………………. HT group: …………...

CATHOLIC JUNIOR COLLEGE JC2 PRELIMINARY EXAM 2010

PHYSICS Higher 1 Paper 2 Structured Questions

2 hours

Candidates answer on the Question Paper. No Additional materials are required. READ THESE INSTRUCTIONS FIRST Write your name and HT group on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Section A (40 marks) Answer all questions. Section B (40 marks) Answer any two questions. At the end of examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. Total marks for Section A and B is 80 marks.


FOR EXAMINER’S USE SECTION A 1 2 3 4 SECTION B 5 6 7

DATA: acceleration of free fall, g = 9.81 m s-2 Speed of light in free space c = 3.00 × 108 m s-1 Elementary charge e = 1.6 × 10-19 C The Planck Constant h = 6.63 × 10-34 J s Unified atomic mass constant u = 1.66 × 10-27 kg Rest mass of electron me = 9.11 × 10-31 kg Rest mass of proton mp = 1.67 × 10-27 kg FORMULAE: uniformly accelerated motion,

s = u t + 21 a t2

v2 = u2 + 2 a s Work done on/by a gas W = pΔV Hydrostatic pressure p = ρgh Resistors in series R = R1 + R2 + … Resistors in parallel

R1

= ++21

11RR …

2

3

Section A Answer all the questions in this section

1 An aeroplane is flying horizontally at a steady speed of 67 m s-1 and an object is

dropped off from the aeroplane.

(a) Assume that the air resistance is negligible.

(i) Show that the vertical component of the velocity of the object is approximately 40 m s-1 when it has fallen 80 m.

[2]

(ii) Determine the magnitude and direction of the resultant velocity of the object at this point.

Magnitude of velocity =…………………..m s-1 Direction of velocity =…………………………………..

[3]

(b) In practice, air resistance acts on the object during the fall. The air resistance

may be assumed to be proportional to the square of the speed.

(i) State and explain how the magnitude of the horizontal and vertical components of the velocity of the object vary with time.

Horizontal component of velocity:

………………………………………………………………………………………. ……………………………………………………………………………………….

[1]

Vertical component of velocity:

………………………………………………………………………………………. ………………………………………………………………………………………. ………………………………………………………………………………………. ………………………………………………………………………………………. ………………………………………………………………………………………. ……………………………………………………………………………………….

[2]

(c) Sketch and label the path of the object in Fig. 1

(i) without air resistance,

(ii) with air resistance.

Fig. 1

[2]Start of fall

Horizontal distance from the point of drop off

vertical distance from the point of drop off

4

2 A water-wheel has eight buckets equally spaced around its circumference as

illustrated in Fig. 2

Fig. 2

The distance between the centre of each bucket and the centre of the wheel is 1.6 m. When a bucket is at its highest point, the bucket is filled with a mass of 40 kg of water. The wheel rotates and the bucket is emptied at its lowest point.

(a) (i) Define the moment of a force.

…………………………………………………………………………………….. …………………………………………………………………………………….. ……………………………………………………………………………………..

[1]

(ii) Write down the number of the bucket that provides the largest moment about the axle of the wheel.

……………………………………………………………………………………..

[1]

(iii) Write down the numbers of those buckets containing water that cause a moment about the axle.

…………………………………………………………………………………….. ……………………………………………………………………………………..

[2]

(iv) Calculate, for the wheel in the position shown in Fig. 2, the total resultant moment about the centre of the wheel of the water in the buckets.

Resultant moment = …………………….N m

[2]

5

6

(b) The wheel makes six revolutions per minute.

Calculate

(i) The total change in potential energy of the water in the buckets in one revolution of the wheel,

Change in potential energy =……………..J

[2]

(ii) The average input power to the wheel.

Power =………………….W

[2]

(c) Suggest why a larger number of small buckets is preferred to a smaller number of large buckets containing the same total mass of water.

………………………………………………………………………………………….. ………………………………………………………………………………………….. …………………………………………………………………………………………..

[1]

7

3 (a) (i) Define linear momentum.

……………………………………………………………………………………….. ………………………………………………………………………………………..

[1]

(ii) Use your definition of momentum to define force.

……………………………………………………………………………………….. ……………………………………………………………………………………….. ………………………………………………………………………………………..

[2]

(iii) Show that this definition leads to the equation F = ma

[2]

(b) An apple and a leaf fall from a tree at the same instant. Both apple and leaf start at the

same height above the ground but the apple hits the ground first.

Use Newton’s Laws of motion to explain why

(i) the leaf accelerates at first then reaches a terminal velocity,

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………………

[3]

(ii) the apple hits the ground first.

……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………………

[2]

4 A photomultiplier tube can be used to detect high-energy charged particles. Fig. 4

shows a diagram of a particular photomultiplier tube.

The incoming charged particle strikes the scintillator material and produces a short burst of visible light. When this light reaches the photocathode, it removes some of the surface electrons due to the photoelectric effect. These electrons are then accelerated towards the first positive dynode because of the 100 V potential difference between it and the cathode. The kinetic energy of the electron is sufficient to liberate, on average, 3 ‘secondary’ electrons from the dynode. These electrons are then accelerated towards the next dynode and the whole process is repeated. Eventually a tiny pulse of charge is detected at the anode. In one particular case, a proton of kinetic energy 0.70 MeV produces 550 photons of light of wavelength 410 nm in the scintillator material. For a photomultiplier with 10 dynodes, a single electron emitted from the photocathode produces a pulse of charge lasting 2.3×10-8s at the anode. The work function energy of the material of the photocathode is 3.5×10-19 J.

(a) Show that the energy of the high-speed proton is 1.1×10-13 J.

[1]

(b) Calculate the energy of a single photon of light of wavelength 410 nm.

Energy = ………………………….J

[2]

Fig. 4

8

9

(c) Determine the percentage of kinetic energy lost by the proton in the scintillator

material.

Percentage of energy lost =………………………%

[1]

(d) Show that the maximum kinetic energy of an electron liberated from the photocathode is about 1×10-19 J.

[2]

(e) Calculate the number of electrons arriving at the anode for each electron emitted from the cathode.

Number =………………………..

[1]

(f) Calculate the average current from the anode due to a single electron leaving the photocathode.

Current =………………………..A

[2]

Section B Answer two of the questions in this section

5 (a) Two transverse waves, P and Q, of equal frequency, have intensities I and 0.64I

respectively. Wave P has amplitude A. Waves P and Q interfere to form an interference pattern.

(i) State two necessary conditions for the waves to produce an observable interference pattern.

…………………………………………………………………………………………………. …………………………………………………………………………………………………. ………………………………………………………………………………………………….

[2]

(ii) Determine, in terms of I, the maximum intensity of the interference pattern.

maximum intensity = ……………………..

[3]

(b) Figure 5.1 shows two loudspeakers S1 and S2 placed in an open field on a still day. Their separation is 3.81 m. D is a microphone placed in the same horizontal plane as the loudspeakers, and at a distance of 10.0 m from S1. The lines S1S2 and S1D are perpendicular to each other. When the speakers are switched on, sound of frequency f = 1650 Hz is emitted in phase. Assume the microphone and loudspeakers are point objects.

Figure 5.1

S2

S1

3.81 m

D 10.0 m

10

11

(i) Given that the speed of sound in air is 330 m s-1, calculate the wavelength of

the sound emitted.

wavelength = …………………….. m

[2]

(ii)

Calculate the distance S2D.

S2D = …………………… m

[1]

(iii) 1. Determine the phase difference between the sound waves reaching D from S1 and S2.

Phase difference = ……………….. rad

[1]

2. Hence explain whether a minimum of intensity or a maximum of intensity would be detected by D.

…………………………………………………………………………………………….. …………………………………………………………………………………………….. ……………………………………………………………………………………………..

[2]

(iv) When the frequency of the sound was slowly increased to a value f1, the

microphone D detected three cycles of change in intensity. Calculate f1.

f1 = ………………………. Hz

[3]

(c) In an experiment to investigate the properties of stationary waves, one end of a rubber

cord is attached to a vibrator, the frequency of which can be varied, and the other end to a rigid support.

Figure 5.2 Figure 5.2, which is to scale 1:10 cm on both axes, shows the cord vibrating at one of its harmonics.

(i) By making measurements on Figure 5.2, 1. determine the wavelength of the stationary wave, and wavelength = …………….. cm 2. its amplitude. Amplitude = ………………. cm

[1] [1]

12

13

(ii) Describe briefly the motion of the cord at each of the points A, B and C

emphasizing any differences. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. ………………………………………………………………………………………………….. …………………………………………………………………………………………………..

[3]

(iii) If the frequency of the vibrator is 400 Hz, calculate the wave speed.

Wave speed = ……………… m s-1

[1]

6 (a) (i) Define electric potential difference and state the SI unit in which it is

measured.

…………………………………………………………………………………………. …………………………………………………………………………………………. …………………………………………………………………………………………. ………………………………………………………………………………………….

[2]

(ii) Use your definition in (i) to show that P, the power dissipation in a resistor of resistance R is given by

RVP

2=

where V is the potential difference across the resistor.

[3]

14

(b) A set of coloured lamps are designed for use with a 240 V supply. The set up have

12 lamps connected as seen in Fig 6.1 below.

Fig. 6.1

However, the lamps do not light up when the set is plugged in. Therefore, a voltmeter is used to test the circuit. For each of the following observations, identify the fault.

(i) The potential difference is zero across every lamp except EF, across which the potential difference is 240 V.

……………………………………………………………………………………….. ………………………………………………………………………………………..

[1]

(ii) The potential difference between A and M is 240 V but the potential difference is zero across every lamp.

……………………………………………………………………………………….. …………………………………………………………………………………………

[1]

(c) (i) Some lamps are designed so that when the filament fails the resistance of the lamp drops to zero. If this happens to one of the lamps in the above set up, calculate the fractional increase in the power dissipated in each of the remaining lamps, assuming that the resistance of these lamps does not change.

Fractional increase = …………………….

[4]

M

240 V

A B C D E F G H I J K L

15

16

(ii) What is likely to happen if failed lamps are not replaced?

……………………………………………………………………………………….. ……………………………………………………………………………………….. ………………………………………………………………………………………… …………………………………………………………………………………………

[2]

(d) A cell of e.m.f. 1.5 V and internal resistance 0.25 Ω is connected in series with a resistor R, as shown in Fig. 6.2

Fig. 6.2

The resistor R is made of metal wire. A current of 0.24 A passes through R for a time of 5.0 minutes. Calculate

(i) The charge that passes through the cell,

Charge = ……………………..C

[1]

(ii) The total energy transferred by the cell,

Energy = ……………………….J

[2] (iii) The energy transferred in the resistor R,

Energy = ……………………….J

[2] (iv) The resistance of R.

Resistance =…………………..Ω

[2]

7 (a) Fig. 7.1 shows a mass initially traveling at right angles to the Earth’s uniform

gravitational field.

Fig.7.1

(i) State the direction of the gravitational force experienced by the mass.

………………………………………………………………………………………………… …………………………………………………………………………………………………

[1]

(ii) Describe the subsequent motion of the mass.

………………………………………………………………………………………………… …………………………………………………………………………………………………

[1]

(b) Fig. 7.2 shows an electron initially traveling parallel to a uniform electric field.

Fig. 7.2

(i) State the direction of the electric force experienced by the electron.

………………………………………………………………………………………………… …………………………………………………………………………………………………

[1]

(ii) Describe the subsequent motion of the electron.

……………………………………………………………………………………………….. ………………………………………………………………………………………………..

[1]

17

(c) Fig. 7.3 shows a long molecule placed in a uniform electric field.

Fig.7.3

The ends of the molecule have equal but opposite charges. Describe the initial motion of the molecule in the electric field.

……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………..

[2]

(d) (i) Define magnetic flux density.

………………………………………………………………………………………………… …………………………………………………………………………………………………

[1]

(ii) Magnetic flux density is a vector quantity. Fig. 7.4 shows the magnetic flux densities at point P due to two current-carrying conductors.

Fig.7.4

On Fig. 7.4 draw a vector diagram to determine the magnitude of the resultant Magnetic flux density at point P.

Magnetic flux density =…………………….mT

[4]

18

(e) Fig. 7.5 shows a flat rectangular coil placed in a uniform magnetic field.

Fig. 7.5

The frame has length a and width b. The magnetic field, of flux density B, is parallel to the plane of the coil. The current in the coil is I. The current-carrying coil experiences a torque T. Show how the torque is related to the cross-sectional area A of the coil.

……………………………………………………………………………………………………… ………………………………………………………………………………………………………

[4]

19

(f) For a particular long straight current-carrying conductor, the magnetic flux density B at a

distance r from the conductor is given by the relation

rB

6103.1 −×=

where the unit of B is tesla and the unit of r is metre.

(i) Determine the distance r from the conductor at which the magnitude of the

magnetic flux density is 160 μT.

r =…………………………..m

[2]

(ii) Another long straight conductor carrying a current of 30 A is placed parallel to the current-carrying conductor. The two conductors are separated by 12 mm. Determine the magnitude of the force per unit length between the two conductors.

Force per unit length = ……………… N m-1

[3]

End of Paper 2

20

© IJC 2010 8866/Prelim1 [Turn over

INNOVA JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION 2 in preparation for General Certificate of Education Advanced Level Higher 1

CANDIDATE NAME CLASS INDEX NUMBER

PHYSICS

Paper 1 Multiple Choice

Additional Materials: Multiple Choice Answer Sheet

8866/01

17 September 2010

1 hour

READ THESE INSTRUCTIONS FIRST Write in soft pencil. Do not use staples, paper clips, highlighters, glue or correction fluid. Write your name, class and index number on the Answer Sheet in the spaces provided unless this has been done for you. There are thirty questions on this paper. Answer all questions. For each question, there are four possible answers A, B, C and D.

Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet. Read the instructions on the Answer Sheet very carefully.

Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet.

This document consists of 14 printed pages

Innova Junior College [Turn over

2

© IJC 2010 8866/Prelim 2 [Turn over

Data

speed of light in free space, c = 3.00 x 108 m s-1

elementary charge, e = 1.60 x 10-19 C

the Planck constant, h = 6.63 x 10-34 J s

unified atomic mass constant, u = 1.66 x 10-27 kg

rest mass of electron, me = 9.11 x 10-31 kg

rest mass of proton, mp = 1.67 x 10-27 kg

acceleration of free fall, g = 9.81 m s-2 Formulae

uniformly accelerated motion, s = ut + ½at2

v2 = u2+ 2as

work done on/by a gas, W = pΔV

hydrostatic pressure, p = ρgh

resistors in series, R = R1 + R2 + … resistors in parallel, 1/R = 1/R1 + 1/R2 + …

3


1 Which pair contains one vector and one scalar quantity?

A displacement and acceleration

B force and kinetic energy

C momentum and velocity

D power and speed 2 A student makes measurements from which she calculates the speed of sound as

327.66 m s-1. She estimates that her result is accurate to ± 3 %.

Which of the following gives her result expressed to the appropriate number of significant figures?

A 327.7 m s-1 B 328 m s-1 C 330 m s-1 D 300 m s-1

3 Four students each made a series of measurements of the acceleration of free fall g. The table shows the results obtained. Which student obtained a set of results that could be described as precise but not accurate?

student results, g / m s-2

A B C D

9.81 9.81 9.45 8.45

9.79 10.12 9.21 8.46

9.84 9.89 8.99 8.50

9.83 8.94 8.76 8.41

4 An object has an initial velocity u. It is subjected to a constant force F for t seconds,

causing a constant acceleration a. The force is not in the same direction as the initial velocity.

A vector diagram is drawn to find the final velocity v.

What does vector X in the diagram represent?

A F B F t C a t D u + at

4


5 A boy throws a ball vertically upwards. It rises to a maximum height, where it is momentarily at rest, and falls back to his hands.

Which of the following gives the acceleration of the ball at various stages in its motion?

Take vertically upwards as positive. Neglect air resistance.

rising at maximum height falling

A B C D

+ 9.81 m s-2

- 9.81 m s-2

- 9.81 m s-2

- 9.81 m s-2

0 0 0

- 9.81 m s-2

- 9.81 m s-2

+ 9.81 m s-2

- 9.81 m s-2

- 9.81 m s-2

6 When a car driver sees a hazard ahead, she applies the brakes as soon as she can

and brings the car to rest. The graph shows how the speed v of the car varies with time t after the hazard is seen.

Which graph represents the variation with time t of the distance s travelled by the car

after the hazard has been seen?

5


7 Which statement about Newton’s laws of motion is correct? A The first law follows after the second law.

B The third law follows after the second law.

C Conservation of energy is a consequence of the third law.

D Conservation of energy is a consequence of the first law.

8 A tennis ball of mass 100 g is struck by a tennis racket. The velocity of the ball is changed as shown.

What is the magnitude of the change in momentum of the ball?

A 1.0 kg m s-1 B 5.0 kg m s-1 C 1000 kg m s-1 D 5000 kg m s-1

9 A stationary body explodes into two components of masses m and 2m. The components gain kinetic energy X and Y respectively.

What is the value of the ratio XY

?

A 0.25

B 0.50

C 2.0

D 4.0

6


10 A car with front-wheel drive accelerates in the direction shown.

Which diagram best shows the direction of the total force exerted by the road on the front wheels?

11 A hinged door is held closed in the horizontal position by a cable.

Three forces act on the door. The forces are the weight W of the door, the tension T in the cable and the force H at the hinge. The diagram is not drawn to scale.

Which list gives the three forces in increasing order of magnitude?

A W, H, T B W, T, H C H, T, W D T, H, W

12 Two springs P and Q both obey Hooke’s Law. They have spring constants 2k and k

respectively. The springs are stretched, separately by the same force. The elastic potential energies

stored in spring P and Q are WP and WQ respectively.

How is WP related to WQ?

A WP = ¼ WQ B WP = ½ WQ C WP = 2 WQ D WP = 4 WQ

7


13 A constant force of 9.0 kN, parallel to a rough inclined plane, moves a body of weight 20 kN through a distance of 40 m along the plane at constant speed. The body gains 12 m in height, as shown.

What is the work done by friction? A 120 kJ B 240 kJ C 360 kJ D 600 kJ

14 A cathode-ray oscilloscope (c.r.o) is used to determine the frequency of a sound wave. The time-base of the c.r.o is set at 0.25 ms per cm and the trace obtained is shown in the diagram.

What is the frequency of this sound wave? A 0.50 Hz

B 1.0 Hz

C 500 Hz

D 1000 Hz

8


15 A displacement-time graph for a transverse wave is shown in the diagram.

The phase difference between X and Y can be expressed as nπ. What is the value of n?

A 1.0 B 1.5 C 2.0 D 3.0

16 A light meter measures the intensity I of the light falling on it. Theory suggests that this

varies with the inverse of the square of the distance d.

Which graph of the results support this theory?

9


17 A stationary wave has a series of nodes. The distance between the first and the sixth node is 30.0 cm.

What is the wavelength of the sound wave?

A 5.0 cm B 6.0 cm C 10.0 cm D 12.0 cm 18 Monochromatic light incident on an adjustable single slit produces on a screen a

distribution of intensity represented by the diagram below.

What is observed on the screen when the width of the slit is reduced? A The central peak decreases in intensity and its width increases.

B The central peak increases in intensity and its width decreases.

C The central peak decreases in intensity and its width remains.

D The central peak increases in intensity and its width remains. 19 In an interference experiment, two slits are illuminated with white light.

What is seen on the screen? A The central fringe is black with black and white fringes on each side.

B The central fringe is black with coloured continuous spectrum on each side.

C The central fringe is white with black and white fringes on each side.

D The central fringe is white with coloured continuous spectrum on each side.

10


20 The current in the circuit is 4.8 A.

What is the rate of flow and the direction of flow of electrons through the resistor R?

rate of flow direction of flow

A B C D

3.0 × 1019 s-1 6.0 × 1018 s-1

3.0 × 1019 s-1 6.0 × 1018 s-1

X to Y X to Y Y to X Y to X

21 The resistivity of aluminum is 2.0 times that of silver. An aluminium wire of length L and diameter d has a resistance R.

What is the diameter of the silver wire, also of length L and resistance R?

A 0.05 d B 0.71 d C 1.4 d D 2.0 d 22 The current I flowing through a component varies with the potential difference V

across it as shown.

Which graph best represents how the resistance R varies with V?

A B C D

11


23 When four identical lamps P, Q, R and S are connected as shown in diagram 1, they have normal brightness.

The four lamps and the battery are then connected as shown in diagram 2.

Which statement is correct?

A The lamps do not light up.

B The lamps are less bright than normal.

C The lamps have normal brightness.

D The lamps are brighter than normal. 24 In the circuit, the battery has an e.m.f. of 12 V and an internal resistance of 3.0 Ω. The

ammeter has negligible resistance. The switch is closed.

What is the reading on the ammeter? A 0.50 A B 1.0 A C 1.3 A D 2.0 A

12


25 A long straight wire XY lies in the same plane as a square loop of wire PQRS which is free to move. The sides PS and QR are initially parallel to XY. The wire and loop carry steady currents as shown in the diagram.

What will be the effect of the loop?

A It will move towards the long wire.

B It will move away from the long wire.

C It will rotate about an axis parallel to XY.

D It will be unaffected. 26 An electron of velocity v is moving along the axis of a solenoid carrying current, I. Which of the following is a correct statement about the magnetic force acting on the

electron?

A The force acts perpendicularly to the direction of motion.

B The force acts in the same direction of motion.

C The force acts in the opposite direction of motion.

D No force acts.

axis of solenoid electron

v

I

13


27 In a photoelectric emission experiment on a certain metal surface, two quantities, when plotted as a graph of y against x, give a straight line passing through the origin.

Which of the following correctly identifies x and y with the photoelectric quantities?

x y

A B C D

photocurrent frequency of incident light

light intensity light intensity

threshold frequency maximum kinetic energy of photoelectrons

photocurrent maximum kinetic energy of photoelectrons

28 In a photoelectric experiment, electrons are ejected from metals X and Y by light of

frequency f. The potential difference V required to stop the electrons is measured for various frequencies.

If Y has a greater work function than X, which graph illustrates the expected results?

A B

C D

14


29 The diagram shows the energy levels for an atom, drawn to scale. The electron transitions give rise to the emission of a spectrum of lines of λ1, λ2, λ3, λ4 and λ5.

What can be deduced from this diagram?

A λ1 > λ2

B λ3 = λ4 + λ5

C λ4 is the shortest of the five wavelengths.

D The transition corresponding to wavelength λ3 represents the ionisation of the atom.

30 Which of the following about line spectrums is true?

A A beam of electrons directed at a vessel of cold gas could cause the formation of either an absorption or emission line spectrum.

B A beam of white light directed at a vessel of cold gas could cause the formation of

only an absorption line spectrum. C A beam of electrons directed at a vessel of cold gas could only cause the

formation of an absorption line spectrum. D A beam of electrons directed at a vessel of cold gas could only cause the

formation of an emission line spectrum.

END OF PAPER


INNOVA JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION 2 in preparation for General Certificate of Education Advanced Level Higher 1

CANDIDATE NAME CLASS INDEX NUMBER

PHYSICS

Structured Questions

Candidates answer on the Question Paper

No Additional Materials are required.

8866/02

17 September 2010

2 hours

READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. For Section A Answer all questions. For Section B Answer any two questions. At the end of the examination, fasten all your work securely together. The number of marks is given in the brackets [ ] at the end of each question or part question.

This document consists of 23 printed pages and 1 blank page.

For Examiner’s Use

Section A

1 6

2 7

3 8

4 6

5 6

6 7

Section B

7 20

8 20

9 20

Total

80

Penalty

Innova Junior College [Turn over

2


For Examiner’s

Use Data







acceleration of free fall, g = 9.81 m s-2

Formulae


v2 = u2+ 2as



resistors in series, R = R1 + R2 + … resistors in parallel, 1/R = 1/R1 + 1/R2 + …

3


For Examiner’s

Use

Section A

Answer all the questions in this section.

1 (a) Complete Fig. 1.1 to show each quantity and its base units. [2]

quantity base units

speed density

…………………… light intensity

m s-1

kg m-3

kg m s-1

……………………

Fig. 1.1

(b) In the classroom, a student wishes to determine the mass of a plastic semi-circular protractor.

Fig. 1.2

(i) Give a reasoned estimate of the mass of the semi-circular protractor and express

your answer in an SI unit.

mass = ………………………… unit ……………. [2]

(ii) State an instrument which is most appropriate for the measurement of the thickness of the protractor x, as indicated in Fig. 1.2.

instrument : ………………………… [1]

(iii) For the measurement of x, suggest a way to reduce random errors. …..…………………………………………………………………………..……………….

……………………………………………………………………………..…..…….….. [1]

x

4


For Examiner’s

Use

2 ‘Clay pigeon shooting’ is a sport whereby the shooter aims and hits the clay disc projected by a launcher. A certain clay disc is launched from the horizontal ground with a velocity of 20 m s-1 at an angle of 30o to the horizontal.

(a) Calculate, for this disc, the initial values of

(i) the vertical component of the velocity, and

vertical component = ………………………… m s-1 [1]

(ii) the horizontal component of the velocity.

horizontal component = ………………………… m s-1 [1] (b) Assuming that air resistance can be neglected, determine (i) the maximum height of the disc, and

maximum height = ………………………… m [2] (ii) the horizontal distance between the point from which the disc is launched and

where it lands on the ground.

horizontal distance = ………………………… m [2] (c) If air resistance is not neglected, state how the maximum height and the horizontal

distance will be affected.

…..………………………………………………………………………………………………

..……………………………………..……………………………………………………… [1]

5


For Examiner’s

Use

3 (a) Use energy considerations to distinguish between electromotive force (e.m.f.) and potential difference (p.d.).

…..………………………………………………………………………………………………

…..………………………………………………………………………………………………

…..………………………………………………………………………………………………

..……………………………………..……………………………………………………… [2] (b) Fig. 3.1 shows the relation between the direct current I in a diode and the potential

difference V across it. When V < 1.8 V, the current is negligible.

Fig. 3.1

Fig. 3.2 shows the above diode connected in series to a resistor of resistance 5.0 Ω

in a circuit where the battery has an e.m.f. E and with negligible internal resistance. The current indicated on the ammeter is 400 mA.

Fig. 3.2

0 0 1 2 3 4 5 V / V

100

200

300

400

500

I / mA

6

A

5.0 Ω

E

6


For Examiner’s

Use

(i) Show that the potential difference across the resistor is 2.0 V [1]

(ii) Hence, calculate the e.m.f. E of the supply.

E = ………………………… V [2] (iii) Calculate the resistance of the diode in this case.

resistance = ………………………… Ω [1] (iv) Using the graph in Fig. 3.1, explain if the diode obeys Ohm’s law.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

…………………………………..……………………………………………………… [2]

7


For Examiner’s

Use

4 Fig. 4.1 shows a battery of e.m.f. 24 V with an internal resistance of 0.70 Ω.

Fig. 4.1

(a) Calculate the current drawn from the battery.

current = ………………………… A [2]

(b) Calculate the power in each of the 5.0 Ω resistor.

power = ………………………… W [2]

(c) Calculate the terminal potential difference.

terminal potential difference = ………………………… V [2]

12 Ω

24 V

5.0 Ω 5.0 Ω 0.70 Ω

8


For Examiner’s

Use

5 (a) Define (i) magnetic flux density,

………………………………………………………………………………………………

………………………………………………………………………………………………

...………………………………..………………………………………………………. [1]

(ii) the tesla

………………………………………………………………………………………………

……………………………………………………………………………………………… ...………………………………..………………………………………………………. [1]

(b) Fig. 5.1 shows an electric motor which is made up of a rectangular coil of wire of 150 turns. The coil is 0.20 m long and 0.12 m wide. The coil has a current of 0.32 A flowing through it and its plane is parallel to a field of magnetic flux density 0.36 T.

Fig. 5.1

(i) Draw arrows on Fig. 5.1 to represent the directions of the magnetic forces acting on the coil. Label them F. [1] (ii) Calculate the magnitude of the magnetic force acting on one side of the coil.

force = ………………………… N [2]

0.32A

0.12 m

0.20 m

X

Y

magnetic field

9


For Examiner’s

Use

(iii) Calculate the torque which is exerted on the coil.

torque = ………………………… N m [1]

10


For Examiner’s

Use

6 Multi-bladed low-speed wind turbines (windmills) similar to the one shown in Fig. 6.1 have been used since 1870, particularly for pumping water on farms.

Fig. 6.1 The turbine blades cover almost the whole surface of the wheel and a tail vane behind

the windmill keeps the wheel facing the wind. The diameters of the wheel of windmills of this type vary from 2 m to a practical maximum of about 12 m. Because of this size limitation, they are not suited to large power outputs. They will start freely with wind speeds as low as 2 m s-1 and, at these low speeds, can produce large torques.

11


For Examiner’s

Use

Fig. 6.2 shows how P, the output power of these windmills, varies with the overall diameter of the wheel for different wind speeds, v.

Fig. 6.1

Fig. 6.2

diameter / m

v = 2.0 m s-1

v = 3.0 m s-1

v = 4.0 m s-1

v = 5.0 m s-1

v = 6.0 m s-1 v = 7.0 m s-1

v = 8.0 m s-1

v = 9.0 m s-1v = 10 m s-1

2.0 4.0 6.0 8.0 10.0

Pow

er P

/ W

12


For Examiner’s

Use

(a) Use the data in Fig. 6.2 to show how, for a particular multi-bladed low-speed windmill with a wheel of diameter 6.0 m, the power output P varies with the wind speed v. Enter your values in the table in Fig. 6.3.

Fig. 6.3 [3]

(b) Use the data in Fig. 6.3, plot a graph of lg (P / W) against lg (v / m s-1).

[1]

v / m s-1 P / W lg (v / m s-1) lg (P / W)

13


For Examiner’s

Use

(c) The relationship between P and v is of the form P = k v n, where n and k are constants. Find the value of n and k. Show your working.

n = …………………………

k = ………………………… [3]

14


For Examiner’s

Use

Section B

Answer two of the questions from this section. 7 (a) (i) State Newton’s first law of motion and show it leads to the concept of force.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

……………………………………………………………………………………………… .………………………………..……..…………………………………………………. [2] (ii) With the aid of a diagram, describe a situation in which an object has an

acceleration in the opposite direction to its velocity. Include labelled arrows in the diagram to illustrate the velocity v and acceleration a.

…....……………………………………………………………………………………….

…....……………………………………………………………………………………….

…....……………………………………………………………………………………….

……....………………………………………………………………………………… [2]

(b) (i) Explain what is meant by the linear momentum of a body.

……………………………………………………………………………………………… .………………………………..……..…………………………………………………. [1] (ii) State the relationship between the linear momentum p of a body of mass m and

its kinetic energy E. ..………………………………………………………………………………………… [1]

15


For Examiner’s

Use

(c) A ship of mass 1.2 × 107 kg is moving backwards with a velocity of 0.50 m s-1 towards a dockside. In order to stop the ship, the engines are ordered full ahead.

(i) Calculate the initial kinetic energy of the ship.

kinetic energy = ………………………… J [1] (ii) Assuming that viscous effects are negligible, calculate the magnitude of the

constant retarding force which must be exerted on the ship if it is to stop in a distance of 15 m.

retarding force = ………………………… N [3] (iii) Calculate the time taken by the ship to stop under these conditions.

time = ………………………… s [2]

(iv) Explain qualitatively how your answer in (iii) would be affected by viscous forces. …......……..…………………………………………………………………………………

…......……..………………………………………………………………………………… …......……..…………………………………………………………………………………

……..……..…………………………………………………………………………………

…......……..…………………………………………………………………………………

...……..………………………………………………………………………………..... [3]

16


For Examiner’s

Use

(v) Calculate the change in momentum of the ship as it comes to a complete halt at the dock.

change in momentum = ………………………… N s [2]

(vi) Using your answer in (v) and with the aid of a diagram, explain how the law of conservation of momentum is applied in this example.

……..……..…………………………………………………………………………………

……..……..…………………………………………………………………………………

……..……..…………………………………………………………………………………

……..……..…………………………………………………………………………………

……..……..…………………………………………………………………………………

...……..……………..…………………………………………………………………... [3]

17


For Examiner’s

Use

8 (a) (i) What do you understand by the term interference? Explain your answer by reference to the fringe pattern when a narrow beam of monochromatic light has passed through a double slit.

..……...……..……………………………………………………………………………… ..……...……..……………………………………………………………………………… ..……...……..……………………………………………………………………………… ….....……..……………………………………………………………………………... [2] (ii) State three conditions necessary for the two light wavetrains to produce a well-

defined interference pattern.

1. ……...……..……………………………………………………………………..……… ……..……………………………………………………………………………............

2. ……...……..……………………………………………………………………..………

….…..……………………………………………………………………………............

3. ……...……..……………………………………………………………………..……… .........……………………………………………………………………………........ [3]

(b) A student sets up the apparatus shown in Fig. 8.1 to demonstrate a two slit

interference pattern on the screen. The set-up was modelled after Young’s double slit experiment. The slits S1 and S2 are of the same width.

Fig. 8.1

d S1

S2 So

double slit

single slit

laser beam

screen

D

18


For Examiner’s

Use

(i) Explain why the single slit So is not necessary in this particular set-up. ………………………………………………………………………………………………

.…...……………………….……………………………………………………………. [1]

(ii) Explain how the result of this experiment provided evidence that light must have

wave properties.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

.…...……………………….……………………………………………………………. [2]

(iii) The laser beam has a wavelength of 630 nm. The separation d is 1.0 mm and the distance D is 2.5 m. Calculate the separation of the fringes on the screen.

separation = ………………………… m [2] (iv) Describe and explain what change would be observed on the screen if both the

slits S1 and S2 are made narrower by half while maintaining the same separation d.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

....……………………….………………………………………………………………. [3]

19


For Examiner’s

Use

(v) Describe and explain what change would be observed on the screen if both the slits S1 and S2 are covered with pieces of light polariser and the polariser in front of S1 is rotated slowly from 0o to 90o.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

…………………………….……………………………………………………………. [4]

(c) The notion that light is waves was brought to question when certain experimental

results based on the photoelectric effect cannot be explained using the wave model. (i) Explain two ways in which the results from the photoelectric effect shows that

light has particle properties instead.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

...………………………….……………………………………………………………. [2] (ii) The results from the Young’s double slit experiment and the photoelectric effect

have led to the nature of light. State the idea. ………………………………………………………………………………………………

....………………………….……………………………………………………………. [1]

20


For Examiner’s

Use

9 (a) (i) Electromagnetic waves have a wave nature as well as a particulate nature. This is known as wave-particle duality. Describe a situation in which particles can be shown to have a wave nature.

……………………………………………………………………………………………… ………………………………………………………………………………………………

………………………………………………………………………………………………

…………………………….……………………………………………………………. [2]

(ii) Calculate the wavelength of a particle of mass 1.82 x 10

−28 kg when travelling with

a speed which equals to 10% of the speed of light.

wavelength = ………………………… m [2] (iii) Fig 9.1 illustrates a phenomenon known as the Compton effect, whereby an

incident X-ray photon is scattered by an electron at rest. The wavelength of the scattered photon λ’ is found to be longer than the wavelength λ of the incident photon.

Fig. 9.1

Using de-Broglie’s relation, suggest how this phenomenon demonstrates the particulate nature of electromagnetic radiation.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

…………………………….……………………………………………………………. [2]

electron after collision

Scattered photon (λ’)

θ

φ

incident photon (λ)

electron at rest

21


For Examiner’s

Use

(b) Fig. 9.2 shows an experimental setup to investigate the photoelectric effect. Ultraviolet (UV) light of wavelength 237 nm is incident on an emitter of area 2.0 cm2 and a current reading of 2.00 nA is registered.

(i) Given that every 1 in 5 photons causes a photoelectron to be emitted from the emitter, show that the rate of photons incident on the emitter is 6.25 × 1010 s-1.

[2] (ii) Calculate the energy of each photon incident on the emitter.

photon energy = ………………………… J [1] (iii) Calculate the intensity of the incident radiation.

intensity = ………………………… W m-2 [3]

I

+ Variable d.c supply _

collector emitter

V UV light

Fig. 9.2

A

22


For Examiner’s

Use

(iv) The battery connections in Fig. 9.2. are reversed so that the emitter is made positive with respect to the collector.

1. Given that the work function of emitter is 4.7 eV, calculate the stopping

potential.

stopping potential = ………………………… V [2]

2. Explain why the stopping potential in (b)(iv)1. remains the same when the intensity of the UV light is increased.

……………………………………………………………..……………………………

……………………………………………………………..……………………………

……………………………………………………………..……………………………

……………………………………………………………..……………………………

..….……………………………………………..………………………………………

.………..……….…………………………..……………………….………………. [3]

(c) Fig. 9.3 represents the energy levels for an atom. The atom at ground state is

bombarded with an electron of energy 17 eV.

Fig. 9.3

(i) State all possible photon energies when the atom returns to its ground state. …...………………..……….……………………………………………………………. [2]

n = 2

n = 1

n = 3 n = 4

-20 eV

-7 eV

-5 eV -2eV

23


For Examiner’s

Use

(ii) On Fig. 9.4, sketch the appearance of the spectrum which corresponds to the frequencies of the emitted photons.

[1]

Fig. 9.4

END OF PAPER

Increasing frequency

1

Innova Junior College 2010 Prelim 2 H1 Physics

Paper I Solutions

Qn Ans Qn Ans Qn Ans 1 B 11 A 21 B 2 C 12 B 22 B 3 D 13 A 23 C 4 C 14 C 24 B 5 D 15 D 25 A 6 C 16 D 26 D 7 A 17 D 27 C 8 B 18 A 28 A 9 C 19 D 29 A

10 B 20 C 30 D 1. A displacement (vector) and acceleration (vector)

B force (vector) and kinetic energy (scalar) C momentum (vector) and velocity (vector) D power (scalar) and speed (scalar)

2.

∴ ±

VVV

V

-1

-1

Δ = 0.03×327.66Δ = 9.8298Δ =10m s (to 1 s.f.)

= 330 10m s

3.

student results, g / m s-2 <g> range of g values

A B C D

9.81 9.81 9.45 8.45

9.79 10.12 9.21 8.46

9.84 9.89 8.99 8.50

9.838.948.768.41

9.8175, accurate 9.6900, accurate 9.1025, not accurate 8.4550, not accurate

0.05, precise 1.18, not precise 0.69, not precise 0.09, precise

4. The vector on side X is the sum of vector : v + (-u) From v = u + at, v – u = at

- u

X

2

5. Since air resistance is neglected, the ball undergoes free fall after it leaves the hand and before it falls back on the hand. Under free-falling, the acceleration is due to gravity and acting downwards (negative by convention) all the time, even when the ball is momentarily at rest at the maximum height.

6. 7. From Newton’s second law, net force is proportional to the rate of change of momentum.

For a case where there is no net force acting on an object, the object will maintain its momentum (i.e. either stay at rest or continue its motion with a constant speed along a straight line) , which is Newton’s first law.

8. Δ p = pf – pi

Sign convention: Take rightwards as positive. Δ p = m vf – m vi

Δ p = [0.100 (–30)] – [0.100 (20)] Δ p = – 5.0 kg m s-1 (to the left) Δ p = 5.0 kg m s-1

9. From Conservation of Momentum, Initial momentum of system = Final momentum of system 0 = px + py

py = – px

Use 2pKE =m2

to establish the ratio,

= = =

xx

y x

ppX m m

pY pm m

22

2 22( ) 2( ) 2.0

2(2 ) 2(2 )

Constant velocity means gradient of s-t graph is constant.

Deceasing velocity to 0 m s-1 means gradient of s-t graph decreases to zero.

3

10. Total force is the sum of the normal force and friction. 11. Considering the forces in the x-direction, Tx = Hx Considering the forces in the y-direction, Ty = Hy + Wy

Since Tx = Hx and Ty > Hy, hence T > H (Only Option A and C) Since Ty > W, and W has no x-component, Hence T > W (Leaving option A as the answer)

12. By Hooke’s Law, F = k x

For spring P, F = (2k) xP

xP = F2k

For spring Q, F = (k) xQ

XQ = Fk

Work done on spring: W = ½ F x Since F is constant, W ∝ x

=

= =12

P P

Q Q

P

Q

W xW x

FW 2k

FWk

WP = ½ WQ

Normal force by road

Friction by road

Ty

Tx

Hx

Hy

4

13. work done by applied force = work done to overcome friction + gain in GPE (9.0 × 103) (40) = work done to overcome friction + (20 × 103) (12) work done to overcome friction = 120 kJ 14. period = time base × number of squares period = (0.25 × 10-3) (8) period = 2.0 × 10-3 s

fT

= = =-3

1 1 500 Hz2.0×10

15.

π

ππ

φ

φ

φ∴

Δ Δ t=2 TΔ 1.5T=2 TΔ = 3

n = 3

16. Since I ∝ 1

2d,

I = k1

2d,

For a graph of I against 1

2d, a straight line passing through the origin is obtained.

17. 2.5 λ = 30.0 cm λ = 12.0 cm 18. Slit width decrease, more diffraction, width of central maxima increase. When the slit width is reduced, less light is allowed to pass through, hence the overall

intensity decreases. 19. The zeroth order fringes of the various wavelengths overlap to give a central bright fringe.

Other than this, the various wavelengths of light are diffracted by different diffraction angles (red, having the largest wavelength, will be diffracted the most), to form coloured fringes on each side.

20. Q = I t Ne e = I t

eNt

=Ie

eNt

= 3.0 × 1019 s-1

The electrons flow from the negative to the positive terminal of the battery. Hence Y to X.

5

21.

2

2

LRR

LRd

ρ

ρ

π

=

=⎛ ⎞⎜ ⎟⎝ ⎠

Since the wires have the same resistance and length,

2

2

alumimium

alumimiumdρ

π ⎛ ⎞⎜ ⎟⎝ ⎠

= 2

2

silver

silverdρ

π ⎛ ⎞⎜ ⎟⎝ ⎠

silver

alumimium

ρρ

=2

2min

silver

alu ium

dd

12

=2

2silverdd

silverd = 0.71 d

22. R is the ratio of VI

. The graph show that the ratio of VI

is initially constant. Subsequently,

the ratio increases with V. Hence Option B. 23. The potential difference across each lamp in diagram 2 is the same as that in diagram 1.

Hence power dissipated in each lamp is the same. Each lamp will light up with normal brightness.

24. The circuit can be redrawn in the following way.

Let the total external resistance be R.

Ω

RR

1 1 1= +6 6

= 3.0

E = I (R+r) 12 = I (3.0 + 3.0) I = 2.0 A Since I1 + I2 = 2.0 A And I1 = I2

I1 = 1.0 A

6

25. XY carrying a current upwards, produces a magnetic field (into the page) in the region where PQRS is. Segment PS, carrying a current upwards experiences a magnetic force directed towards XY while segment QR, carrying a current downwards will experience a magnetic force away from XY. However, the strength of the magnetic field decreases with distance from XY, hence PS being nearer to XY will experience a larger force compared to QR. Hence, the coil experiences a net force towards XY and it will move in that direction.

The magnetic force acting on PQ upwards and the magnetic force acting on SR is downwards. These 2 forces are equal in magnitude and opposite in direction, hence they cancel.

26. The magnetic field is directed along the axis of the solenoid (by Right Hand Grip Rule).

The electron does not have a component of the velocity that is perpendicular to the magnetic field. Hence no magnetic force acts.

27. As light intensity increases, the number of photons arriving at the metal surface per unit

time increases. An increase in the number of photons per unit time by a certain proportion will lead to an increase in the number of photoelectrons per unit time (hence photocurrent) in the same proportion.

28. From photoelectric effect equation:

φ

φ=

S

S

h f = + e Vh V f -e e

Since Y has a greater work function, the graph of Y should have a y-intercept which is more negative than the y-intercept for the graph of X.

Since he

is a constant, both graphs have the same gradient.

Hence, option A. 29. From

λhcE = , energy of photon 1 is smaller than energy of photon 2, hence λ1 > λ2.

30. Option A: only emission spectrum is formed Option B: both absorption and emission spectrums could be observed depending on the direction of viewing. (Refer to 2008 H1 P2 Q4) Option C: only emission spectrum is formed

1

Innova Junior College 2010 Prelim 2 H1 Physics

Paper 2 Solutions 1 (a) kg m s-1 = [mass] × [velocity] = [momentum] or [impulse] [B1]

P E masI = = =A At At

I-2

-32

(kg) (m s ) (m)= = kg s(m )(s)

[m][a][s][ ] =[A][t]

[B1]

(b)

(i) Estimate the density of plastic to be 2 times that of water = 2 g cm-3

Mass of protractor = (Volume) (Density) Mass of protractor = ½ π r 2 x ρ Mass of protractor = ½ π (5.0)2 (0.1) (2) Mass of protractor = 7.9 g [M1] for logical reasons [A1] for acceptable range of 5 to 50 g

(ii) Micrometer Screw Gauge [B1]

(iii) Repeat the measurement of x at different parts of the protractor and taking average. [B1]

2 (a) (i) === o

y uu 3020 sin)(sinθ 10.0 m s-1 [A1]

(ii) === ox uu 3020 cos)(cosθ 17.3 m s-1 [A1]

(b) (i) Taking into consideration, the vertical components of the motion

ghuv yy 222 +=

h).().( 81920100 2 −+= [M1] h = 5.10 m [A1]

(ii) The time taken to reach maximum height gtuv yy += t).(. 8190100 −+= t = 1.02 s [C1]

The horizontal distance (or the range)

= ))(( flightoftimeux = (17.3)(1.02×2) = 35.3 m [A1]

(c) The maximum height and the horizontal distance will both be reduced. [B1]

2

3 (a) EMF refers to the change in energy from other forms to electrical by the source per

unit charge driven round a complete circuit.

Potential difference between two points is defined as the change in energy from electrical to other forms per unit charge between the two points.

Correct statements with regards to energy conversion. [B1]

Both statements must include ‘per unit charge’. [B1] (b) (i) The p.d. across the resistor = IR = (0.400) (5.0) [M1]

= 2.0 V [A0]

(ii) From Fig.3.1, when the current is 400 mA, the p.d. across the diode is 4.5 V.

The emf E = sum of the p.d. = 2.0 + 4.5 = 6.5 V [A1]

(iii) Resistance of diode = 4.50 11.3

0.400VRI

= = = Ω [A1]

(iv) The graph in Fig. 3.2 is not a straight line passing through the origin. [M1]

Thus, the current is not directly proportional to the potential difference. [A1] (Note: No marks for stating Ohm’s law but making no reference to the graph.)

4

(a) 1 1 1 2

5.0 5.0 5.0netR= + =

The net resistance of the resistors in parallel = 5.0 / 2 = 2.5 Ω The combined resistance in the circuit = 0.70 + 2.5 + 12 = 15.2 Ω [M1] The current drawn from battery = E / Combined resistance

= 24 / 15.2 = 1.58 A [A1]

(b) The power in each of the 5.0 Ω resistor

2

2 1.58 (5.0)2

P I R ⎛ ⎞= = ⎜ ⎟⎝ ⎠

[M1]

= 3.12 W [A1] (c) The terminal potential difference = Current × External resistance

V = (1.58)(2.5 + 12) [M1] V = 22.9 V [A1]

Or V = E - Ir V = 24 – (1.58)(0.70)

V = 22.9 V

3

5 (a) (i) Magnetic flux density is the magnetic force acting on a straight wire per unit length

per unit current flowing through it, when the wire is placed perpendicular to the magnetic field. [B1]

(ii) It is the amount of magnetic flux density of a uniform magnetic field when a magnetic

force per unit length per unit current of 1 newton per metre per ampere acts on a straight wire placed perpendicular to the magnetic field. [B1]

(b) (i)

Correct direction for forces acting on each side of the coil showing a couple [B1]

(ii) Magnitude of magnetic force on one side of the coil F = NBIL sinθ

= (150)(0.36)(0.32)(0.20) sin 90o [M1] = 3.46 N [A1]

(iii) Torque of a couple = (Magnitude of one force)×(perpendicular distance between forces) = (3.46)(0.12) = 0.415 N m [A1]

F

F

0.32A

0.12 m

0.20 m

X

Y

Magnetic field

4

6 (a)

[B1] for 8 sets of readings of v and P values. [B2] for calculation of lg v and lg P values. Allow 1 mistake in calculation. Deduct 1 mark for each subsequent mistake. Note that s.f. is not the priority here.

(b) [B1 for graph]

v / m s-1 P / W lg ( v / m s-1) lg (P / W) 2.0 50 0.30 1.70 3.0 150 0.48 2.18 4.0 350 0.60 2.54 5.0 675 0.70 2.83 6.0 1150 0.78 3.06 7.0 1825 0.85 3.26 8.0 2750 0.90 3.44 9.0 3950 0.95 3.60

0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

1.5

1.0

2.0

2.5

3.0

3.5

lg (P / W)

lg (v / m s-1)

0.91, 3.45

0.38, 1.90

x

x

x

x

x

x

x

x

5

v

(c) Linearise the equation P = k vn by taking lg on both sides,

lg P = lg (kvn) lg P = lg k + n lg v [B1]

Gradient = 3.45 -1.900.91- 0.38

n = 2.93 (to 3 s.f) [A1] for n = 2.95 ± 0.05 Sub (0.38, 1.90) and gradient = 2.93, 1.90 = (2.93) (0.38) + y-intercept y-intercept = 0.7866 lg k = 0.7866 k = 6.12 [A1] 7 (a) (i) Newton’s First Law of Motion states that every body continues in its state of rest or uniform motion in a straight line unless a net external force acts on it to change that state. [B1]

Hence, if we observe an object initially in a state at rest but which suddenly moves, or an object moving at uniform speed in a straight line, but which suddenly accelerates or changes its velocity [B1], we say that there must be a net external force acting on it.

(ii)

(Diagram with 2 arrows- B1)

An object that is projected vertically upwards.[B1]

(b) (i) Linear momentum of a body is the product of its mass and its linear velocity. [B1]

(ii) =2

2pEm

[B1]

(c) (i)

2 7 2

6

1 1Initial KE (1.2 10 )(0.5)2 2

1.5 10 J [A1]

mu= = ×

= ×

a

6

u

Fws

Fsw

(ii) = +

+

= ×

×

2 2

2

2

27

5

Using 2 0=(0.5) 2 (15)

-(0.5) = [C1]2(15)

-(0.5)Required force= (1.2 10 )[ ] [M1]2(15)

= -1.0 10 N

v u asa

a

ma

[A1]

(iii)

= +

−= +

×=

2

Using ,(0.50)0 0.50 [ ] [M1]2 15

60 s [A1]

v u at

t

t

(iv) Viscous force DF v∝ − where v is the instantaneous velocity [B1]

The viscous force will provide a greater retardation force [B1], and the time taken to stop the ship will be shorter [B1]. (Remarks: Viscous force will be greatest initially as the initial speed is greatest, and it will reduce to zero when the final speed is zero)

(v)

Δ = × −

Δ ×

m v u 7

6

p = ( - ) 1.2 10 (0 0.50) [M1]p = - 6.0 10 N s [A1]

Fws = force exerted by water on the ship Fsw = force exerted by ship on the water [B1] for diagram. (vi) By considering the ship and the water as an isolated system and with no

external forces acting on the ship and the water [B1], the momentum lost by the ship is equal to the momentum gained by the water [B1].

7

8(a)(i) Interference is the phenomenon that occurs when two or more waves overlap to produce an effect that is equal to the combined effects of the component waves in accordance with the principle of superposition. [B1]

In regions where the waves combined in phase, constructive interference occurs. Here, bright fringes are observed. In regions where the waves combined completely out of phase, destructive interference occurs. Here, dark fringes are observed. [B1]

(ii) (1) The component waves must overlap or superposed. [B1]

(must be mentioned)

(2) The component waves must be coherent (ie have a constant phase difference between them).

(3) The amplitudes of the component waves must be nearly the same.

(4) The component light waves must be unpolarised or if not, must share the same plane of polarization.

Any other two of the above (2)-(4) [B2]

(b)(i) The single slit So is not necessary because the light source used is a laser which is already coherent by its own nature. [B1]

(ii) The observation that there are bright and dark fringes on the screen is an indication

that interference has taken place. [B1] Bright fringes are where constructive interference takes place while dark fringes are where destructive interference takes place. The summation of the two combined light rays is a direct consequence of the principle of superposition which applies to waves. Thus, light has wave properties. [B1]

(iii) Separation of fringes 9

3

(630 10 )(2.5)(1.0 10 )

Dxdλ −

−

×= =

× [M1]

= 1.58×10-3 m = 1.58 mm [A1]

(iv) Since the separation d of the slits is maintained, the separation x of the fringes remains unchanged. [B1]

When the slits are made narrower by half, the amplitude of the lights emerging from the slits will be reduced by half. [B1] Since the intensity is directly proportional to the square of the amplitude, when the amplitude is halved, the intensity of the bright fridges will be reduced to a quarter. [B1]

8

(v) The light rays emerging from the two polarisers will be plane polarized. At 0o, where the planes of polarizations are parallel, the interference pattern is very clear and distinct. [B1] As the angle is increased towards 90o, the interference fringes become progressively less distinct. [B1] At 90o, when the two light waves have their planes of polarisation perpendicular to each other, the interference pattern would disappear and only a uniform patch of illumination is seen on the screen. [B1] When the angle increases from 0o to 90o, the interference pattern gradually becomes less contrasting because the amplitude of one wave that has plane parallel to the other is decreasing. At right angle, the two waves do not share amplitudes in the same direction of polarization, thus interference do not occur.

[B1]

(c) (i) - When light ray is incident on a metal surface, photoelectrons are emitted only

when the frequency is above a minimum threshold frequency. Below this frequency, no photoelectrons were emitted even when the intensity of illumination is increased.

- Above the threshold frequency, the maximum kinetic energy of the photoelectrons is dependent on the frequency rather than on the intensity of the illumination.

- There was no time lag between the absorption of light and the emission of photoelectrons when the intensity of illumination on the surface is varied.

2 × [B1] for any 2 of the above points.

(ii) Young’s double slit experiment showed us the light has wave properties while the

photoelectric effect showed us that light has particle properties. Thus, light has a dual nature. Light is both a wave and a particle. [B1]

θ = 90o

0o ⟨θ⟨ 90o

intensity

θ = 0o

9

9 (a) (i) A beam of electrons passes through the graphite ‘diffraction grating’ [B1]. An interference pattern of circular concentric rings is seen on the screen [B1]. (ii)

34

28 8

-13

6.63 10 [M1](1.82 10 ) (0.10 3.0 10 )

=1.21 10 m [A1]

hmv

λ

−

−

=

×=

× × × ×

×

(iii) As a result of collision, the momentum of the electron increases and the momentum of the photon decreases as the momentum of the scattered photon

λ'h

is less than the momentum of the incident photon λh

(since λ’ is longer than λ). [B1] From the principle of conservation of linear momentum [B1], the decrease in the momentum of the incident photon displays the particulate nature of electromagnetic radiation.

(b) (i) Rate of electrons produced = 9

1019

2.00 10 1.25 101.6 10

−

−

×= ×

×[M1]

−

= × ×

×

10

10 1

Rate of incident photons 1.25 10 5 [M1]6.25 10 s [A0]

=

(ii)

34 8

9

19

6.63 10 3.0 10237 10

8.39 10 J [A1]

hcEλ

−

−

−

× × ×= =

×= ×

(iii) power = 19 10 88.39 10 6.25 10 5.24 10 W− −× × × = × [M1]

Intensity =

−

−

− −

×=

×= ×

8

4

4 2

power 5.24 10 [M1]area 2.0 10

2.62 10 W m [A1]

(iv) 1.

10

( )

φ

φ− −

−

= +

× − ×−= =

×=

s

s

hf eV

hfVe

19 19

19

8.39 10 4.7 1.6 10[M1]

1.6 10 0.544 V [A1]

2. Increasing intensity does not affect the photon energy and the photon

energy remains the same as the frequency of UV light is constant. [B1]. The radiation is incident on the same emitter surface (work function is also

constant)[B1]. The maximum kinetic energy of the photoelectron does not change [B1].

Hence the stopping potential does not change. (c) (i) 2 eV, 13 eV & 15 eV [Deduct B1 for each incorrect answer] (ii)

3 distinct lines drawn with 2 lines closely spaced on the right of the spectrum [B1]


Class Adm. No. Candidate Name: ________________________________

This document consists of 14 printed pages. [Turn Over

Preliminary Examinations II Pre-university 2

H1 PHYSICS 8866/01

Friday 24 Sep 2010 1 hour

OMR forms are required.

INSTRUCTIONS TO CANDIDATES

Do not turn over this page until you are told to do so. Write your full name, class and admission number in the spaces at the top of this page and on any separate answer paper used. Section A Answer all 30 MCQ questions. Shade your answers on the separate Optical Mark Reader (OMR) Form provided.

2

Data

speed of light in free space, c = 3.00 x 108

m s-1

elementary charge, e = 1.60 x 10-19

C

the Planck constant h = 6.63 x 10-34 Js

Unified atomic mass constant u = 1.66 x 10-27 kg

rest mass of electron, me = 9.11 x 10

-31

kg

rest mass of proton, mp = 1.67 x 10

-27

kg


Formulae

uniformly accelerated motion, s = ut + ½ at2

v

2

= u2

+ 2as

work done on/by a gas, W = p∆V


Electric potential V = Q / 4πεor

resistors in series, R = R1 + R

2 + ....

resistors in parallel, 1/R = 1/R1 + 1/R

2 + ....

3

Section A (30 marks)

1 When a beam of light is incident on a surface, it delivers energy to the surface. The intensity of the beam is defined as the energy delivered per unit area per unit time. What is the unit of intensity, expressed in SI base units?

A kg m2 s-3 B kg m2 s3 C kg s-2 D kg s-3

2 Shown below are four target boards from a shooting competition. Which of the following

indicates a small random error but a large systematic error?

3 The figure below shows three force vectors. Which of the vectors A, B, C, D would be most

likely to represent their resultant?

A B C D

[Turn Over

4

4 The velocity-time graph below depicts the motion of an object travelling in a straight line. Which of the following statements is a correct interpretation of the graph?

A During the first 20 s of the motion, the object accelerates and travels a distance of 200m.

B The acceleration of the object increases during the first 20 s to become a maximum when the velocity is 10 ms-1.

C The acceleration of the object when t = 5 s is equal to the acceleration when t = 35 s.

D The object decelerates during the final 20 s of its motion, the most rapid deceleration occurring at t = 40 s.

5 The graph below shows how the distance s, travelled by a body from its starting point varies with the time t.

The shape of the curve indicates that 1. the acceleration is increasing at X. 2. the speed is increasing at Z.

3. the body is at rest at Y. Which of the following shows the correct answers? A 1, 2, 3 B 1, 2 only C 2, 3 only D 3 only

5

6 From the top of a cliff overlooking a lake, John throws two stones. The stones have identical

initial speeds vO. Stone 1 is thrown downwards at an angle below the horizontal, while stone 2 is thrown upward at the same angle above the horizontal (see figure below). Neglecting the effect of air resistance, which of the following is true?

A stone 1 strikes the water with a greater velocity than stone 2.

B stone 2 strikes the water with a greater velocity than stone 1.

C both stones strike the water with the same speed but at a different angle above the water surface.

D both stones strike the water with the same velocity.

7 An object of mass 20 kg moves along a straight line on a smooth horizontal surface. A force F acts on the object in its direction of motion. A graph of F against t is shown below.

What is the velocity of the object at t = 6 s if its velocity at t = 4 s is 4.0 m s-1 ?

A 3.0 m s-1 B 3.3 m s-1 C 4.7 m s-1 D 5.0 m s-1

8 An object is projected vertically upwards. Neglecting air resistance, which one of the following statements is correct?

A according to the principle of conservation of energy, the total energy of the object is constant throughout the motion.

B according to the principle of conservation of momentum, the momentum of the object is constant throughout the motion.

C the object travels equal distances during equal periods of time during the ascent and descent.

D the gravitational potential energy of the object increases uniformly with time during the ascent.

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6

9 The diagram shows an object of weight 30 N suspended from a rod, attached to a wall. The rod is kept in equilibrium by a wire attached at point Z of the rod.

The force exerted by the rod at point Z is F, and the tension in the wire is 60 N. Which diagram represents the three forces acting at point Z?

A

B

C

D

10 The extension-force of a spring of spring constant k, is shown in the figure below. The work done in extending the spring from x1 to x2 is given by

At which point must a vertical force of 6 N act to keep the bar in equilibrium?

A 12212

1xxFF

B 11222

1

2

1xFxF

C 12212

1xxFF

D 12212

1xxFF

7

11 The diagram below shows two bodies X and Y connected by a light cord passing over a

light, free-running pulley. X starts from rest and moves on a smooth plane inclined at 30 to the horizontal.

What will be the total kinetic energy of the system when X has travelled 3.0 m along the plane? A 20 J B 59 J C 88 J D 206 J

12 A constant force is applied to a body which is initially stationary but free to move in the direction of the force. Assuming that the effects of friction are negligible, which of the following graphs best represents the variation of P, the power supplied, with time t? A

C

B

D

13 In an attempt to find the frequency of a wave with a CRO, the timebase was set to 5 ms per division and a trace of the waveform is as shown.

What is the frequency? A 16.7 Hz B 33.3 Hz C 50.0 Hz D 100 Hz

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8

14 A loudspeaker emits a continuous sound of frequency 400 Hz. The graph in the figure below shows the displacements of the air particles, along a straight line x, from their undisturbed positions at one instant. Using the sign convention that displacement of the air particles to the right is positive, at which point, A, B, C, D is the instantaneous pressure at its peak value?

15 The figure below shows a transverse wave on a rope. The wave is travelling from left to right. At the instant shown, the points P and Q on the rope have maximum and zero displacement respectively.

Which of the following describes the direction and magnitude of the acceleration of the

points P and Q at this instant?

A P – maximum down; Q - zero

B P – zero; Q – maximum down

C P – zero; Q – maximum up

D P – maximum up; Q - zero

16 When a stationary wave pattern is set up in a pipe open at both ends, which of the following statements is correct?

A The frequency of the sound wave emitted is not equal to the frequency of the stationary wave in the pipe.

B Nodes are found at the open ends.

C The wavelength of the stationary wave at the fundamental frequency is twice the length of the pipe.

D Two nodes can be detected along the pipe at the fundamental frequency.

9

17 The figure shows two identical loudspeakers driven in phase from a common audio-frequency source.

When a student moves along a line such as XV, he notices that there are regions in which the sound heard is alternately loud and quiet. Regions in which the sound is loud may be moved closer together by

A decreasing the distance d.

B increasing the distance L.

C increasing the frequency of the audio-frequency source.

D increasing the power output from the audio-frequency source.

18 A and B are two coherent sound sources which are out of phase. Point X shows permanent zero displacement.

Calculate the sound wave with the minimum wavelength that can satisfy this condition. A 0.75 m B 1.5 m C 2.0 m D 3.0 m

19 A wire carries a current of 2.0 A for 1.0 hour. How many electrons pass a point in this time?

A 1.2 x 10-15

B 7.2 x 103

C 1.3 x 1019

D 4.5 x 1022

20 In the circuit below, all the resistors have the same value. A high resistance voltmeter is connected between two points in the circuit. Between which two points of connection would the meter read zero?

A Q and U

B P and T

C Q and W

D S and U

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10

21 The diagram shows the relation between the direct current I in a certain conductor and the potential difference V across it. When V < 1.0 V, the current is negligible.

Which statement about the conductor is correct?

A It obeys Ohm's law and when V > 1.0 V, resistance = 20.0 .

B It obeys Ohm's law and when V > 1.0 V, resistance = 40.0 .

C It does not obey Ohm's law and when V > 1.0 V, resistance = 20.0 .

D It does not obey Ohm's law and when V > 1.0 V, resistance = 40.0 .

22 The diagram shows a circuit in which a 24 V d.c. supply is connected to 5 resistors.

What is the current flowing through the 4 resistor?

A 0 A B 3 A C 4 A D 6 A

23 The figure below shows four identical lamps, J, K, L and M, which are all lit. Lamp K is now removed from the circuit.

Which one of the following statements is true?

A J, L and M are equally bright.

B J is brighter than before, but not as bright as L and M.

C J is dimmer than before, but not as bright as L and M.

D J is dimmer than before, but brighter than L and M.

11

24 A coil, mounted on an axle, has its plane parallel to the flux lines of a uniform magnetic field B as shown.

When a current I is switched on, and before the coil is allowed to move, A there are no forces due to B on the sides SP and QR.

B there are no forces due to B on the sides PQ and RS.

C sides SP and QR tend to attract each other.

D sides PQ and RS tend to attract each other.

25 A plotting compass is placed next to a vertical wire PQ. When there is no current in the wire the compass points North as shown in the diagram.

Which diagram shows a possible direction for the compass to point when a current passes from Q to P?

A B C D

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26 The diagram below shows a cross-sectional view of four long straight current-carrying wires. The wires are parallel to each other and are perpendicular to the plan of the page, passing through the points W, X, V, Z at the corners of a square. O is the intersection of the diagonals of the square.

If the magnetic flux density at the point O is zero, which of the following statements must be true? I The currents in all four wires must be in the same direction. II The currents in all four wires must be of the same magnitude. III The current in Y must be in the same direction as that in W and the current in X must be in the same direction as that in Z. IV The current in Y must be in the opposite direction as that in W and the current in X must be in the opposite direction as that in Z. A I and II B II and III C III only D II and IV

27 Which of the following set-up will not emit any photoelectrons?

Intensity / W ms-2 Work function of metal / eV

Wavelength of incoming radiation /m

A 1.0 2.0 3.0 X 10-7

B 0.5 3.0 3.0 X 10-7

C 0.5 2.0 6.0 X 10-7

D 1.0 3.0 6.0 X 10-7

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28 A beam of monochromatic light incident on a metal surface causes the emission of photoelectrons. The length of time that the surface is illuminated by this beam is varied, but the intensity of the beam is kept constant.

Which graph best represents the relationship between the total number of photoelectrons emitted and the length of time of illumination? A

B

C

D

29 Given that the de Broglie wavelength of the tennis ball served with a speed of 72 km h-1 is 5.53 x 10-34 m, what is the best estimate of its kinetic energy? A 1.2 J

B 2.4 J

C 12 J

D 24 J

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30 The figure shows some energy levels of an atom. The transition E3 to E1 corresponds to the emission of visible light. A transition corresponding to the emission of infrared radiation could be

END OF PAPER

Class Adm. No. Candidate Name: ________________________________

This document consists of 21 printed pages and 1 blank page. [Turn over

Preliminary Examinations 2010

Pre-university 2

PHYSICS 8866/02

Higher 1

Friday 17 Sep 2010 2 hours

Paper 2 Structured questions

Candidates answer on the Question Paper.


READ THESE INSTRUCTIONS FIRST

Write your name, class and admission number on all the work you hand in.

Write in dark blue or black pen on both sides of the paper.

You may use a soft pencil for any diagrams, graphs or rough working.

Do not use staples, paper clips, highlighters, glue or correction fluid.

Sections A

Answer all questions.

Sections B

Answer any two questions.

At the end of the examination, fasten all your work securely together.

The number of marks is given in brackets [ ] at the end of each question or part question.

For examiner’s use

Section A

1 /6

2 /9

3 /7

4 /6

5 /12

Section B

6 /20

7 /20

8 /20

Total /80

2

Data

speed of light in free space c = 3.00 x 108 m s-1

elementary charge e = 1.60 x 1019 C

the Planck constant h = 6.63 x 1034 J s

unified atomic mass constant u = 1.66 x 1027 kg

rest mass of electron me = 9.11 X 1031 kg

rest mass of proton mp = 1.67 X 1027 kg

acceleration of free fall g = 9.81 m s2

Formulae

uniformly accelerated motion, s = ut + 2

1at2

v2 = u2 + 2as

work done on/by a gas W = p∆V

hydrostatic pressure p = gh

resistors in series, R = R1 + R2 + ...

resistors in parallel 1/R = 1/R1 + 1/R2 + ...

3

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Section A Answer all the questions in this section

For Examinar’s Use

1 (a) Define acceleration. …………………………………………………………………………………………...……… ………………………………………………………………………………………...………[1]

(b) Fig. 1.1 shows the variation of velocity with time for an object accelerating uniformly.

Fig. 1.1 The initial velocity of the object is u. After a time t, the velocity of the object is v. Show that the displacement s of the object is given by

tvus )(2

1

[2]

4

(c) The graph shown in Fig. 1.2 shows the variation with time t of the velocity of a tennis ball from the moment it is hit vertically upwards. Assume that air resistance is negligible.

Fig. 1.2


(i) Use Fig. 1.2 to determine the maximum vertical height attained by the tennis ball.

height = ……………………….. m [2]

(ii) On Fig 1.2, sketch the graph assuming that air resistance is not neglected.

[1]

5

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2 (a) Define the moment of a force. …………………………………………………………………………………..….…………… ……………………………………………………………………………………...…………[1]


(b) To increase the extension of a stiff spring for a given load, a student set up the system shown in Fig. 2.1. The weight of the metal bar was 5.0 N and the tension the student achieved in the spring was 37 N. The spring constant k of the spring is 550 N m-1.

Fig. 2.1

(i) Apply the principle of moments to calculate the mass of the load that the student used.

mass = ………….. kg [2]

(ii) Calculate the magnitude of the force exerted on the metal bar at the pivot.

magnitude of the force = ………………………. N [2]

(iii) On Fig. 2.1, draw and label the forces acting on the metal bar by the spring (Fs) and pivot (Fp). [2]

6

(iv) Calculate the energy stored in the spring.

energy stored = ………………………. J [2]


3 As shown in Fig. 3.1, a dry cell has an e.m.f. E and internal resistance r and is connected to an external circuit. There is a current I in the circuit when the potential difference across the terminals of the cell is V.

Fig. 3.1

(a) State expressions, in terms of E, V, r and I where appropriate, for

(i) the total power supplied by the cell.

……………………………………………………………………….…………...…[1]

(ii) the power dissipated in the cell.

……………………………………………………………………….…………...…[1]

(iii) the power dissipated in the external circuit.

…………………………………………………………………………….……...…[1]

(b) Use your answers to (a) to derive a relationship between V, E, I and r.

………………………………………………………………………………….……………[1]

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(c) The graph in Fig. 3.2 shows the variation of V with I for the dry cell connected to a variable

resistor (rheostat), a voltmeter, and an ammeter.

Fig. 3.2


(i) Use the graph to determine the e.m.f. E of the cell.

e.m.f. E = ……………….. V [1]

(ii) Use the graph to determine the internal resistance r of the cell.

8

internal resistance r = ………………….. [2] 4 (a) State two differences between a progressive and a stationary wave.

………………………………………………………………………………….……………… …………………………………………………………………………………….…………… …………………………………………………………………………………….…………… ……………………………………………………………………………………….………[2]


(b) In order to investigate stationary waves on a stretched wire, a student sets up the apparatus as illustrated in Fig. 4.1. One end of the horizontal wire is attached to a vibrator while the other end is passed over a pulley. The wire is kept in tension by means of a weight. Five light pieces of paper are placed along the wire randomly. When the vibrator is operated at a frequency of 75 Hz, a stationary wave is created along the stretched wire. The light pieces of paper shift along the stretched wire and finally come to a rest at the nodes as shown in Fig. 4.1.

Fig. 4.1

(i) State what is meant by a node? ……………………………………………………………………….………………… ………………………………………………………………………….……………[1]

(ii) Calculate the wavelength of the vibration produced in the wire.

wavelength = ……………………. m [1]

(iii) Use your answer in (b)(ii) to calculate the speed of the wave on the wire.

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speed = ………………………. m s-1 [2] 5 Two prominent commercial airplane manufacturers are Boeing and Airbus. Singapore

International Airlines has at least 18 Airbus and 76 Boeing airplanes in full flight operations. The general specifications and flight information of a typical small size Airbus is given below:


Mass of airplane, including crew and equipment 45 000 kg

Maximum capacity of fuel tanks (including reserve fuel) 25 000 kg

Maximum number of passengers 200

Average mass of a passenger with baggage 100 kg

Average use of fuel per kilometre 5.0 kg

Safety reserve of fuel at the end of journey 3000 kg

Take-off speed 75 m s-1

Length of runway used Changi Airport 1500 m

Many factors are taken into consideration to ensure safety in air travel. Some factors include maximum mass of load carried by the airplane, length of runway, airport design as well as fuel capacity. It is a requirement that every commercial airplane maintain a certain amount of reserve fuel at the end of each journey as a safety measure.

(a) Calculate the total mass of the airplane before take-off assuming that it is carrying the maximum number of passengers and that its fuel tanks are filled to full capacity.

mass = ………………….. kg [1]

(b) (i) The range of an airplane refers to the maximum distance it can fly without utilizing the reserve fuel. Calculate the range for the airplane from the information given.

range = ……………………… km [1]

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(ii) What is the minimum further distance the airplane can fly if the airport it is

scheduled to land is closed due to poor weather conditions?

minimum further distance the airplane can fly = ……………………… km [2]


(c) (i) Calculate the acceleration of the airplane before leaving the ground if it uses the full length of the runway for take-off.

acceleration = ……………………… m s-2 [2]

(ii) Calculate the force required to provide this acceleration.

force = ……………………… N [1]

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(d) There is always a safety buffer distance for emergency braking at the end of the

runway if the pilot decides to abort take-off. Supposing that just before leaving the ground, the pilot discovers that there is something wrong with the airplane and he decides to abort the take-off. Calculate


(i) the braking force needed to stop the airplane given that the deceleration of the airplane is 2.8 m s-2.

braking force = ……………………… N [2]

(ii) the time taken to bring the airplane to a stop.

time taken = ……………………… s [2]

(e) Discuss one disadvantage of using a short runway for take-off. ……………………………………………………………………………….………………… ……………………………………………………………………………….………………… ….……………………………………………………………………………………………… …………………………………………………………………………………….…………… ………………………………………………………………………………………….……[1]

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Section B

Answer TWO questions from this section.


6 (a) State Newton's laws of motion. ……….……………………………………………………………………….………………… ……….……………………………………………………………………….………………… ……….……………………………………………………………………….………………… ………..…………………………………………………………………………………...…[3]

(b) A school is celebrating her 200th Anniversary. To raise funds, the school's most well-loved teachers, Mr. Wong and Mdm Chen are volunteered to perform an unusually dangerous stunt. Mdm Chen, weighing 45.0 kg, jumps out of a hovering helicopter reluctantly without any parachute and falls down vertically. Mr. Wong, weighing 75.0 kg, jumps out soon after. His task is to rescue Mdm Chen and ensure that they will both parachute to safety. Mdm Chen attains a terminal velocity of 30 m s-1 soon after leaving the hovering helicopter. Mr.Wong also attains terminal velocity and continues to fall vertically towards Mdm Chen. When Mr. Wong passes Mdm Chen, she 'catches on' to Mr. Wong's safety harness and together, they continue to fall. It may be assumed that the viscous drag force Fv experienced by a falling person is proportional to v2, where v is the speed of the person. Upthrust due to air may be ignored.

(i) Draw a free body diagram to show the forces acting on a person falling at terminal velocity.

[2]

(ii) Calculate the terminal velocity that Mr. Wong would attain assuming his horizontal velocity is negligible.

terminal velocity = …………………… m s-1 [3]

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(iii) Determine the velocity of Mr. Wong and Mdm Chen immediately after she

'catches on' and the energy loss in the process.

velocity = …………………. m s-1

energy loss = ………………… J [4]


(c) Mr. Wong then opens the parachute. At a height of 1500 m above the ground, they descend with a constant velocity of 10 m s-1 .They approach the ground at an angle of 82o from the horizontal as a result of wind condition. Upon landing, they execute a 'break-fall' procedure so that they bend their knees rather than stand upright. The duration of the impact with the ground lasted 1.6 s.

(i) Determine the work done in overcoming the viscous drag for the last 1500 m of the descend.

work done = …………………. J [2]

(ii) What is the magnitude of the impulsive force experienced by the teachers upon landing assuming that this force is constant over the whole duration of the impact?

force = …………………. N [2]

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(iii) What is the purpose of executing the 'break-fall' procedure?

………………………………………………………………….……………………… ……………………………………………………………………………….………… ……………………………………………………………………………….………… ……………………………………………………………………….………………… ………………………………………………………………………….……………[2]


(iv) If Mr. Wong had jumped without the parachute instead, explain whether it would have been possible for Mdm Chen to save him.

………………………………………….……………………………………………… …………………….…………………………………………………………………… …………………………………….…………………………………………………… …………………………….…………………………………………………………… ………………………………………….……………………………………………[2]

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7 (a) (i) Define magnetic flux density.

………………………………………………………….……………………………… ……………………………………………………………………………….………[1]


(ii) Define the tesla. ……………………………………………………………………………………… ……………………………………………………………………………………[1]

(b) Fig. 7.2 (a) shows the cross-section of a motor and Fig. 7.2 (b) shows its front view. A current of 2.0 A is carried by the square coil of 30 turns. PQ has length 40 cm and OR has length 50 cm. It is placed between a pair of strong magnet producing uniform magnetic field of 0.60 T.

Fig. 7.2 (a)

Fig. 7.2 (b)

(i) On Fig. 7.2 (b), indicate the direction of magnetic forces acting on the section of wires PQ & SR. [1]

(ii) Find the magnitude of the force acting on the section of wires along PQ.

force = …………………………… N [2]

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(iii) Find the magnitude of the torque of the couple on the coil when it is in the

position shown.

torque = …………………………… N m [2]


(c) (i) Distinguish between systematic error and random error. ……………………………………………………………………………………...…. ……………………………………………………………………………………...…. ……………………………………………………………………………………...…. ……………………………………………………………………………………...…. …………………………………….…………………………………………………[1]

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(ii) Suggest one source of systematic error and one source of random error while

using one such setup as a galvanometer as shown in Fig. 7.3.

Fig. 7.3

Systematic: ……..…………………………………...……………………………… ……………………………………………………………………………………...…. ……………………………………………………………………………………...…. Random: ………..…………………………………………………………………… ……………………………………………………………………………………...…. ………………………………………………………………………………..…… [2]


(iii) Suggest and explain two ways to improve the system if the needle was found to deflect too little for all currents I.

………………………………………………………………………………….....…… ………………………………………………………………………………….....…… ………………………………………………………………………………….....…… ………………………………………………………………………………….....…… ………………………………………………………………………………….....…… ………………………………………………………………………………….....…… ………………………………………………………………………………….....…… …………………………………...………………………………………….………[4]

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(d) A student uses a current balance setup shown in Fig. 7.4 to find the magnetic flux

density of a U-shaped magnet. He uses a steel rod to balance the setup.

Steel Rod

Steel Rod

N S

A

Fig. 7.4

The following results were obtained:

Diameter of steel rod (50 1) 104m

Length of steel rod (15.0 0.1) cm

Density of steel rod (7800 100) kg m3

Distance DQ (2.0 0.1) cm

Distance CQ (10.0 0.1) cm

Distance l (5.0 0.1) cm

Ammeter reading (2.10 0.05) A


(i) Calculate the weight of the steel rod.

weight = …………………………… N [2]

(ii) Hence, calculate, with its uncertainty, the value of the magnetic flux density of the U-shaped magnet.

19

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magnetic flux density = …………...…± ……..………… T [4] 8 (a) Fig. 8.1 shows a setup used to demonstrate the photoelectric effect.

Fig. 8.1


(i) Describe what will happen to the galvanometer reading when the radiation frequency is gradually increased from the infrared region to the ultraviolet region.

…………………………………………………………………………….…………… …………………………………………………………………………….…………… …………………………………...………………………………….………………[2]

(ii) State and explain one application of the photoelectric effect. …………………………………………………………………………….…………… …………………………………………………………………………….…………… …………………………………...………………………………………….………[2]

(iii) State and explain one application of the photoelectric effect. (1) .……………………………………………………………………………………. .……………………………………………………………………………………. (2) .……………………………………………………………………………………. .……………………………………………………………………………………. (3) .……………………………………………………………………………………. ……………………………………………………………………………….…[3]

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(b) This question involves the Young’s Double Slit experiment.


(i) Show how the principle of superposition of waves can be used to explain the formation of two-source interference fringes.

…………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………...………………………...…………………………[2]

(ii) Two-source interference fringes using light can only be obtained if light from the two

sources is coherent. Explain

(1) the meaning of the term coherent. .……………………………………………………………………………………… …………………………………………………………………………….………[1]

(2) why, in practice, interference fringes can be seen only if light from a single source

is passed through a single slit first before the double slit.

.……………………………………………………………………………………… …………………………………………………………………………….………[1]

(iii) Two narrow and parallel slits 0.2 mm apart are illuminated by a monochromatic light source. It is found that the interference pattern on a screen 0.95 m away has the first order bright fringe located at 3 mm from the central bright fringe.

(1) What is the wavelength of the light?

Wavelength = ………………………. m [2]

(2) State the distance of the second-order dark fringe from the central bright fringe?

…………………………………………………………………...……….…...…[1]

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(c) This question involves the Electron Diffraction Experiment.


(i) Sketch the layout of the electron diffraction experiment so that the diffraction pattern may be experimentally observed.

[2]

(ii) Given that the mass of an electron is 9.1 x 10-31 kg, calculate the de Broglie wavelength of an electron whose kinetic energy is 3.00 MeV. (1 MeV = 1.6 x 10-13 J)

[3]

(iii) A practical device that relies on the wave characteristics of electrons is the electron microscope. A 3.00 MeV transmission electron microscope is used for viewing flat, thin samples. In many aspects, it is similar to an optical microscope, but the electron microscope has a much greater resolving power than optical microscopes. Suggest a reason for this greater resolving power.

…………………………………………………………………………………..……… ……………………………………………..…………………………………………… …………………………………...………………….……………….…….…………[1]

*** END OF PAPER ***

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BLANK PAGE

Mark Scheme for PU2 H1 Promo 2 Exam 2010

1 2 3 4 5 6 7 8 9 10

D B C D C D C A B A

11 12 13 14 15 16 17 18 19 20

C B D D A C C A D A

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D B D B D B D B C D

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Direction of current and magnetic field are parallel to each other, hence there is no force acting.

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Current-carrying conductors with current in opposite directions will create zero magnetic field at the mid-point between the two conductors. For III, there will be a neutral point at O. The currents need to be of the same magnitude as the distance from the conductors to point O is the same.

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Millennia Institute Physics 8866

PRELIMINARY 2 EXAMINATION 2010 PU 2 H1

Mark Scheme PAPER 1:

1 2 3 4 5 6 7 8 9 10

D B C D C D C A B D

11 12 13 14 15 16 17 18 19 20

C B D D A D C A D A

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D B D C D C D B C D

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PAPER 2 - Section A 1 (a) Rate of change of velocity.

B1

1 (b) s = area under the velocity-time graph

B1

s = area of trapezium = h

ba

2

)( or t

uvuts )

2(

tvu

s2

)(

B1

1 (c i) height = area under graph = ½ × 25 × 2.5 =12.5 = 13 m

M1 A1

1 (c ii)

Shape of graph & time taken is shorter

A1

2 (a) The moment of a force about a point is the product of the force and the perpendicular of its line of action from the point.

B1

2 (b i) Taking moments about the pivot, Total CW moments = Total CCW moments (5.0)(0.45) + M(9.81)(0,85) = 37(0.15) M = 0.396 kg

M1 A1

2 (b ii) In the vertical direction, Fy = 0 F + 37 - 5.0 - (0.396)(9.81) = 0 F = -28.1N Magnitude = -28.1 N

M1 C1

2 (b iii)

Fp

Fs

Fp

Fs

A2

2 (b iv) Energy stored = ½ Fe = ½ F(F/k) = ½ (37)(37/550) = 1.24 J

M1 A1

3 (a i) EI

A1

3 (a ii) I2r

A1

3 (a iii) VI

A1

3 (b) Any one of the following: EI = I

2r + VI;

V = E – Ir E = V + Ir;

A1

3 (c i) E = V when I = 0; so E = 1.5 V;

B1

3 (c ii) resistance r = gradient

Gradient = (1.3 – 0.8 ) / (0.58 – 0.16 ) = 1.20

M1 C1

3 (a) Difference: Standing wave has nodes / Energy of a standing wave is localized / All points within adjacent nodes oscillate in phase.

B2

4 (b i) A point with zero displacement (at all times)

B1

4 (b ii) 2 = 0.64

= 0.32 m

A1

4 (b iii) v = f = 75 x 0.32 = 24 m s

-1

M1 C1

5 (a) M = 45000 + 25000 + 200(100) = 90 000 kg A1

5 (b i) Range = (25 000 – 3000) / 5.0 = 4400 km

A1

5 (b ii) Fuel available = 3000 kg

Max Distance it can fly = 3000/5.0 = 600 km

C1 C1

5 (c i) asuv 222 )1500)((2075 22 a

a = 1.88 m s-2

M1 C1

5 (c ii) F = ma = (90 000)(1.88) = 170 000 N

C1

5 (d i) Braking force = 90 000 x 2.8

= 250 000 N

M1 C1

5 d ii v = u + at 0 = 75 + (-2.8)t

t = 27 s

M1 C1

5 (e) Any ONE:

1. A larger acceleration is required to bring the aircraft to take-off speed if it is carrying maximum no. of passengers (Greater force acts on passengers or Higher fuel consumption).

2. In order to maintain the normal acceleration, the total mass of the plane must be reduced

fewer passengers (hence, profitability reduces), OR

carry less fuel which leads to a shorter range (however, the plane cannot change the requirements for safety reserve fuel)

B1

Section B 6 a Newton's First Law:

A body will remain in its state of rest or motion in constant velocity provided no net force acts on it. Newton's Second Law: Rate of change of momentum of a body is directly proportional to the resultant force acting on the body and acts in the direction of the resultant force. Newton's Third Law: If a body A exerts a force on body B, body B will exert a force which is equal in magnitude but opposite in direction on body A.

B3

6 bi

A2

6 bii Fv = kv2

At terminal velocity, Fv = mg kv

2 = mg

kvw2 = mwg ---(1)

kvc2 = mcg ---(2)

(1) / (2)

c

w

2

c

2

w

m

m

v

v

45.0

75.0

30.0

v2

2

w vw = 38.7 m s-1

M1 C2

6 b iii By the principle of conservation of momentum, mwuw +mcuc = (mw +mc)v (75.0)(38.7) + (45.0)(30.0) = (75.0 + 45.0)v v = 35.4 m s

-1

Energy loss = ½ mwuw

2 + ½ mcuc

2 – ½ (mw +mc) v

2

= ½ (75.0)(38.72) + ½ (45.0)(30.0

2) – ½ (75.0 + 45.0)(35.4

2)

= 1224 J = 1.22 kJ

M1 C1 M1 C1

6 c i During the last 1500 m, the kinetic energy is a constant. Therefore, the loss in gravitational potential energy must be accounted for as the work done to overcome air resistance (work done by atmospheric drag). Energy loss

=mgh =(75.0+45.0)(9.81)(1500) = 1765800 J = 1.77 MJ

M1 C1

6 c ii Force = Rate of change of momentum

= t

vvm

if

)( =

6.1

)100()0.450.75(

= 750 N

M1 C1

6 c iii The 'break-fall' procedure increases the time of impact. This reduces the impulsive force for a given momentum change. Hence, the possibility of injury may be minimized.

B1 B1

6 c iv Since Fv experienced by a free-falling person is proportional to v2, the man who is

heavier will attain a greater terminal velocity than the woman. Thus, if he were to jump first, it will be impossible for the woman to catch up with him.

B1 B1

7 a i The magnetic flux density is the force experienced by a conductor of unit length, places perpendicular to the magnetic field and carrying unit current.

B1

7 a ii The tesla is equivalent to a force of 1 N experienced by a conductor 1 m long, placed perpendicular to the magnetic field and carrying a current of 1 A.

B1

7 b i

A1

7 b ii) F = NBILsin = 30 x 0.6 x 2 x 0.4

F = 14.4 N,

M1 C1

7 b iii)

= F(dsin) = 14.4(0.5sin20o)

= 2.46 Nm

M1 C1

7 c i Systematic errors are either all positive or negative whereas random error can be either.

B1

7c ii) Systematic: Spring is readjusted after calibration, Magnet lose strength, zero error Random: parallax error incurred in reading

B2

7c iii) Any TWO: 1. add a iron core within the rectangular coil between the pivots. The iron core will intensify the magnetic field that the rectangular coil experiences and so the magnetic force generated will be higher for the same current. 2. change the spring to one that is less stiff The reduced stiffness will mean greater deflection before the same countering moment is generated. 3. Change the magnet to a stronger type. Intensified magnetic field will generate greater force for the same current thus more deflection.

B4

7 d i) Weight = Vg = (7800) ( (25104

)20.15)9.81

= 0.225 N

M1 C1

7 d ii) W 0.02 = 0.1 (B2.100.05)

B = 0.429 T

( r2 L) (g) ( DQ )= CQ(BIl)

B = ( r2 L) (g) ( DQ )

(I l) (CQ)

10

1.0

5

1.0

1.2

05.0

2

1.0

15

1.0

50

12

7800

100

429.0

2

B

CQ

CQ

l

l

I

I

DQ

DQ

L

L

r

r

B

B

B = 0.07 T

B = (0.43 0.07) T

M1 A1 M1 C1

8 a i) When the frequency is increased, There will be a point where the galvanometer reading increases suddenly After that, the galvanometer deflection remains constant throughout even if f increases.

B1 B1

(ii) By changing the metal used, we can control the type of frequency that the photoelectric meter. For example, by using a metal that has a work function of Infrared radiation, we can create a Night Vision Goggles Any infra-red given by human bodies or any hot object will trigger photoelectric radiation. When observed, the humans or object will appear brighter on the Night Vision Goggles

B2

(iii) any 3 of the following 4 statements:

For a given metal, electrons are only emitted above a certain threshold frequency of the EM radiation, irrespective of its intensity.

The maximum KE of the emitted electrons depends only on the frequency of the EM radiation.

The number of photoelectrons emitted per second depends only on Intensity of the EM radiation, for a single frequency.

* Low intensity EM radiation (above the threshold frequency) results in immediate emission of electrons.

B3

(b i) When 2 waves are in phase, constructive interference results in a maximum or bright fringes

When 2 waves are out of phase, destructive interference results in a minimum or dark fringe

B2

(b) (ii) 1 Constant Phase difference and same frequency

B1

(b) (ii) 2. So that they can be made coherent

B1

(b) (iii) 1. Use of equation /a = x/d to give = 630 nm M1 A1

(b) (iii) 2. State 4.5 mm

A1

(c) (i) Diagram to include Electron-gun, Crystal target, and screen

Correct layout of the apparatus listed above

B1 B1

(c) (ii) Since KE = ½mv2

Calculate the momentum p = mv

Since = h / p

= 7.09 x 10-13

m

M1 A1 C1

(c) (iii) The deBroglie wavelength of the electron is much more shorter than that of light.

B1

MERIDIAN JUNIOR COLLEGE

Preliminary Examination Higher 1

______________________________________________________________________________

H1 Physics 8866/1

Paper 1 24 September 2010

1 Hour ______________________________________________________________________________ INSTRUCTION TO CANDIDATES

Class Reg Number

Candidate Name _____________________________

Do not open this booklet until you are told to do so. Multiple Choice Questions

There are 30 Multiple Choice Questions in this section. Answer all questions. For each question, there are four possible answers labelled A, B, C and D.

Choose the one you consider correct and record your choice in soft pencil on the separate Optical Mark Sheet (OMS).

Read very carefully the instructions on the Optical Mark Sheet (OMS).

Write your name and class in the spaces provided on the Optical Mark Sheet

Shade your Index Number column using the following format: 1) first 2 digits is your index number in class (eg 5th student is shaded as “05”); 2) ignore the last row of alphabets;

______________________________________________________________________________

This document consists of 15 printed pages.

Preliminary Examination Meridian Junior College 24th September 2010 JC2 H1 Physics 2010 _________________________________________________________________________________

2

DATA AND FORMULAE Data


elementary charge e = 1.60 x 10-19 C

the Planck constant h = 6.63 x 10-34 J s

unified atomic mass constant u = 1.66 x 10-27 kg

rest mass of electron me = 9.11 x 10-31 kg

rest mass of proton mp = 1.67 x 10-27 kg

acceleration of free fall g = 9.81 m s-2

Formulae

uniformly accelerated motion s = ut + 1

2at2

v2 = u2 + 2as

work done on/by a gas W = pΔV

hydrostatic pressure p = ρgh

resistors in series R = R1 + R2 + …

resistors in parallel 1/R = 1/R1 + 1/R2 + …

Preliminary Examination Meridian Junior College 24th September 2010 JC2 H1 Physics 2010 _________________________________________________________________________________ 1 The length of a rectangle is given as L ± ℓ and its width as W ± w.

What is the uncertainty in its area?

A l+ w

B L Wl+ w C L W lw +

D L W+

l w

2 For which quantity is the magnitude a reasonable estimate? A frequency of a radio wave 500 μHz

B mass of an atom 500 pg

C the acceleration due to free fall 981 mm s-2

D wavelength of green light 500 nm 3 A student takes multiple readings of potential difference across a resistor in a circuit.

The readings are 2.016 V, 2.018 V, 2.017 V and 2.016V. He took the average of these but does not take into account the zero error on the voltmeter. The average measurement of the potential difference is

A precise and accurate

B precise but not accurate

C accurate but not precise

D not accurate and not precise 4 A 10 kg mass box is pushed up an inclined plane of 40° above horizontal with a net

acceleration of 12.5 m s-2 with an initial speed of 1.60 m s-1. Determine the change in vertical height of the box during the first interval of 1.25 s.

A 11.8 m B 9.01 m C 7.56 m D 6.31 m 5 A housewife released a bag of rubbish weighing 54 N from rest into a refuse chute from

her unit in a HDB flat. The rubbish passes through two speed detectors at different locations and the readings shown in the detectors are 14.7 m s-1 and 49.1 m s-1 respectively. Neglecting the effect of air resistance, the distance between the two speed detectors is

A 20.3 m B 31.9 m C 71.7 m D 112 m

3

Preliminary Examination Meridian Junior College 24th September 2010 JC2 H1 Physics 2010 _________________________________________________________________________________ 6 A ball is thrown upwards at an angle to the horizontal with an initial speed. Assuming

that air resistance is not negligible, which of the following statement is incorrect?

A The time taken for the flight up to the highest point is longer than the time taken for the flight down.

B The maximum height reached by the ball is smaller than that with negligible air resistance.

C Horizontal range of the ball is shorter than that with negligible air resistance. D The path of the ball is asymmetrical about the highest point.

7 A car of weight Wc is driven across a uniform bridge of length l and weight Wb. The

bridge is supported by two ropes having tensions T1 and T2 when the car is a distance x from the rope on the left as shown in the figure below.

Which of the following expressions for the tensions T1 and T2 is correct?

Tension T1 Tension T2 A

lxWW cb +

2 )1(

2 lxW

Wc

b −+

B x

lWW cb +2

)1(2 x

lWW

cb −+

C 22

cb WW+

22cb WW

+

D )1(

2 lxW

Wc

b −+ l

xWW cb +2

l

T1

Wb Wc

x

T2

4

Preliminary Examination Meridian Junior College 24th September 2010 JC2 H1 Physics 2010 _________________________________________________________________________________ 8 Three identical stationary discs P, Q, and R are placed in a line on a horizontal, flat,

frictionless surface. Disc P is projected straight towards disc Q. If all consequent collisions are perfectly elastic, predict the final motion of the three discs.

P Q R A moving left moving left moving right B moving left stationary moving right C stationary stationary moving right D moving right moving right moving right

R QP

9 The graph shows how the extension of a spring varies with the force used to stretch it.

What is the elastic potential energy stored in the spring when the extension is 4.0 cm?

A 60 J B 120 J C 600 J D 1200 J

extension / cm

force / kN

10 A pendulum bob hangs from the ceiling in a carriage in a train and is just above a

certain mark on the floor when the train is at rest. When the train is moving with constant velocity forward, the bob

A oscillates about the mark because of the unbalanced force due to the motion of the train.

B remains over the mark because the motion of the train produces no additional force on the bob.

C is behind the mark so that the pendulum thread is along the resultant of the forces due to the motion of the train and gravity.

D is in front of the mark in a position in which the horizontal force exerted by the train on the bob is larger than the horizontal component of the tension in the thread.

5

Preliminary Examination Meridian Junior College 24th September 2010 JC2 H1 Physics 2010 _________________________________________________________________________________ 11 An object falls vertically at its terminal velocity through air and then strikes soft ground

in which it becomes embedded. Its deceleration during impact is constant. If P represents the point of impact, which one of the following graphs best represents the variation of the resultant force R on the stone with distance s?

A

B

C

D

R R

0 P 0 P s s

R R

0 P0 P s s

12 A sphere of mass 3.00 kg rests on a frictionless slope inclined at 30o above horizontal.

The spring constant is 500 N m-1. Determine the compression of the spring.

A 51.0 mm B 34.3 mm C 29.4 mm D 7.67 mm

Wall 30˚

6

Preliminary Examination Meridian Junior College 24th September 2010 JC2 H1 Physics 2010 _________________________________________________________________________________ 13 Tarzan, whose mass is 80.0 kg, needs to swing across a river filled with crocodiles in

order to save Jane of mass 45.0 kg, at the middle of the river as shown in the diagram below. He has to swing from a branch, which is assumed to be fixed in position, on a vine of length 30.0 m, and initially making angle of 50.0o with the vertical. Tarzan swings towards Jane and grabs hold of her. Assuming that this is a completely inelastic collision, determine their common speed just after the collision.

A 19.5 m s-1 B 15.6 m s-1 C 12.4 m s-1 D 9.28 m s-1

30.0 m50o

14 A small metal sphere of mass m is moving through a viscous liquid of height h.

When it reaches a constant downward velocity v, which of the following describes the changes with time of the kinetic energy and gravitational potential energy of the sphere?

Kinetic Energy Gravitational Potential Energy A constant and equal to ½mv2 decreases at a rate mgv B constant and equal to ½mv2 decreases at a rate mgh C increases at a rate ½mv2 decreases at a rate (½mv2 – mgv) D increases at a rate mgv decreases at a rate (mgv – ½mv2) 15 A single traveling light wave in vacuum is able to

A carry momentum B create interference patterns C create a standing wave D propagate at any velocity

7

Preliminary Examination Meridian Junior College 24th September 2010 JC2 H1 Physics 2010 _________________________________________________________________________________ 16 The diagram below illustrates an experimental arrangement that produces interference

fringes with a double slit. When slit S2 was covered with a very thin plate of glass as shown,

A the fringe pattern moved towards Y. B the fringe pattern moved towards X. C the separation of the fringes increased. D the separation of the fringes decreased.

X

thin glass plate

S1

S2 *

monochromatic source

O

Y

17 In a two-slit interference experiment, one slit transmits twice the amplitude of the other

slit. If the maximum intensity of the interference pattern is Io, the minimum intensity in the pattern would be

A zero B Io/2 C Io/4 D Io/9 18 A microwave source S is placed in front of a detector D, and a metal reflecting screen R

is placed beyond D such that its plane is perpendicular to the line joining S to D. As the detector is moved slowly away from the source, it registers a series of maxima and minima.

It is observed that the detector moved through a distance of 5.6 cm between the first and fifth minimum. What is the frequency of the microwaves in GHz?

A 5.4 B 10.7 C 13.4 D 27.5

D R S

8

Preliminary Examination Meridian Junior College 24th September 2010 JC2 H1 Physics 2010 _________________________________________________________________________________ 19 When double–slit interference pattern is investigated using light of wavelength 600 nm,

the spacing between the bright fringes is 1.44 mm. If the screen is 1.2 m away from the slits, how far apart are the slits?

A 0.050 mm B 0.25 mm C 0.50 mm D 2.5 mm 20 A row of 30 decorative lights, connected in series, is connected to a mains transformer.

When the supply is switched on, the lights do not work. The owner uses a voltmeter to test the circuit. When the voltmeter is connected across the fifth bulb in the row, a reading of zero is obtained. Which of the following scenarios described is not possible?

A Only the filament of the fifth bulb has broken. B The fuse in the mains transformer has blown. C The filament of at least one of the other bulbs has broken. D There is a break in the wire from the supply to the transformer. 21 In the circuit diagram below, D is an ideal diode. The voltage supply has negligible

internal resistance and the voltmeter reads 12 V.

If the connections to the terminals of the voltage supply are reversed, the voltmeter reading would be

A 6.0 V B 8.0 V C 9.0 V D 18 V

2.0 Ω

V

2.0 Ω

D

2.0 ΩVoltage supply

9

Preliminary Examination Meridian Junior College 24th September 2010 JC2 H1 Physics 2010 _________________________________________________________________________________ 22 The circuit shown in Fig. 1 may be used to determine the internal resistance of a

battery. An oscilloscope is connected across the battery as shown. Fig. 2 represents the screen of the oscilloscope.

Fig. 1 Fig. 2 The time base of the oscilloscope is switched off throughout the experiment. Initially the switches S1 and S2 are both open. Under these conditions, the spot on the oscilloscope screen is at A. Switch S1 is now closed, with S2 remaining open. The spot moves to B. Switch S1 is kept closed and S2 is also closed. The spot moves to C. The vertical sensitivity of the oscilloscope is 0.50 V per division. Calculate the internal resistance of the battery.

A 0.24 Ω B 2.3 Ω C 14.0 Ω D 16.4 Ω

23 The diagram shows a network of three resistors. Two of these marked R, are identical.

The other one has a resistance of 5.0 Ω. The resistance between Y and Z is found to be 2.5 Ω. Determine the resistance between X and Y.

A 0.53 Ω B 1.9 Ω C 2.5 Ω D 4.8 Ω

R

R

5.0 Ω

X

Y

Z

10


24 The diagram shows three resistors of resistance 4 Ω, 10 Ω and 6 Ω connected in series. A potential difference of 10 V is maintained across them, with point X being earthed. Which graph represents the change in potential along the resistor network?

A

B

C

D

11

Preliminary Examination Meridian Junior College 24th September 2010 JC2 H1 Physics 2010 _________________________________________________________________________________ 25 A beam of electrons is directed into a region of uniform magnetic field as shown in the

figure below.

In which direction should an electric field be applied so that the electrons pass through the region undeflected?

A Downwards B Upwards C Into the page D Out of the page

26 In the diagram below, P is a horizontal circular coil of wire carrying a steady current .

A conducting rod, which is free to move, is supported by 2 fixed horizontal parallel rails TQ and SR which are perpendicular to the length of the conducting rod and carry a constant current as shown in the diagram below.

1I

2I

The conducting rod will

A move towards TS with a constant speed. B move towards TS with increasing speed. C move towards QR with increasing speed. D be lifted off the horizontal parallel rails momentarily.

P

I2 I2

T

Q

S

I2

R

I1

12

Preliminary Examination Meridian Junior College 24th September 2010 JC2 H1 Physics 2010 _________________________________________________________________________________ 27 The wire WX is free to move vertically while the wire YZ is fixed in position. Suppose

that both wires carry equal currents of 100 A in opposite directions and that the mass per unit length for each wire is 20 g m-1. Calculate the final height which the wire WX is above wire YZ. (You may assume that the magnetic field, B at a distance r from a wire

carrying current I to be o

2B

rμπ

=I

and you may take μo = 4π x 10-7 H m-1)

A zero, wires WX and YZ are attracted to each other.

B 0.102 cm

C 1.02 cm

D 10.2 cm

I = 100 A

I = 100 A

W X

Y Z

28 A sodium vapor lamp is placed at the centre of a large hollow metal sphere that absorbs

all the light reaching it. The lamp operates a voltage of 200 V when the current flowing through it is 1.5 A. Assume that the emission is entirely at a wavelength of 590 nm. At what rate are the photons absorbed by the sphere?

A 4.0 × 1020 s-1 B 5.9 × 1020 s-1 C 7.0 × 1020 s-1 D 8.9 × 1020 s-1

13

Preliminary Examination Meridian Junior College 24th September 2010 JC2 H1 Physics 2010 _________________________________________________________________________________ 29 In a photoelectric effect experiment, the relationship between the photoelectric current

and potential difference applied between the emitter and the collector using 2 different intensities of electromagnetic radiation I1 and I2, where I1 > I2. The photoelectric current increases with potential difference until a maximum value because

A The incident electromagnetic radiation has caused all the free electrons from the

metal to be released. B The collector has been made sufficiently positive to attract all the emitted

photoelectrons C The photoelectrons are emitted with a maximum kinetic energy that depends on the

incident wavelength and work function of the metal

D The circuit resistance rises proportionally with V such that the ratio VR

is a constant

due to the effects of heating.

^ I / A

I2.

I1

/ V V>

14


15

30 The graph below shows the variation of stopping potential, Vs, against wavelength,λ, for a photoelectric effect experiment. Determine the work function of the metal used in the experiment.

A 1.9 eV B 2.4 eV C 3.8 eV D 6.2 eV

λ/nm

Vs/V

END OF PAPER 1

MERIDIAN JUNIOR COLLEGE

Preliminary Examination Higher 1

______________________________________________________________________________

H1 Physics 8866/2

Paper 2 15 September 2010

2 Hours ______________________________________________________________________________ INSTRUCTION TO CANDIDATES Class Reg Number

Candidate Name _____________________________

Do not open this booklet until you are told to do so.

Examiner’s Use

Section A

Q1 / 4

Q2 / 8

Q3 / 6

Q4 / 10

Q5 / 12

Section B

Q6 / 20

Q7 / 20

Q8 / 20

Deductions

Total / 80

Section A

Answer all questions. Section B Answer any two questions. Circle the two questions you attempt in the box on the right. Note: only the first two questions will be marked if all three are attempted. You are advised to spend about one hour on each section. Write your answers on this question booklet in the blanks provided.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the end of each question or part question. Marks will be deducted if units are not stated where necessary or if answers are not quoted to the appropriate number of significant figures.


2 [Turn Over

All working for numerical answers must be shown. You are reminded of the need for good English and clear presentation of your answers.

______________________________________________________________________________



3 [Turn Over



elementary charge e = 1.60 x 10-19 C

the Planck constant h = 6.63 x 10-34 J s

unified atomic mass constant u = 1.66 x 10-27 kg

rest mass of electron me = 9.11 x 10-31 kg

rest mass of proton mp = 1.67 x 10-27 kg

acceleration of free fall g = 9.81 m s-2

Formulae

uniformly accelerated motion s = ut +

12

at2

v2 = u2 + 2as



resistors in series R = R1 + R2 + …

resistors in parallel 1/R = 1/R1 + 1/R2 + …


4 [Turn Over

Section A Answer all the questions in the spaces provided.

1

Distinguish in detail, between a progressive wave and a stationary wave by completing Table 1.1.

[4]

Progressive waves Stationary waves

Amplitude of vibration

The amplitude of vibration is the same at all points

Wavelength

Equals to twice the distance between a pair of adjacent nodes or antinodes

Phase Every particle within one wavelength varies in phase from each other

Energy

No net transfer of energy

Table 1.1


5 [Turn Over

2 (a) A charged body falls vertically in a vacuum near the Earth’s surface. The variation with time t of its vertical speed v is shown in Fig 2.1 below.

Fig 2.1 An electric field induces a horizontal force on the body that causes the body to accelerate horizontally at 2.25 m s-2. Calculate the displacement of the body after falling 0.50 s.

displacement = ................................m

angle = ........................... [4]

v / m s-1

t / s 0


6 [Turn Over

(b) The variation with time of the velocity of another object moving in a straight line is shown in Fig 2.2.

Fig 2.2

(i) Sketch on Fig 2.2, a graph of the variation with time of the

acceleration of the same object within the same time frame.

[2]

(ii) Explain your sketch in (b)(i) between time t1 and t2.

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………….……………………………………………… [2]

0 t2 t1

v / m s-1

t / s


7 [Turn Over

3

(a) A thin layer of copper is deposited uniformly on the surface of an iron wire of radius 0.60 mm and length 3.0 m shown in Fig 3.1.

Fig 3.1 Determine the effective resistance between the ends of the copper-plated wire, given that the thickness of the copper is 1.78 x 10-5 m. [Resistivity of iron = 8.90 x 10-8 Ω m; resistivity of copper = 1.60 x 10-8 Ω m]

effective resistance = …………………. Ω [3]

iron wire

thin layer of copper

I


8 [Turn Over

(b) Fig 3.2 shows a system in which an unmodulated audio frequency signal is transmitted from the transmitter to the receiver through a cable. The cable consists of two strands of insulated copper wire.

Fig 3.2 The power output of the transmitter is 12.5 mW and the corresponding current in each wire is 2.5 mA. Power is lost to the surroundings due to the rise in temperature produced by this current. For transmitted signal to be detected, the power input to the receiver must be at least 1.5 mW. The resistance per unit length of the copper wire used in the cable is 0.27 Ω m-1.

Calculate the maximum distance between the transmitter and receiver at which

the transmission can be detected successfully. maximum distance = ……………………m [3]

Iinsulation

transmitter 12.5 mW

receiver

copper wire

I


9 [Turn Over

4 (a) Define magnetic flux density and state its S.I unit.

……………………………………………………………………………………………...

……………………………………………………………………………………………...

……………………………………………………………………………………………...

………………………………………………………………………………………. [2]

(b) Fig 4.1 shows the position of a wire in the radial magnetic field of an electric

motor while the magnetic flux density is 0.20 T.

Fig 4.1

The wire, which is of length 0.060 m, carries a current of 4.5 A out of the plane of the paper.

(i) Sketch the combined magnetic field due to the current in the wire and the motor’s magnet in the diagram below.

[3]


10 [Turn Over

(ii) Calculate the force acting on the wire and sketch the direction of this force in Fig 4.1.

Force = …………………….. N [3] (iii) Describe the energy changes experienced by the wire.

......................................................................................................................

............................................................................................................. [1]

(iv) If the wire is now replaced with a charged particle, explain whether there

will be a magnetic force acting on the charged particle.

......................................................................................................................

............................................................................................................. [1]

5

Table 5.1 shows how the resistance of a thermistor varies with temperature. θ / oC 0 30 60 90 120 T / K 273 303 333 363 393 R / Ω 16300 5000 1320 457 159 lg(R / Ω)

Table 5.1

(a) Deduce the relation between temperature θ / oC and T / K [1]

(b) Complete Table 5.1, leave your answers in 3 significant figures. [1] (c) Plot a graph of lg(R / Ω) against T / K. [3]


11 [Turn Over

lg(R / Ω)

T / K


12 [Turn Over

(d) Suggest a reason for plotting resistance of a thermistor on a logarithmic scale.

……………………………………………………………………………………………...

……………………………………………………………………………...…….… [1]

(e) With reference to the graph you have plotted in (c), explain why this thermistor is

called a negative temperature coefficient (NTC) thermistor.

……………………………………………………………………………………………...

……………………………………………………………………………...…….… [1]

(f) One of these thermistors is connected in a circuit, in series with a 15 Ω fixed

resistor and a variable resistor as shown in Fig 5.2. Point X is connected to a device called a transistor. When the potential at X rises above 0.70 V, the transistor gets activated and operates a relay which switches on a lamp.

Fig 5.2 With the aid of the graph you have plotted in (c), determine the resistance of the variable resistor if the lamp lights up when the temperature reaches 323 K.

Resistance of variable resistor = ……………….. Ω [3]

thermistor

15 Ω

+ 12 V

0 V

to transistor X


13 [Turn Over

(g) State and explain the purpose of the 15 Ω fixed resistor in the circuit.

……………………………………………………………………………………………...

……………………………………………………………………………………………...

……………………………………………………………………………………………...

……………………………………………………………………………...….…… [2]


14 [Turn Over

Section B Answer any two questions.

6 (a) (i) State Newton’s 1st law of motion and show it leads to the concept of force.

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………………...

………………………………………………………………………………. [2]

(ii) Express the unit of force in terms of S.I. base units.

S.I. base units of force is ….....…………… [1] (b) Michael drove his car of mass 1200 kg to a maximum speed of 150 km h-1.

During a driving test, it was found that the average retarding force due to air resistance and friction from the ground is 1200 N when the car was accelerating uniformly.

(i) Calculate the forward driving force when the car accelerated uniformly from rest to its maximum speed in 11.0 s under driving test conditions.

forward driving force= ……………… N [3]


15 [Turn Over

(ii) Hence, find the maximum power delivered by the engine.

maximum power = ……………… W [2] (c) Michael wishes to find out how his car will fare during a car crash.

He visited a laboratory where several cars like his own were used in controlled car crash testing. The magnitude F of the force required to crush the barrels is shown below as a function of the distance x the automobile had moved into the cushion. In a particular crash test, the car was travelling at 100 km h-1 before it struck a crash cushion in which the car was brought to rest by successively crushing steel barrels.

170

130

90

0.0 1.5 4.0

F / kN

x/ m

y

x


16 [Turn Over

(i) Neglecting friction, using the Work Energy Theorem, determine the distance the car would move into the cushion of steel barrels before coming to rest.

distance = ……………… m [4] (ii) State and explain in terms of energy considerations, whether the actual

distance travelled by his car would be longer or shorter than the value in (c)(i).

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………………

………………………………………………………………………...

[2]


17 [Turn Over

(d) In another car crash laboratory test, a crash test dummy of mass 75 kg is belted into the driver’s seat of the car and the car is travelling at 39.6 km h-1 before it struck head-on to a solid wall and come to rest in 0.10 s.

(i) Determine the impulse experienced by the dummy in the crash. impulse = …………….…… kg m s-1 [2] (ii) In the crash, the dummy is brought to rest by the seat belt from a speed of

39.6 km h-1, in a time of 0.14 s. Show that the average force on the dummy is about eight times its weight.

[2] (e) The seat belt does not stop the head of the dummy from moving forward.

Without an airbag, the head could strike the steering wheel. An airbag is installed such that it will begin to deflate by the time the head strikes it.

Suggest a reason why it is safer for the airbags to be deflating when the head strikes them.

………………………………………………………………………………..…………….

…………………………………………………………………………………………..….

………………………………………………………………………………………..…….

………………………………………………………………………………….……

[2]


18 [Turn Over

7 (a)

Fig 7.1

Fig 7.1 shows what can be observed when plane waves pass through slits in a barrier. The waves undergo diffraction at the two slits and interfere to form the patterns observed.

(i) Explain what is meant by diffraction.

……………………………………………………………………………………...

………………………………………………………………………………. [1]

(ii) The pattern produced by the waves is in accordance to the Principle of

Superposition. State the Principle of Superposition.

……………………………………………………………………………………...

……………………………………………………………………………..……….

………………………………………………………………………………. [2]

(iii) On Fig 7.1, draw one line joining the points to show the line of

destructive interference (nodal lines). [1]

(b) When a player blows into a flute as shown in Fig 7.2a, the air within the flute

Plane Waves

Barrier


19 [Turn Over

vibrates. The flute produces sound in a column of air like a tube with both ends open.

Fig 7.2a: Flute

Fig 7.2b shows the fundamental frequency of the standing wave formed in the tube of a given length. Fig 7.2b : Fundamental frequency at given length

(i) The black dots below the tube in Fig 7.2b correspond to equilibrium positions of the air molecules. Sketch on Fig 7.2b the displacement vector of these air molecules when a fundamental frequency is produced in the tube.

[2]

(ii) On Fig 7.2b, label the regions of maximum pressure, H and regions

of minimum pressure, L. [1]

(iii) A standing wave corresponding to the fundamental frequency of 262 Hz is

obtained when the length of the tube is 0.655 m. For the same length of air column, determine the frequencies of the next two overtones.

2nd overtone = …………………. Hz

3rd overtone = …..……………… Hz

[2]

(iv) Using information from (b)(iii) and assuming no end correction, determine


20 [Turn Over

the length of the air column for another resonant fundamental frequency of 294 Hz.

length of air column = ……………….m

[3]

(v) The flutist can change the musical note by covering or uncovering the

holes of the flute to change the length of the air column. Suggest another way in which the flutist varies the pitch (frequency).

………………………………………………………………………………..…….

……………………………………………………………………………….

[1]

(c) A transmitter T on Earth emits radio wave of wavelength 2.0 x 103 m. The radio


21 [Turn Over

waves from transmitter T travel to the receiver R located 2500 km away, by two paths as shown in Fig 7.3. (not to scale)

Fig 7.3 For the first path, the wave travels directly from T to R. For the second path, it travels up to the ionosphere and is reflected down to R. Assume that this reflection takes place at a point midway between receiver and transmitter and there is no change in phase of the radio wave upon reflection at the ionosphere.

(i) When the ionosphere is in position shown in Fig 7.3, at a distance h

above the signal, the signal detected at R is a maximum. Explain in terms of the paths taken by the wave, how the maximum is caused in this situation.

…………………………………………………………………………….………..

…………………………………………………………………………….………..

……………………………………………………………………………….

[2]

(ii) Determine that the minimum height h of the ionosphere that will produce a

2500 km

ionosphere

h

Transmitter T Receiver R


22 [Turn Over

maximum signal at R. (Assume that the curvature of Earth is negligible.)

[3]

(iii) At night when the atmosphere cools down, the ionosphere moves down

towards Earth. The same signal is emitted at T and the signal received at receiver R fades every 20 minutes.

Determine the speed at which the ionosphere is descending towards the Earth.

speed = …………………m s-1

[2]

8 (a) A sheet of potassium foil is at a distance of 3.5 m from an isotropic light source


23 [Turn Over

that emits 1.5 W of power. The work function, Φ, of potassium is 2.2 eV. Assume for the time being that wave theory of light applied and that the energy was transferred to the target foil in a smooth and continuous manner. Assume also that the foil totally absorbs all the energy reaching it and that the to-be-ejected electron collects energy from a circular area of radius 5.0 x 10-11 m of the foil, the approximate size of an atom of the foil.

(i) Calculate the intensity of light at a distance of 3.5 m from the isotropic light

source.

intensity = ……………… W m-2 [2] (ii) Calculate the power received by the circular patch of foil of radius

5.0 x 10-11 m.

P = ………………. W [2] (iii) Hence determine how long it would take for enough energy to accumulate

on the circular patch of foil in order to liberate an electron.

time taken = …….…………. s [2] (iv) Hence, with reference to what is actually observed in the photoelectric


24 [Turn Over

experiment, explain how the answer to (a)(iii) above conflicts with wave theory of light and how the quantum theory of light addresses the problem of Time Delay.

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………….

[3]

(v) Besides the problem of Time Delay, describe another observation from the

photoelectric experiment that conflicts with the wave theory of light but can be successfully explained by the quantum theory of light.

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………….

[2]

(b) Fig 8.1 shows a high voltage supply set up to produce energetic electrons to

bombard the cool sodium gas in the discharge tube, giving rise to a line spectrum through a prism. Fig 8.2 shows some energy levels of sodium. Assume that each bombarding electron has a kinetic energy of 3.70 eV.

(i) Explain what gives rise to these spectral lines.

High voltage supply

Collimator slit prism

Detector

Sodium gas n = 1

n = 2

n = 3

n = 4n = 5

-5.17 eV

-3.07 eV

-1.98 eV

-1.56 eV-1.42 eV

Fig 8.1 Fig 8.2


25 [Turn Over

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………….

[1]

(ii) Explain why only six spectral lines can be detected, identifying the

transitions responsible for them.

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………………...

………………………………………………………………………………. [2]

(iii) Sketch and label the relative positions of the spectral lines for only the

transitions which terminates at n = 1 in Fig 8.3 below. The line due to the transition from level n = 2 to n = 1 has been drawn for you.

Fig 8.3

[1] (iv) Determine the range of kinetic energy of the recoiling electrons after they

have excited the sodium atoms?

Range : ______ eV ≤ KE ≤ ______ eV [3]

n = 2 to n = 1



26 [Turn Over

(v) Fig 8.4 shows another cool gas X placed between the discharge tube and the collimator slit. Its energy levels are shown in Fig 8.5.

Cool gas X

-0.48 eVn = 4-0.90 eVn = 3High

voltage supply

Collimator slit prism

Detector

Sodium gas

n = 2 -1.49 eV

n -3.00 eV= 1

Fig 8.4 Fig 8.5 Determine the number of emission spectral lines that will be detected.

Explain your answer.

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………………...

……………………………………………………………………………………...

………………………………………………………………………………. [2]

END OF PAPER 2

MJC H1 Physics Preliminary Examinations 2010 Paper 1 Suggested Solutions: (30 marks) 1 C 11 A 21 C 2 D 12 C 22 B 3 B 13 D 23 B 4 C 14 A 24 D 5 D 15 A 25 A 6 A 16 A 26 B 7 D 17 D 27 C 8 C 18 B 28 D 9 C 19 C 29 B 10 B 20 A 30 B MCQ 1: (C) A LW

AA L W

A AL W

A L W

=Δ

= +

⎛ ⎞Δ = +⎜ ⎟⎝ ⎠

Δ =

l w

l w

w + l MCQ 2: (D) Frequency of radio wave ranges from 3 Hz to 300 GHz Question: 500 μHz = 500 x 10-6 Hz---- too small Mass of lightest atom; Hydrogen-1 is 1.007825u; ~ 1.66 x 10-27 kg Mass of heaviest stable atom; Lead-208 is 207.9766521u ~ 3.45 x 10-25 kg Question: 500 pg = 500 x 10-12 g = 5 x 10-10 kg (too heavy) Acceleration due to free fall 981 mm s-2 (too small--- should be 9810 mm s-2) MCQ 3: (B) Since the readings are very close to each other. The readings are precise. Since zero error has not been taken into account, there is lack of accuracy in the readings. MCQ 4: (C) v=u+at v = 1.60 + 12.5(1.25) v = 17.225 m s-1 v2=u2+2as 17.2252 = 1.62 + 2(12.5)s s= 11.766 m vertical height = 11.766 sin(40)= 7.56 m

1 JC2 H1 Physics Prelim Exam 2010 Solutions


MCQ 5: (D) v2=u2+2as 49.12 = 14.72 + 2(9.81)s s= 111.86 m; 112m MCQ 6: (A) The time taken for the flight up to the highest point should be shorter than the time taken for the flight down. MCQ 7: (D) To find T1, take pivot at rightmost end of bridge

1

1

( ) ( )2

( )2

(1 )2

⎛ ⎞ + − =⎜ ⎟⎝ ⎠

⎛ ⎞ + −⎜ ⎟⎝ ⎠=

= + −

b c

b c

bc

lW W l x T l

lW W lT

lW xW

l

x

To find T2, take pivot at leftmost end of bridge

2

2

( ) ( )2

( )2

( )2

⎛ ⎞ + =⎜ ⎟⎝ ⎠

⎛ ⎞ +⎜ ⎟⎝ ⎠=

= +

b c

b c

bc

lW W x T l

lW WT

lW xW

l

x

MCQ 8: (C) As linear momentum is conserved, there is total transfer of momentum during collision as all 3 discs are identical. MCQ 9: (C) Elastic potential energy = area under the force – extension graph = 0.50 x 0.04 x 30000 = 600 J MCQ 10: (B) As the train is moving with constant velocity, the pendulum bob will also possess the same constant velocity as the train. The bob will therefore not experience any resultant force acting on it, hence it will remain over the mark.


MCQ 11: (A) For s less than point P, the object is falling with terminal velocity, hence it will not experience any resultant force, R = 0. After the point P, the object’s deceleration during impact is constant, since the vertical axis is the resultant force, using Fnet=ma, constant a implies constant resultant force, R. MCQ 12: (C) By Hooke’s Law, the component of the sphere’s weight down the incline causes the spring to compress by a value e.

0

sin(3.00)(9.81)sin30

5000.029429.4

mg ke

e

m mm

θ =

=

≈=

MCQ 13: (D) By the principle of conservation of energy,

2

2

-1

10 02

180.0(9.81)(30.0 30.0cos50 ) (80.0)214.5 m s

i i f

o

PE KE PE KE

mgh mv

v

v

+ = +

+ = +

− =

=

f

By the principle of conservation of momentum,

-1

( )80.0(14.5) 0 (80.0 45.0)

9.28 ms

T T J J T Jm u m u m m vv

v

+ = +

+ = +

= MCQ 14: (A) The kinetic energy is ½mv2 and remains constant as it reaches constant velocity, Rate of change of GPE = mgh / t = mg(h/t) = mgv MCQ 15: (A) For option B and C, we require two progressive waves to create interference pattern and standing wave. Light wave only travels at the speed of light, not at any velocity. A wave can also behave as a particle. As such, it can carry a momentum.

MCQ 16: (A) The velocity of the wave passing through S2 and the thin glass plate will have a lower velocity. Hence, distance between S2 and screen is longer than distance between S1 and screen. The central maximum (for which path difference is zero) will shift downwards. Fringe pattern shifts downwards MCQ 17: (D) I α A2

For maximum intensity, Io α (3A)2

For minimum intensity, I α (A)2

I/Io = (A/3A)2 I = Io/9 MCQ 18: (B) 2λ = 0.056 v = fλ (3.0 x 108) = f(0.056/2) f = 10.7 GHz MCQ 19: (C) Δx = λD/a (1.44 x 10-3) = (600 x 10-9)(1.2)/a a = 0.50 mm MCQ 20: (A) Only A is the conclusion we can draw from the information given. If the filament of the fifth bulb has broken, the voltmeter will register the voltage across the transformer and not a zero reading. We cannot conclude that C is correct. B and D are possible but further testing need to be done.


MCQ 21: (C) 2.0 Ω Before voltage supply is reversed, diode is forward-bias.

2.0 Ω Z Y

X

V

D

2.0 Ω

Total current in circuit = V / RX = 12 / 2 = 6.0 A

Since diode is ideal, hence current across resistor Y or Z = 6.0 / 2 = 3.0 A

Potential difference across resistor Y or Z = I (R) = 3.0 x 2 = 6.0 V

Hence, potential difference across voltage supply = 12 + 6.0 = 18 V

After voltage supply is reversed, diode is reverse-bias, no current will flow through the diode.

Effective resistance = 2.0 + 2.0 = 4.0 Ω

Total current in circuit = V / R = 18 / 4.0 = 4.5 A

Hence, voltmeter reading = Iacross X (R) = 4.5 x 2 = 9.0 V

MCQ 22: (B) p.d across the 14 Ω resistor = 3 x 0.5 = 1.5 V I = V / R = 1.5 / 14 = 0.11 A (or 0.107 A) ε = 3.5 x 0.5 = 1.75 V Using ε = V +Ir 1.75 = 1.5 + 0.107r r = 2.3 Ω or use ε = I(R+r) with I = 0.107, r = 2.4 Ω


MCQ 23: (B) The equivalent networks are: and

X

R

R 5.0 Ω R R

5.0 Ω

Y Z Y

11 15 2

1 2 52.5 5(2 )

2.5

YZRR

RR

R

−⎛ ⎞= +⎜ ⎟⎝ ⎠

+=

= Ω

1

1

1 15.0

1 12.5 7.5

1.88

XYRR R

−

−

⎛ ⎞= +⎜ ⎟+⎝ ⎠

⎛ ⎞= +⎜ ⎟⎝ ⎠

= Ω

MCQ 24: (D)

p.d. across 4 Ω = 4 (10)4 10 6+ +

= 2 V

p.d. across 10 Ω = 10 (10)20

= 5 V

p.d. across 6 Ω = 6 (10)20

= 3 V

Hence, the potential value at P is 2.0 V, Q is 0 V (earthed), R is -5 V and S is -8 V. MCQ 25: (A) Using LHR, the magnetic force acting on the electrons is directed downwards. Hence for electrons to pass through un-deflected, the electric force must be directed upwards, Since electrons are negatively charged, they will experience an electric force opposite to the direction of the E-Field lines. Thus the E-Field must be directed downwards. MCQ 26: (B) B field within coil P will be directed upwards. Using LHR, force on wire will be directed towards TS. Hence rod will move towards QR with constant acceleration i.e. uniformly increasing speed.


MCQ 27: (C) o

B

2o

2oB

B

2o

7 2

7 2

2

2

2

Since the wire is suspended,

2

4 10 100.0 (0.020)(9.81)2

2 10 100.0 0.020 9.81

IF I Ld

I LdIF

L d

F mgL L

I m gd L

d

d

μπ

μπμπ

μπ

ππ

−

−

= × ×

=

=

=

⎛ ⎞= ⎜ ⎟⎝ ⎠

× ×=

× ×=

× 0.0102 m

1.02 cm==

MCQ 28: (D) .

MCQ 29: (B) MCQ 30: (B) hf = (hc/λ) = Φ + KEmax

Therefore Φ = (hc/λ) - KEmax

= (hc/515 × 10-9) –e(0)

= 3.9 x 10-19 J = 2.4 eV

Paper 2 Suggested Solutions: (80 marks)



1

Progressive waves Stationary waves

Amplitude of vibration

The amplitude of vibration is the same at all points

Amplitude of vibration varies with position Varies from zero at the nodes (permanently at rest) to a maximum at the antinodes.

Wavelength Distance between adjacent particles which have the same phase

Equals to twice the distance between a pair of adjacent nodes or antinodes

Phase No 2 particles within one wavelength are in phase

All particles between consecutive nodes have the same phase. Particles in adjacent segments of the length λ/2 have a phase difference of π rad.

Energy Energy translation in the direction of travel of the wave and is transported at a speed given by the product of its frequency and wavelength.

No net transfer of energy

2 (a) Sx = ut + ½ at2

[B1]

[B1]

[B1]

[B1]

Sx = ½ (2.25) 0.502 Sx = 0.281 m Sy= ut + ½ at2 Sy= 0.5 x 9.81 x 0.502 Sy= 1.23 m Net displacement = sqrt( Sx

2+ Sy2) = 1.26 m

Angle with respect to horizontal = 77.1 degree below horizontal

[M1] [M1] [A1] [A1]

(b) (i) Graph must be negative before any mark is awarded.

Graph: 1 mark for identifying that acceleration is zero at start and end of graph Graph: 1 mark for identifying that acceleration is constant at middle part of graph

(ii) The acceleration between time t1 and t2 is negative value because the

negative slope of v-t graph. The acceleration between time t1 and t2 is a constant maximum negative value since it corresponds to the steepest gradient of the v-t graph.

[B1] [B1]


3 (a) (i) ironiron

iron

RAρ

π

=

=

= Ω

-8

-3 2

8.90 x 10 (3.0) (0.60 x 10 )

0.236

l

copper

coppercopper

coppercopper

copper

RA

RA

ρ

π

ρ

π π

=

=

= Ω

=

=−

= Ω

-8

-3 -5

-8

-3 -5 2 -3 2

1.60 x 10 (3.0) 2 (0.60 x 10 )(1.78 x 10 )0.715

or

1.60 x 10 (3.0) (0.60 x 10 +1.78 x 10 ) (0.60 x 10 )0.705

l

l

When copper is deposited on the surface of the wire, it acts as a parallel shunt to the iron wire.

eff iron copper

eff

R R R

R−

= +

⎡ ⎤= +⎢ ⎥⎣ ⎦= Ω

1

1 1 1

1 1 0.236 0.715

0.178

[M1] [M1] [A1]

(b) Method 1

Power loss per metre of cable (consist of 2 wires) = I2R x 2 = (2.5 x 10-3)2 x 0.27 x 2 = 3.38 x 10-6 W Power loss in cable = 12.5 – 1.5 = 11.0 mW Maximum distance = 11.0 x 10-3 / 3.38 x 10-6 = 3.25 x 103 m Method 2 Power loss in cable = 12.5 – 1.5 = 11.0 mW Resistance of one wire = P / I2 = 5.5 x 10-3 / (2.5 x 10-3)2 =880 Ω Maximum distance = Rwire / Rper m = 880 / 0.27 = 3.26 x 103 m

[M1] [M1] [A1] [M1] [M1] [A1]


Method 3 Power loss in cable = 12.5 – 1.5 = 11.0 mW Power loss in cable = 11 x 10-3 = I2Reff’ Reff’ = (11 x 10-3) / (5 x 10-3)2

= 440 Ω Reff per m of both wires = (1/0.27 + 1/0.27)-1 = 0.35 Ω Maximum distance = Reff’ / Reff per m = 440 / 0.35 = 3.26 x 103 m

4 (a) Magnetic flux density is defined as the force acting per unit length of a

conductor, carrying unit current, placed at right angles to the magnetic field. S.I unit : Tesla

[B1] [B1]

(b) (i)

[B1] Field lines pointing upwards and slightly to the right [B1] Show the field created by wire in correct direction [B1] Appropriate spacing between field lines

(ii) [M1]



[A1] [B1]

(iii) Electrical energy was being converted to kinetic energy of the wire. [B1] (iv) If the charged particle is stationary or moves in the direction of the

magnetic field , there will not have any magnetic force acting on it. [B1]

OR

If the charged particle is moving with a component of its velocity perpendicular to the magnetic field direction, a magnetic force will act on it.

5 (a) T / K = θ / oC + 273 [A1]

(b) T / K 273 303 333 363 393 R / Ω 16300 5000 1320 457 159 lg(R / Ω) 4.21 3.70 3.12 2.66 2.20

*all answers must be correct to obtain the mark.

[A1]

(c) see graph below

[B1] – both axis is maximized [B1] – all points plotted correctly [B1] – appropriate best fit line drawn

(d) The logarithmic scale is able to represent very widely varying numbers on a

very compressed scale. OR The changes in values of R are very much larger than the changes in values of T.

[B1]

(e) This thermistor is called a negative temperature coefficient (NTC)

thermistor as the lg(R / Ω) against T / K graph gives a negative gradient, where as temperature increases, resistance decreases.

[B1]

F

Note: F must be perpendicular to field line and touching the wire

(f) From the graph, at 323 K, lg(R / Ω) = 3.34 hence R = 103.34 = 2188 Ω Using potential divider rule,

thermistorthermistor

thermistor variable resistor constant resistor

variable resistor

variable resistor

variable resistor

2188 12 12 0.72188 15

26256 11.32203

121

R E VR R R

R

RR

⎛ ⎞=⎜ ⎟+ +⎝ ⎠

⎛ ⎞= −⎜ ⎟+ +⎝ ⎠

=+

= Ω

*answers may vary depending on value read off from graph.

[M1] [M1] [A1]

(g) The 15 Ω resistor is included to prevent a large surge of current through the

circuit when the temperature is high and the resistance of the thermistor is low.

[B1] [B1]



6 (a) (i) First Law - An object will remain at rest or move along a straight line with constant speed, unless it is acted upon by a resultant (or net) external force. [B1] This implies that an object resist change of its state of rest or motion. A force is needed to change the state of the body. [B1]

(ii) F = ma (N2L simplified)

units of F = units of m x units of a = kg m s-2 [B1]

(b) (i) 150 km h-1 = 150 x 1000 / 3600 = 41.67 m s-1

v = u + at 41.666 = 0 + a (11) a = 3.7879 m s-2 [M1] F = ma = 1200 x 3.7879 = 4545.45 N [M1] Fd - f = ma Fd = 4545.45 + 1200 = 5745.45 N = 5740 N [A1]

(ii) Pmax = Fd vmax

= 5745.45 x 41.67 [M1] = 239.393 kW = 239 kW (to 3 sf) [A1]

(c) (i) Solving strategy:

1 – Find initial KE, E1 2 – Equate Loss in KE = WD in crushing barrels 3 – Find Area under graph to WD in crushing barrels 4 – Showing Area UP TO 1.5 m: 135 kJ < E1 4.0 m: 460 kJ < E1 5 - Finally showing Area UP TO 4.02 m : 464 kJ = E1 Loss in KE:

ΔK = ( ) ( ) ( )2 2 21 1 1200 27 8 02 2

463704 J

m u v− = −

=

. [B1]

For x ≤ 1.5 m W = Fx = (90000)(1.5) = 135000 J For x ≤ 4.0 m Wtot = (90000)(1.5) + (130000)(4.0 − 1.5) = 460000 J [C1] As this is less than the loss in KE, x0 > 4.0 m, where x0 is the greatest distance the car moved into the cushion of barrels


before coming to rest. By the Work Energy Theorem, Loss in KE = work done against the force provided by the cushion of steel

barrels 463704 = 460000 + 170000(x0 − 4.0) [M1] x0 = 4.02m [A1]

(ii) The actual distance would be shorter than 4.02 m [A1] The presence of friction / other dissipative forces would result in less than its original KE to be dissipated by the barrels. The car’s kinetic energy would be converted into heat, sound and work involved in deforming the car body. [M1]

(d) (i) change in momentum = mΔv

= 75 x (39.6 x 1000/3600 – 0) [M1] = 825 kg m s-1 [A1]

(ii) average force = change in momentum / time taken

= 825 / 0.14 = 5890 N [B1] weight of dummy = 75 x 9.81 = 735.75 N 8 x 735.75 = 5886 N ≈ 5890 N (shown) [B1]

(e) Deflating means the head will move a longer distance/ take a longer time before coming to a stop [B1] This reduces the amount of force that the head will experience. [B1]


7 (a) (i) Diffraction is the bending or spreading out of waves when they travel through a small opening or when they pass round a small obstacle. [A1]

(ii) Principle of Superposition states that when two waves of the same kind

meet at a point in space, the resultant displacement at that point is the vector sum of the displacements that the two waves would separately produce separately at that point. [A2]

(iii)

Barrier

Plane Waves


(b)

(i) [B1] maximum displacement at antinodes and zero displacement at node. [B1] opposite directions for air molecules in each quadrant

(ii) [B1] H at node. L at antinode. (iii) For open tube;

second harmonic = 2 f1 = 524 Hz. Third harmonic = 3 f1= 786 Hz

[B1] [B1]

(iv)

2

2

L

vLf

λ=

=

0.655 = 2(262)

v ----- [M1]

v = 343.22 ms-1 v will be the same. Let L’ be the new length.

'

''

'2

2

L

vLf

λ=

=

= 343.222(294)

[M1]

= 0.584 m [A1] (v) By varying the pressure at which the flutist blows into the flute. [B1]

L L H



(c) (i) A maximum is obtained as the path difference between the reflected

wave (reflected at R) and the direct wave is equivalent to n λ . [B1] When the waves meet, they superpose constructively and resultant wave amplitude is the vector addition of the individual wave amplitude. [B1]

(ii) Minimum path difference = 1 λ = = 2 000 m

(Distance of path taken by reflected beam) – (2500 × 103) = 1 λ

(Distance of path taken by reflected beam) – (2500× 103) = 2 000 m [M1]

Distance of path taken by reflected beam =2 502 000 m Using Pythagoras Theorem,

2 2

22502000 2500000 h2 2

⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

[M1]

h = 45 km [A1]

(iii) Signal fades/becomes a minimum when the ionosphere has moved a distance = ½ λ = 1000 m Distance moved by ionosphere in 20 min = 1000 m Speed at which it descends = 1000 /(20 x 60) [M1] = 0.833 m s-1 [A1]

8 (a) (i)

[M1]

=9.74418×10-3 = 9.74 × 10-3 W m-2 [A1] (ii) P = IA = (9.74418 × 10-3) [ π × (5.0 × 10-11)2] [M1] = 7.65306 × 10-23 = 7.65 × 10-23 W [A1] (iii)

[M1]

=4600 s (2 s.f) or 4610 s (3 s.f.) (= 1.3 hrs) [A1] (iv) Photoelectrons are observed to be emitted practically immediately

during the actual photoelectric experiment.

[B1]

Classical wave theory predicts that light incident on the metal needs some time to accumulate enough energy to eject photoelectrons, requiring longer for low intensity light (e.g. 1.3 hours according to ans (iii))

[B1]

The quantum theory of light hypothesizes that light is delivered in discrete bundles of energy called photons, with each photon energy given by E = hf, instead of continuously. As long as hf exceeds the work function Φ of the material it will emit photoelectrons.

[B1]

(v) Students can discuss either point with supporting explanation EITHER

The existence of a threshold frequency, below which no photoelectrons are emitted • For a given metal, no photoelectrons are emitted if the frequency of the

incident light is lower than the threshold frequency for that metal, • regardless of the intensity of the incident radiation is or for how long it

falls on the surface. • (mention of “threshold freq, award 1st [B1]) • (elaboration of what happens or does not happen beyond or before

that, award 2nd [B1])

[B1] [B1]

OR Independence of maximum KE on the intensity of illumination. • Photoelectrons emitted from a metal have a range of velocities from

zero up to a maximum vmax. (describing in terms of a range of KE’s also acceptable)

• The maximum kinetic energy 21max2 mv was found to depend linearly on

the frequency of the radiation and is independent of its intensity.

[B1] [B1]

(b) (i) The downward transitions/de-excitations of the electrons from

higher/excited energy states to lower energy releases a photon,


giving rise to the spectral lines. [B1]

(answers like “Transitions between energy levels” not accepted as it does not distinguish between absorption or emission)

(ii) The highest energy level the 3.70 eV bombarding electrons can

excite the sodium to is n = 4; E= -1.56 eV. The maximum number of downward transitions from the n=4 state is 4C2 = 6.

[B1]

The transitions are 4 → 3; 4 → 2; 4 → 1; 3 → 2; 3 → 1; 2 → 1) [B1] (answers like “there are only 6 possible transitions not accepted) (iii)

3 to 1 4 to 1 n = 2 to n = 1


[B1]

(looking for correct ordering/sequence of the lines) (iv) 3.70 –[(-3.07) – (-5.17)] = 1.60 (for the 1 → 2 transition) [M1] 3.70 – [(-1.56) – (-5.17)] = 0.09 (for the 1 → 4 transition) [M1] 0.09 eV ≤ KE ≤ 1.60 eV [A1] (v) 4 spectral lines will be observed.

[B1]

The photons of energy 1.51 eV (from n = 1 to n = 2) and 2.10 eV (from n = 1 to n = 3) will be absorbed. Only photons of energy corresponding exactly to the difference between the ground state and an excited state will be absorbed. While they are re-emitted, the intensity in the forward direction would be very weak.

[B1]


NANYANG JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION Higher 1

PHYSICS 8866/01Paper 1 Multiple Choice 28 September 2010

1 hourAdditional Materials: Multiple Choice Answer Sheet


Write in soft pencil. Do not use staples, paper clips, highlighters, glue or correction fluid. Write your name, class and tutor’s name on the Answer Sheet in the spaces provided unless this has been done for you.

There are thirty questions on this paper. Answer all questions. For each question there are four possible answers A, B, C and D. Choose the one you consider correct and record you choice in soft pencil on the separate Answer Sheet.

Read the instructions on the Answer Sheet very carefully.



[Turn over

2


speed of light in free space c = 3.00 x 108 m s

–1

elementary charge e = 1.60 x 10–19

C

the Planck constant h = 6.63 x 10–34

Js

unified atomic mass constant u = 1.66 x 10–27

kg

rest mass of electron me = 9.11 x 10–31

kg

rest mass of proton mp = 1.67 x 10–27

kg

acceleration of free fall g = 9.81 m s–2

Formulae

uniformly accelerated motion s = ut + ½ at2

v2 = u2 + 2as



resistors in series R = R1 + R2 + ....

resistors in parallel 1/R = 1/R1 + 1/R2 + ....

NYJC 2010 8866/01/PRELIM/10

3

1 In which of the pairs of quantities listed have the same basic units?

A Impulse and force B Momentum and rate of change of displacement C Energy and moment of a force D Electromotive force and magnetic force

2. In a mass-spring experiment to determine the spring constant k, the equation used is

km

T π2=

where the period, T is found to be ( s when the mass, m is g. The value of k and its uncertainty is

) )

)

)

1.0±8.2 ( 1±50

A Nm−1 B ( ) Nm−1 ( 01.0±25.0 02.0±25.0

C Nm−1 D ( 20±250 ( )20252 ± Nm−1

3 Fig. 3.1 shows the graphs of velocity v against time t for two cars A and B traveling along a

straight level road in the same direction.

At time t = 0, both cars are side by side. Find the time at which car A overtakes car B.

A 1.2 s B 2.3 s C 2.8 s D 4.0 s

[Turn over

12

10

6

8

2 4 6 8 10

14

16

18

20

22

24

26

v / m s-1

t / s

A

B

0

Fig 3.1

NYJC 2010 8866/01/PRELIM/10

4

4 A basketball player throws a ball with an initial velocity of 12.0 m s-1 at an angle of 25.0o to the vertical. Assuming that air resistance is negligible and the horizontal distance the ball travels to the hoop is 10.6 m, determine the speed at which the ball enters the hoop.

10.6 m

12.0 m s-1

25.0o

Hoop

A 4.49 m s-1 B 9.63 m s-1 C 10.9 m s-1 D 11.8 m s-1

5 Which of the following statements relating to Newton’s third law is not correct?

A The two forces must be opposite in direction. B The two forces are acting on a body in equilibrium. C The two forces must be of the same type. D The two forces must have the same magnitude.

6 A body of mass 5.0 kg, moving at 5.0 m s-1, is acted on by a force in the opposite direction

which varies with time as shown. What is the magnitude of the momentum of the body at time t = 6.0 s?

e / s tim0 2 4 6 8

10

force / N

A 25 N s B 45 N s C 50 N s D 75 N s 7 Two spheres, one of mass 3m and another of mass m, are traveling with speed v and moving

towards each other. The spheres have a head-on elastic collision. v v

m 3m Which statement is correct? A The spheres stick together after impact and have a resultant speed of 0.5mv. B The kinetic energy of mass m after impact is 2mv2. C The sum of their momenta after impact is 4mv. D Mass 3m has more kinetic energy than mass m after impact.

NYJC 2010 8866/01/PRELIM/10

5

8 A wire that obeys Hooke’s Law is of length x1 when it is in equilibrium under a tension T1. Its length becomes x2 when the tension is increased to T2. What is the extra energy stored in the wire as a result of this process?

A ( ) (2 1 2 114

T T x x+ − ) B ( ) (2 1 2 114

T T x x+ + ) C ( ) (2 1 2 112

T T x x+ − ) D ( ) (2 1 2 112

T T x x+ + )

9 The diagram below shows a ladder resting on a rough floor and against a rough wall. Which arrow shows a possible direction of the force exerted on the ladder by the wall?

A

10 An electron is projected horizontally into the vertical electric field in the space between two horizontal charged plates. A magnetic field is pointing into the plane of the paper between the charged plates. The electron passes through undeflected. Which row correctly identifies the direction of the forces acting on the electron?

Electric Force Electromagnetic Force Gravitational Force

A upwards downwards downwards

B upwards downwards upwards

C upwards upwards downwards

D downwards upwards downwards

Rough floor Rough wall

B

C

D

Ladder

× × × ××

× ××××

× × × × ×

+

–

electron path

electric field

magnetic field

[Turn overNYJC 2010 8866/01/PRELIM/10

6

11 A stone of mass M is fired from a catapult at an initial speed v at an angle θ to the horizontal at a point where the acceleration of free fall is g. The speed of the stone when it has risen to a height y above the point of release depends only on

A M, θ, v and g. B θ, v, g and y. C M, v, g and y D v, g and y. 12 4.0 kg 10.0 kg

30° The frictional force between the 4.0 kg mass and the plane of the slope is 4.0 N. If the distance

moved by the 10.0 kg mass is 2.0 m, the kinetic energy gained by the system is A 118 J B 149 J C 157 J D 165 J 13 The graph below shows how an applied force varies with displacement.

force / N 50 What is the net work done by the force? A 1050 J B 1250 J C 2450 J D 4900 J 14 A plane wave of amplitude A is incident on a surface of area S placed so that it is perpendicular

to the direction of travel of the wave. The energy per unit time intercepted by the surface is E. The amplitude of the wave is increased to 2A and the area of the surface is reduced to S/2. How much energy per unit time is intercepted by this smaller surface?

A 4E B E C 2E D E/2

displacement / m

0 50 70

−20

NYJC 2010 8866/01/PRELIM/10

7

15 The graph below shows the variation of displacement y with time t for particles P and Q in a progressive wave with wavelength λ.

particle P particle Q

What is the distance of particle Q from particle P?

A λ/2 B 3λ/4 C λ/4 D 3λ/8

16 The given diagram show the relative position of two generators, S1 and S2, that produce water

waves of wavelength 4.0 m. When operated by itself, each produces waves which have an amplitude A at point P. If the generators are operating anti-phase, what is the amplitude of the oscillation at P?

S1

P

8.0 m 2.0 m

S2 A 0 B A C 2A D 4A 17 When coherent monochromatic light falls on a double slits, interference pattern is observed on a

screen some distance from the slits. Which of the following will increase the separation of the fringe pattern? A decreasing the distance between the screen and the slits B increasing the distance between the slits C using monochromatic light of lower frequency D immense the whole set up in water

[Turn overNYJC 2010 8866/01/PRELIM/10

8

18 A stationary sound wave has a series of nodes. The distance between the first and fifth node is 20.0 cm.

What is the wavelength of the sound wave?

A 4.0 cm B 5.0 cm C 10.0 cm D 13.3 cm

19 The graph above shows the I-V characteristic curve of the diode in the circuit. If the resistance

of the rheostat is lowered, how will the resistance of the diode change?

A remains constant at infinite resistance. B remains constant at zero. C increases. D decreases.

20 The diagram below shows a simplified model of an atom in which two electrons move around

the nucleus in a circular orbit. The electrons complete one full orbit in 1.0 × 10-15 s.

electron

electron nucleus

What is the current caused by the motion of the electrons in the orbit?

A 1.6 × 10-34 A B 3.2 × 10-34 A C 1.6 × 10-4 A D 3.2 × 10-4 A

NYJC 2010 8866/01/PRELIM/10

9

21 A cell of e.m.f E and internal resistance r is connected to a resistor of resistance R as shown in the diagram. A voltmeter of infinite resistance is connected in parallel with the resistor.

E

r

R

V When the value of R is 2.0 Ω, the voltmeter reading is 3.0 V. When R is 4.0 Ω, the voltmeter

reading is 4.0 V. The internal resistance of the cell is

A 0.5 Ω B 1.0 Ω C 2.0 Ω D 4.0 Ω

22 Determine the effective resistance between terminals A and B.

B

10.0 Ω

10.0 Ω

10.0 Ω

10.0 Ω

10.0 Ω A

A 5.0 Ω B 6.3 Ω C 20 Ω D 35 Ω

23 Determine the value of the potential at point X in the circuit below.

12.0 Ω

X

3.0 V

3.2 6.0

A 0.92 V B 2.4 V C 2.8 V D 3.0 V

[Turn over

Ω

Ω

3.2 Ω

NYJC 2010 8866/01/PRELIM/10

10

24 A lighting circuit consists two lamps connected to a constant ideal d.c. source. Resistance of lamp X is twice that of lamp Y. The variable resistors RX and RY control the relative intensities of the lamps.

RY

If power output of lamp X is thrice that of lamp Y, the ratio of the currents in RX to that in RY should be A

1 : 3

B 1 : 3

2

C

32

: 1 D

3 : 1

25 A small rectangular coil carrying constant current is placed at one end of a horizontal solenoid.

The initial position of the coil plane is vertical, with its shorter axis of symmetry coinciding with the axis of the solenoid.

When a steady current is passed through the solenoid, A the coil is pulled into the solenoid B the coil is pushed out of the solenoid C the coil experiences a torque about a horizontal axis D the coil experiences a torque about a vertical axis

26 A long vertical wire carries a current of 5.0 A in a magnetic field of flux density 1.0 x 10-3 T. The magnetic field is at an angle of 30o below the horizontal. What is the force per unit length acting on the wire? A 2.2 x 10-3 N m-1 B 2.5 x 10-3 N m-1 C 3.8 x 10-3 N m-1 D 4.3 x 10-3 N m-1

coil solenoid

Y

X

RX

X

X

Shorter axis of coil along axis of solenoid

NYJC 2010 8866/01/PRELIM/10

11

27 The magnetic flux density B at the centre of a flat circular coil of radius r consisting of N turns carrying a current I is given by the equation

0 Iμ NB = 2 r

Two such coils, X and Y, each with 100 turns, are arranged as shown in the diagram.

X has radius 0.050 m and carries a current of 3.0 A, Y has a radius 0.10 m and carries a current of 6.0 A in the opposite direction to X. What is the magnitude of the total magnetic flux density at the centre of the coils? A zero B 1500 μo C 3000 μo D 4500 μo

28 An electron of mass m traveling with speed u collides with an atom and its speed is reduced to

v. The speed of the atom is unaltered, but one of its electrons is excited to a higher energy level and then returns to its original state, emitting a photon of radiation. If h is the Planck constant, the frequency of the radiation is

A 2 2( )2

m u vh− B

2 2(2

m v uh− ) C

2 2(2

m u vh+ ) D

2

2mv

h

29 Which of the following are explained by wave-like ideas? 1. Using an electron beam in an electron microscope to form images of very small objects. 2 Using γ-radiation to knock electrons out of atoms. 3 Deflecting an electron beam by using a magnetic field.

A 1 only B 1 and 3 only C 2 and 3 only D 1, 2 and 3. 30 A monochromatic beam of red light falls on one electrode of a photo-cell and electrons are

emitted. The light beam is then replaced by a blue beam delivering the same energy per unit time to the cell. Which one of the following quantities decreases as a result of this change? A The maximum kinetic energy of the electrons emitted. B The number of photons striking the metal per unit time. C The energy of each photon striking the electrode. D The work function of the metal.

--------- End of Paper ---------

NYJC 2010 8866/01/PRELIM/10

NYJC 2010 8866/01/PRELIM/10

12

Answers 1 C 11 D 21 C 2 B 12 B 22 B 3 B 13 A 23 B 4 C 14 C 24 C 5 B 15 D 25 D 6 A 16 C 26 D 7 B 17 C 27 A 8 C 18 C 28 A 9 D 19 A 29 A 10 A 20 D 30 B


CANDIDATE NAME

CLASS

TUTOR’S NAME

PHYSICS 8866/02Paper 2 Structured questions 15 September 2010

2 hours

Candidates answer on the Question Paper. No Additional Materials are required


Write your name and class on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid.

Section A Answer all questions.


Section A

1

2

3

4

5

Section B

6

7

8

Section B Answer any two questions. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.

Total


[Turn over

2 For Examiner’s

Use DATA AND FORMULAE Data speed of light in free space c = 3.00 x 10

8 m s

–1


C the Planck constant h = 6.63 x 10

–34 Js


kg rest mass of electron me = 9.11 x 10

–31 kg


kg acceleration of free fall g = 9.81 m s

–2

Formulae uniformly accelerated motion s = ut + ½ at2

v2 = u2 + 2as





NYJC 2010 8866/02/PRELIM/10

3

NYJC 2010 8866/02/PRELIM/10 [Turn over

For Examiner’s

Use Section A

Answer all the questions in this section

1 A 450 g football is kicked off the top of a building as shown in Fig. 1 below. θ

Building 30 m

Ground

24 m

Fig. 1 The football leaves the building at an angle θ and takes 3.0 s to hit the ground. Determine, for the football as it is kicked off the building, (a) the horizontal component of the velocity of the football,

horizontal component of the velocity = m s-1 [1]

(b) the angle θ.

angle θ = [3]

4 For Examiner’s

Use (c) Find the speed at which the football lands on the ground.

speed = [1]

The football lands on the ground and does not rebound. (d) Calculate the magnitude of the average force acting on the football as it lands if the

football stops in 0.12 s.

average force = N [2] 2 (a) State the conditions necessary for a body to be in equilibrium.

[2]

(b) Fig. 2.1 shows a 1000 N uniform thin rod being towed and moving at constant horizontal velocity.

T

θ

30o A floor

. Fig. 2.1 (i) Draw and label the 2 other forces on Fig 2.1 and show that the forces acting on

the block meet at a point. Mark that point P. [2]

NYJC 2010 8866/02/PRELIM/10

5 For Examiner’s

Use (ii) Given that T = 1500 N, show that θ = 40o.

[2]

(iii) In practice, wheels are installed at point A to reduce wear and tear at A, where the block is in contact with the floor. Given that that θ is fixed, explain how the motion of the rod will change.

[1] 3 Fig. 3.1 shows a light dependent resistor (LDR), a 200 Ω resistor and a light bulb of

resistance 1.0 kΩ when operated normally connected to form a potential divider. The resistance of the LDR is 1000 Ω and 100 Ω in the dark and in bright light conditions respectively.

The light bulb requires a potential difference of 12 V to operate normally and it is designed to be turned on when the room is in the dark.

(a) Calculate the effective resistance between P and Q when the LDR is placed in a dark

room and the bulb is operating normally.

effective resistance = Ω [1]

200 Ω

P

Q

R S

power supply

Fig. 3.1


6 For Examiner’s

Use (b) Calculate the potential at P when the room is in the dark.

potential at P = V [2] (c) Calculate the power dissipated by the bulb when operated normally

power dissipated = W [1] (d) Sketch the Ι-V characteristic graph of a filament bulb and thermistor below. [2]

(e) A student decides to connect a semi-conductor diode between S and R such that the

bulb will not light up. Draw the semiconductor on Fig. 3.1. [1]

V

ΙΙ

V

Filament bulb Thermistor

NYJC 2010 8866/02/PRELIM/10

7 For Examiner’s

Use 4 (a) Define the term tesla.

[2] (b) Fig. 4.1 shows a piece of wire carrying a current of 2.0 A placed perpendicularly to a

uniform magnetic field.

Fig. 4.1

The uniform magnetic field is of dimensions 10 cm by 2.0 cm and its magnetic flux

density is 0.10 mT. The magnetic field is into the page. (i) Calculate the length of the wire in the magnetic field

length of wire = m [1] (ii) Hence calculate the electromagnetic force exerted on the wire.

force on wire = N [3]

2.0 A

Region of uniform magnetic field

300

B

2.0 cm

10 cm


8 For Examiner’s

Use (c) Fig. 4.2 shows a negatively charged particle of velocity v entering a region of uniform magnetic field.

Region of uniform magnetic field v

Fig. 4.2 The electromagnetic force acting on the particle is into the page. Draw the direction of the magnetic field on Fig. 4.2. [1] 5 In the design of structure, such as buildings, towers or bridges, an engineer may use a

cantilever beam to allow for overhanging structure without external bracing. A cantilever is a beam supported only on one end.

The engineer will make calculations to ensure that the cantilever beam is strong enough to

withstand any forces applied on it and ensure that there is not too much vertical deflection. An appropriate beam can then be chosen based on the maximum allowable load to be applied.

Fig. 5.1 illustrates a cantilever of length L loaded with a point load P at its end. A vertical

deflection y of the free end of the cantilever will result from the loading.

A student was asked to investigate the behaviour of such an arrangement and found out from a book that the expression relating the vertical deflection of a loader cantilever. This was given as Equation 1:

3

3

4PLykbh

= (Equation 1)

where k is a constant b = breath of cantilever h = height of cantilever

P

Fig. 5.1

L

y

NYJC 2010 8866/02/PRELIM/10

9 For Examiner’s

Use (a) The student first used two steel cantilevers to investigate the relationship between y, P and L. He first kept L constant and varied P and obtained the results as shown in Fig. 5.2:

P (N) 10 20 40 50 70 90

y (mm) for Cantilever A 1.9 3.9 7.8 9.9 13.8 17.7

y (mm) for Cantilever B 10.8 16.0 26.9 34.8 46.2 57.9

Fig. 5.2

By plotting this result on a graph, he was able to deduce a relationship between y and P for both cantilevers. This appeared to be of the same form for each, although there seemed to be some form of systematic error in the results for B. The graph showing the relationship between y and P for Cantilever A has been sketched on Fig. 5.3.

(i) On Fig. 5.3, draw a best fit line through the plots to show the relationship

between y and P for Cantilever B. [1]

Graph of Deflection y (mm) against Point Load P (N)

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70 80 90 100

P / N

y / m

m

Cantilever A

Fig. 5.3


10 For Examiner’s

Use (ii) From Fig. 5.3, describe the relationship between y and P for Cantilever A and discuss whether the data in Fig. 5.2 for Cantilever A support Equation 1.

[2]

(iii) Suggest a reason why the student thinks the measurements for Cantilever B were subjected to systematic error.

[2] (iv) From the graphs plotted, estimate the amount of this error.

error = mm [1]

(b) The student continued his investigation by keeping P constant and varying L, obtaining the results for Cantilever A as shown in Fig. 5.4.

L (m) 1.0 1.5 2.0 2.5 3.0 3.5 4.0

y (mm) 1.6 5.3 12.5 24.6 42.4 67.2 99.9

Fig. 5.4 These results did not suggest direct proportionality between y and L. The student proceeded to sketch a graph showing the variation of lg y against lg L as shown in Fig. 5.5.

NYJC 2010 8866/02/PRELIM/10

11 For Examiner’s

Use

Graph of lg (y/mm) against lg (L/m)

0.0

0.5

1.0

1.5

2.0

2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

lg (L/m)

lg (y

/mm

)

Fig. 5.5

(i) Determine the gradient of the graph. Show your working.

gradient = [1]

(ii) Hence discuss whether the data in Fig. 5.4 support Equation 1.

[2]


12 For Examiner’s

Use (c) After researching further into the subject, the student found out that the constant k in Equation 1 is known as the Young’s Modulus which is a property of the material which the cantilever is made from.

(i) Use Equation 1 to show that the S.I. unit of k is Pa. [2]

(ii) A steel cantilever has width 0.12 m, height of 0.040 m and length of 2.0 m as shown in Fig. 5.6. If a point load of 1.0 kN is applied at the end, a vertical deflection of 2.0 cm was measured at the end. Calculate the Young’s Modulus of steel.

Young’s Modulus of steel = Pa [1]

Fig. 5.6

2.0 m

PointLoad

0.12 m

0.040 m

NYJC 2010 8866/02/PRELIM/10

13 For Examiner’s

Use Section B

Answer two questions from this section. 6 A sports car of mass 1500 kg is speeding along a straight road at 110 km h-1. A lorry

suddenly appears in front of the car. In the time interval between the lorry being spotted and the brakes on the car coming into operation, the car moves forward a distance of 10.6 m. With the brakes applied, the front wheels of the car leave skid marks on the road that are 4.2 m long, as illustrated in Fig. 6.1.

It is estimated that, during the skid, the magnitude of the deceleration of the car is 0.85 g, where g is the acceleration of free fall.

(a) Determine

(i) the speed v of the car before just before it collide with the stationary lorry.

speed v = m s-1 [2] (ii) the time interval between the lorry appearing and the collision taking place.

time interval = s [2]

10.6 m 4.2 m

Skid mark 110 km h-1

Fig. 6.1

lorry


14 For Examiner’s

Use (b) Fig. 6.2 shows the side view of the

passenger of mass 65 kg in the front seat. The forces acting on him at the instant when the brake is applied is also shown.

Frictional force

Normal reaction force.

Weight of passenger

C.G. x Fig. 6.2 (i) With reference to the forces acting on him, explain why the driver will lean

forward during this instant.

[2] (ii) State the net force acting on the passenger.

net force = N [1]

(c) Given that the sport car make a completely inelastic collision with the stationary lorry of mass 2500 kg.

(i) Explain what is meant by a completely inelastic collision.

[2] (ii) Calculate the velocity of the car right after collision, stating any assumption made.

velocity = m s-1 [3]

NYJC 2010 8866/02/PRELIM/10

15 For Examiner’s

Use (iii) The airbag in the sport car is deployed almost immediately after the collision. Explain how the airbag help to minimize the injuries to the front seat passenger.

[2] (d) After the accident, the sports car of mass 1500

kg had to be towed by a 2000 kg lorry up a slope at a constant speed of 5.0 m s-1 as shown in Fig. 6.3. The power P delivered by the lorry is 55 kW.

5.0 ms-1

10o Fig. 6.3 (i) By considering the sports car and the lorry as a whole system, find the rate of

increase of the gravitational potential energy of the system.

rate of increase of GPE = J s-1 [2] (ii) Using the principle of conservation of energy, show that the total resistive force,

fR acting on the whole system (sports car + lorry) is approximately 5000 N.

[2] (iii) Hence determine the driving force, F acting on the lorry, explaining your answer.

driving force = N [2]


16 For Examiner’s

Use 7 The diagram below shows visible light waves spreading through a single slit a before spreading at slits b and c.

θ (a) State the name of this experiment.

[1] (b) With reference to the waves spreading from the slits b and c, explain why interference

occurs only where waves from both sources overlap.

[2] (c) Explain what diffraction is, and describe the part played by diffraction in this experiment.

[2] (d) Label one part of the screen view where destructive interference has occurred with the

letter D. [1]

(e) Explain in detail why constructive interference occurs at N.

[2]

screenS2

S1

Image seen on screen

N

X

Y

M

NYJC 2010 8866/02/PRELIM/10

17 For Examiner’s

Use (f) State a condition necessary for observable interference, and explain how this experiment ensures that the condition is met.

[2] (g) The monochromatic light used in this experiment has a wavelength 589 nm. The

distance between S1 and S2 is 0.200 m while the distance between S2 and the screen is 2.5 m. The distance between slits b and c is 0.80 mm.

Calculate the distance between two consecutive bright lines on the screen.

distance = m [2] (h) If a piece of plastic is placed in front of slit b, the light waves from b will be caused to

slow down, without any change in frequency. Some of the wave energy will be absorbed by the plastic as well.

(i) State how the wavelength of the wave from b will change.

[1] (ii) State how the amplitude of the wave from b will change.

[1] (iii) Based on your answer in (h)(i), predict whether there will be more or fewer

waveforms in the plastic piece as compared to the number of waveforms in an equal thickness of air.

[1] NYJC 2010 8866/02/PRELIM/10 [Turn over

18 For Examiner’s

Use (iv) Using your answers in (h)(ii) and (iii), explain how the image on the screen will change, in terms of position, separation and contrast, when a piece of plastic is placed in front of slit b.

[5]

NYJC 2010 8866/02/PRELIM/10

19 For Examiner’s

Use 8 Electromagnetic radiation is incident normally on the surface of a metal. Electrons are emitted from the surface and these are attracted to a positively charged electrode, as shown in Fig. 8.

electrode

evacuated enclosure

metal surface μA

electromagnetic radiation

Fig. 8

(a) Name the effect which gives rise to the emission of the electrons.

[1]

(b) State a word equation, base on the principle of conservation of energy, which describes this effect

[2] (c) The current recorded on the mircroammeter is 2.1 μA. Calculate the number of

electrons emitted per second from the surface.

number per second = [2]


20 For Examiner’s

Use (d) The incident radiation has wavelength 240 nm. Show that the energy of a photon incident on the surface is 8.28 x 10-19 J.

[1]

(e) The intensity of the incident radiation is 8.2 × 103 W m-2. The area of the surface is 2.0 cm2. Calculate

(i) the power of the radiation incident on the surface,

power of radiation = W [1] (ii) the number of photons incident per second on the surface.

number per second = [2] (iii) Hence determine the ratio

number of electrons emitted per secondnumber of photons incident per second

ratio = [1]

(f) Comment on your answer to (e)(iii).

[1]

NYJC 2010 8866/02/PRELIM/10

21

NYJC 2010 8866/02/PRELIM/10

For Examiner’s

Use

[Turn over

(g) When the wavelength of the radiation is gradually increased to 310 nm, the reading in the microammeter just drops to zero. Explain this phenomenon and calculate the maximum kinetic energy of the electrons emitted from the metal surface when the wavelength of the radiation remains at 240 nm.

[2]

maximum k.e. = J [2]

(h) (i) Calculate the momentum of the photon given in (d).

momentum = N s [1]

(ii) If there are altogether 1.5 x 1018 photons striking onto the metal surface per second and are all absorbed, determine the force exerting on the metal surface. Show your working clearly.

force on metal surface = N [4]

2010 NYJC Prelim H1 Paper 1 Solutions

1 C 11 D 21 C

2 B 12 B 22 B

3 B 13 A 23 B

4 C 14 C 24 C

5 B 15 D 25 D

6 A 16 C 26 D

7 B 17 C 27 A

8 C 18 C 28 A

9 D 19 A 29 A

10 A 20 D 30 B


CANDIDATE NAME

CLASS

TUTOR’S NAME

PHYSICS 8866/02Paper 2 Structured questions 15 September 2010

2 hours

Candidates answer on the Question Paper. No Additional Materials are required


Write your name and class on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid.

Section A Answer all questions.


Section A

1

2

3

4

5

Section B

6

7

8

Section B Answer any two questions. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.

Total


[Turn over

2 For Examiner’s

Use DATA AND FORMULAE Data speed of light in free space c = 3.00 x 10

8 m s

–1


C the Planck constant h = 6.63 x 10

–34 Js


kg rest mass of electron me = 9.11 x 10

–31 kg


kg acceleration of free fall g = 9.81 m s

–2

Formulae uniformly accelerated motion s = ut + ½ at2

v2 = u2 + 2as





NYJC 2010 8866/02/PRELIM/10

3


For Examiner’s

Use Section A


1 A 450 g football is kicked off the top of a building as shown in Fig. 1 below.

θ

Building 30 m

Ground

24 m

Fig. 1 The football leaves the building at an angle θ and takes 3.0 s to hit the ground. Determine, for the football as it is kicked off the building, (a) the horizontal component of the velocity of the football,

1

24 (3.0)

8.0 m s

x x

x

x

s u tu

u −

===

horizontal component of the velocity = m s-1 [1] (b) the angle θ.

angle θ = [3] C

Taking upwards as positive, 2

2

-1

0

12

130 (3.0) (9.81)(3.0)2

4.715 m s

tan

31

y y y

y

y

y

x

s u t a t

u

uuu

θ

θ

= +

− = −

=

=

=

4 For Examiner’s

Use (c) Find the speed at which the football lands on the ground.

speed = [1]

below the initial launch point.

-1

4.715 9.81(3.0)24.715 m s

y y yv u a t= += −= −

Speed of football as it lands = 2 2

-1

(8.0) ( 24.715) 25.97826 m s

+ − =

=

The football lands on the ground and does not rebound. (d) Calculate the magnitude of the average force acting on the football as it lands if the

football stops in 0.12 s.

average force = N [2]

Final momentum of the football = 0 N s Initial momentum of the football = 0.450 x 25.978 = 11.690 N s Taking upwards as positive,

Average force = 0 ( 11.690) 97 N0.12

ifp pt− − −= =

2 (a) State the conditions necessary for a body to be in equilibrium.

[2]

The vector sum of forces acting on the body must be equal to zero. The resultant torque of a body must be zero

NYJC 2010 8866/02/PRELIM/10

5 For Examiner’s

Use (b) Fig. 2.1 shows a 1000 N uniform thin rod being towed and moving at constant horizontal velocity.

. T (i) Draw and label the 2 other forces on Fig 2.1 and show that the forces acting on

the block meet at a point. Mark that point P. [2] (ii) Given that T = 1500 N, show that θ = 40o.

[2]

(iii) In practice, wheels are installed at point A to reduce wear and tear at A, where the block is in contact with the floor. Given that that θ is fixed, explain how the motion of the rod will change.

[1]

Fig. 2.1

θ

30o A floor

R

W

P

αR = Total reaction force from the ground W = Gravitational force on the rod

Taking moment about point A,

: ( ) cos30 ( ) cos 02

73.2230 90

46.8 49

oA

o

o o

o o

lW T lτ α

α

α θ

θ

− =

=

+ − =

= ≈

∑

When wheels are installed, the frictional force at A will reduce significantly and since θ is fixed, T must remain the same to maintain vertical equilibrium of forces, therefore, there must be a net force in the horizontal direction and the rod will accelerate to the right.


6 For Examiner’s

Use 3 Fig. 3.1 shows a light dependent resistor (LDR), a 200 Ω resistor and a light bulb of resistance 1.0 kΩ when operated normally connected to form a potential divider. The resistance of the LDR is 1000 Ω and 100 Ω in the dark and in bright light conditions respectively.

The light bulb requires a potential difference of 12 V to operate normally and it is designed to be turned on when the room is in the dark.

(a) Calculate the effective resistance between P and Q when the LDR is placed in a dark

room and the bulb is operating normally.

effective resistance = Ω [1] (b) Calculate the potential at P when the room is in the dark.

potential at P = V [2]

200 Ω

P

Q

R S

power supply

Fig. 3.1

11 1( ) 5001000 1000

R −= + = Ω

The potential between P and Q is 12 V

By potential divider, 500 12

(500 200)16.8

PR

PR

V V

V V

× =+

=

(-16.8 V is also accepted)

NYJC 2010 8866/02/PRELIM/10

7 For Examiner’s

Use (c) Calculate the power dissipated by the bulb when operated normally

2 212 0.144 0.141000

VP W WR

= = = ≈

power dissipated = W [1] (d) Sketch the Ι-V characteristic graph of a filament bulb and thermistor below. [2]

(e) A student decides to connect a semi-conductor diode between S and R such that the

bulb will not light up. Draw the semiconductor on Fig. 3.1. [1] 4 (a) Define the term tesla. (b) Fig. 4.1 shows a piece of wire carrying a current of 2.0 A placed perpendicularly to a

uniform magnetic field.

One tesla is defined as the strength of a magnetic field in which a force of one newtonmust act on a wire of length one meter carrying one ampere of current in a direction perpendicular to the field.

Thermistor

I

V

Filament bulb

I

V


8 For Examiner’s

Use

Fig. 4.1

The uniform magnetic field is of dimensions 10 cm by 2.0 cm and its magnetic flux

density is 0.10 mT. The magnetic field is into the page. (i) Calculate the length of the wire in the magnetic field

length of wire = m [1] (ii) Hence calculate the electromagnetic force exerted on the wire.

force on wire = N [3] (c) Fig. 4.2 shows a negatively charged particle of velocity v entering a region of uniform

magnetic field.

2.0 A

Region of uniform magnetic field

300

B

2.0 cm

10 cm

02.0 sin304.0 cm0.040 m

ll

===

3 2

6

sin0.1 10 2.0 4.0 10 sin908.0 10 N

F BIl0

θ− −

−

== × × × × ×= ×

NYJC 2010 8866/02/PRELIM/10

9 For Examiner’s

Use Region of uniform magnetic field v Direction of

magnetic field

Fig. 4.2 The electromagnetic force acting on the particle is into the page. Draw the direction of the magnetic field on Fig. 4.2. [1] 5 In the design of structure, such as buildings, towers or bridges, an engineer may use a

cantilever beam to allow for overhanging structure without external bracing. A cantilever is a beam supported only on one end.

The engineer will make calculations to ensure that the cantilever beam is strong enough to

withstand any forces applied on it and ensure that there is not too much vertical deflection. An appropriate beam can then be chosen based on the maximum allowable load to be applied.

Fig. 5.1 illustrates a cantilever of length L loaded with a point load P at its end. A vertical

deflection y of the free end of the cantilever will result from the loading.

A student was asked to investigate the behaviour of such an arrangement and found out from a book that the expression relating the vertical deflection of a loader cantilever. This was given as Equation 1:

3

3

4PLykbh

= (Equation 1)

where k is a constant

b = breath of cantilever h = height of cantilever

Load

Fig. 5.1

L

y


10 For Examiner’s

Use (a) The student first used two steel cantilevers to investigate the relationship between y, P and L. He first kept L constant and varied P and obtained the results as shown in Fig. 5.2:

P (N) 10 20 40 50 70 90

y (mm) for Cantilever A 1.9 3.9 7.8 9.9 13.8 17.7

y (mm) for Cantilever B 10.8 16.0 26.9 34.8 46.2 57.9

Fig. 5.2

By plotting this result on a graph, he was able to deduce a relationship between y and P for both cantilevers. This appeared to be of the same form for each, although there seemed to be some form of systematic error in the results for B. The graph showing the relationship between y and P for Cantilever A has been sketched on Fig. 5.3.

(i) On Fig. 5.3, draw a best fit line through the plots to show the relationship

between y and P for Cantilever B. [1]

Graph of Deflection y (mm) against Point Load P (N)

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70 80 90 100

P / N

y / m

m

Cantilever A

Cantilever B

Fig. 5.3 NYJC 2010 8866/02/PRELIM/10

11 For Examiner’s

Use (ii) From Fig. 5.3, discuss whether the data in Fig. 5.2 support Equation 1.

The graph shows a linear relationship between y and P.

The data support Equation 1 as y is proportional to P.

[2]

(iii) Suggest a reason why the student thinks the measurements for Cantilever B were subjected to systematic error.

When no point load is being applied to cantilever B (P = 0), there should

not be any deflection (y = 0). However, from the graph, there seems to

be a deflection when P = 0 for Cantilever B, suggesting the presence of a

systematic error. [2] (iv) From the graphs plotted, estimate the amount of this error.

Error = any answers between 5 – 6 mm [1]

(b) The student continued his investigation by keeping P constant and varying L, obtaining the results for Cantilever A as shown in Fig. 5.4.

L (m) 1.0 1.5 2.0 2.5 3.0 3.5 4.0

y (mm) 1.6 5.3 12.5 24.6 42.4 67.2 99.9

Fig. 5.4 These results did not suggest direct proportionality between y and L. The student proceeded to sketch a graph showing the variation of lg y against lg L as shown in Fig. 5.5.


12 For Examiner’s

Use

Graph of lg (y/mm) against lg (L/m)

0.0

0.5

1.0

1.5

2.0

2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

lg (L/m)

lg (y

/mm

)

Fig. 5.5

(i) Determine the gradient of the graph. Show your working.

2.000 0.500Gradient 3.000.600 0.100

−= =

−

choose a gradient triangle more than half the area of the grids

Gradient = [1]

(ii) Hence discuss whether the data in Fig. 5.4 support Equation 1.

The data supports Eq 1 as the gradient of the graph lg y against lg L

gives the order of the relation between y and L. From the data, y is

proportional to L3 which support Equation 1. [2]

NYJC 2010 8866/02/PRELIM/10

13 For Examiner’s

Use (c) After researching further into the subject, the student found out that the constant k in Equation 1 is known as the Young’s Modulus which is a property of the material which the cantilever is made from.

(i) Use Equation 1 to show that the S.I. unit of k is Pa. [2]

3

3

3

3

4

4

PLykbhPLk

ybh

=

=

3 3

3 3 2

[ ][ ] ( )[ ][ ][ ][ ] ( )( )

P L N m Nk Py b h m m m m

= = = a=

(ii) A steel cantilever has width 0.12 m, height of 0.040 m and length of 2.0 m as shown in Fig. 5.6. If a point load of 1.0 kN is applied at the end, a vertical deflection of 2.0 cm was measured at the end. Calculate the Young’s Modulus of steel.

3

3

3 3 311

3 3

4

4 4(1.0 10 )(2.0) 2.08 100.020(0.12)(0.040)

PLykbhPLk P

ybh

=

×= = = × a

Young’s Modulus of steel = Pa [1]

Fig. 5.6

2.0 m

PointLoad

0.12 m

0.040 m


14 For Examiner’s

Use Section B

Answer two questions from this section. 6 A sports car of mass 1500 kg is speeding along a straight road at 110 km h-1. A lorry

suddenly appears in front of the car. In the time interval between the lorry being spotted and the brakes on the car coming into operation, the car moves forward a distance of 10.6 m. With the brakes applied, the front wheels of the car leave skid marks on the road that are 4.2 m long, as illustrated in Fig. 6.1.

It is estimated that, during the skid, the magnitude of the deceleration of the car is 0.85 g, where g is the acceleration of free fall.

(a) Determine

(i) the speed v of the car before just before it collide with the stationary lorry.

speed v = m s-1 [2] (ii) the time interval between the lorry appearing and the collision taking place.

time interval = s [2]

10.6 m 4.2 m

Skid mark 110 km h-1

Fig. 6.1

lorry

110 km h-1 = 30.6 m s-1. v2 = u2 +2as = (30.6)2 + 2(0.85)(-9.91)(4.2) v = 29.1 m s-1.

t1 = 10.6/30.6 = 0.346 s. t2 = v-u/a = (29.1 - 30.6)/(0.85)(-9.81) = 0.180 s total time = t1 + t2 = (0.346 + 0.180) = 0.53 s

NYJC 2010 8866/02/PRELIM/10

15 For Examiner’s

Use (b) Fig. 6.2 shows the side view of the

passenger of mass 65 kg in the front seat. The forces acting on him at the instant when the brake is applied is also shown.

Frictional force

Normal reaction force.

Weight of passenger

C.G. x Fig. 6.2 (i) With reference to the forces acting on him, explain why the driver will lean

forward during this instant.

From the diagram shown, the frictional force will provide a clockwise moment about the C.G. resulting in the driver rotating clockwise. Hence the driver will lean forward during this instant.

[2] (ii) State the net force acting on the passenger.

∑F = ma = (65)(0.85)(9.81) = 542 N \\

net force = N [1]

(c) Given that the sport car make a completely inelastic collision with the stationary lorry of mass 2500 kg.

(i) Explain what is meant by a completely inelastic collision.

[2]

A completely inelastic collision is one in which the 2 bodies move with a common velocity after collision and the total kinetic energy of the system before and after collision is not conserved.


16 For Examiner’s

Use (ii) Calculate the velocity of the car right after collision, stating any assumption made.

velocity = m s-1 [3] (iii) The airbag in the sport car is deployed almost immediately after the collision.

Explain how the airbag help to minimize the injuries to the front seat passenger.

[2] (d) After the accident, the sports car of mass 1500

kg had to be towed by a 2000 kg lorry up a slope at a constant speed of 5.0 m s-1 as shown in Fig. 6.3. The power P delivered by the lorry is 55 kW.

5.0 ms-1

10o

The airbag helps to increase the time of impact and by Newton 2nd law, F = Δp/t, this will greatly reduce the force of impact on the passenger.

∑pinitial = ∑pfinal (1500)(29.1) = (1500+2500)(v) v = 10.9 m s-1

Fig. 6.3 (i) By considering the sports car and the lorry as a whole system, find the rate of

increase of the gravitational potential energy of the system.

Rate of increase of GPE = mgvy = (3500)(9.81)(5.0sin10o) = 29 800 J

rate of increase of GPE = J s-1 [2] (ii) Using the principle of conservation of energy, show that the total resistive force,

fR acting on the whole system (sports car + lorry) is approximately 5000 N.

Power delivered = Rate of increase of GPE + rate of work done against fR 55 000 = 29800 + fR(5.0) fR = 5000 N

[2]

NYJC 2010 8866/02/PRELIM/10

17 For Examiner’s

Use (iii) Hence determine the driving force, F acting on the lorry, explaining your answer.

driving force = N [2] 7 The diagram below shows visible light waves spreading through a single slit a before

spreading at slits b and c.

S1

S2Error! Not a valid link. screen Image seen

D

Y

M

N

∑F = 0 F - mgsinθ - fR = 0 F = (3500)(9.81)(sin10o)+ 5000 = 11 000 N

on screen (a) State the name of this experiment.

[1] (b) With reference to the waves spreading from the slits b and c, explain why interference

occurs only where waves from both sources overlap.

[2]

Young’s Double Slit experiment

Interference is the result of superposition of two wavetrains, thus will

only occur where there are waves from both sources.

(c) Explain what diffraction is, and describe the part played by diffraction in this experiment.

[2]

Diffraction is the spreading of light waves past an opening. Diffraction

from b and c ensures that waves from two sources meet so that

interference can occur. NYJC 2010 8866/02/PRELIM/10 [Turn over

18 For Examiner’s

Use (d) Label one part of the screen view where destructive interference has occurred with the letter D.

[1] (e) Explain in detail why constructive interference occurs at N.

[2]

Constructive interference occurs because the path difference between

aN and bN is 2λ. The waves will meet in phase, and thus the result of

superposition is reinforcement: the resultant amplitude is the sum of

the individual amplitudes (f) State a condition necessary for observable interference, and explain how this

experiment ensures that the condition is met.

[2]

Coherence of the sources is necessary for observable interference. Slit

a is used to spread light from the same source to b and c so that they

are coherent sources.

OR The superposing waves must be of the same amplitude. Making slit (g) The monochromatic light used in this experiment has a wavelength 589 nm. The

distance between S1 and S2 is 0.200 m while the distance between S2 and the screen is 2.5 m. The distance between slits b and c is 0.80 mm.

Calculate the distance between two consecutive bright lines on the screen.

)λ -9

-3-3

D (589x10 ) (2.5)x = = = 2.9 x 10 ma (0.8 x 10

distance = m [2] (h) If a piece of plastic is placed in front of slit b, the light waves from b will be caused to

slow down, without any change in frequency. Some of the wave energy will be absorbed by the plastic as well.

(i) State how the wavelength of the wave from b will change.

[1]

The wavelength will be smaller (from v = f λ)

(ii) State how the amplitude of the wave from b will change. NYJC 2010 8866/02/PRELIM/10

19 For Examiner’s

Use

[1]

The amplitude will be smaller.

(iii) Based on your answer in (h)(i), predict whether there will be more or fewer

waveforms in the plastic piece as compared to the number of waveforms in an equal thickness of air.

[1]

There will be more waveforms in the plastic piece.

(iv) Using your answers in (h)(ii) and (iii), explain how the image on the screen will

change, in terms of position, separation and contrast, when a piece of plastic is placed in front of slit b.

[5]

Because the amplitude of one wavetrain is smaller, the amplitude

of constructive interference would be smaller while the amplitude

of destructive interference would be bigger, so the contrast

between the fringes would be smaller.

The separation of the fringes remains unchanged.

Because there are more waveforms in the plastic piece than in the

same thickness of air, the centre of the interference pattern (where

there are exactly the same number of waveforms between both the

sources and the centre) would be nearer the side X.


20 For Examiner’s

Use 8 Electromagnetic radiation is incident normally on the surface of a metal. Electrons are emitted from the surface and these are attracted to a positively charged electrode, as shown in Fig. 8.

electrode

evacuated enclosure

metal surface μA

electromagnetic radiation

Fig. 8

(a) Name the effect which gives rise to the emission of the electrons.

Photoelectric effect. (b) State a word equation, base on the principle of conservation of energy, which describes this

effect Energy of a photon is equal to the sum of the minimum energy required to remove an

electron from the metal surface and the maximum kinetic energy of the electron emitted.

(c) The current recorded on the mircroammeter is 2.1 μA. Calculate the number of electrons

emitted per second from the surface. I = (N/t) e (N/t) = 2.1 x 10-6/ 1.60 x 10-19 = 1.31 x 1013 s-1 (d) The incident radiation has wavelength 240 nm. Show that the energy of a photon incident on

the surface is 8.28 x10-19 J.

hf = hc/λ = 6.63 x 10-34 x 3.00 x 108 / 240 x 10-9 = 8.28 x10-19 J

NYJC 2010 8866/02/PRELIM/10

21 For Examiner’s

Use (e) The intensity of the incident radiation is 8.2 x 103 W m-2. The area of the surface is 2.0 cm2. Calculate (i) the power of the radiation incident on the surface, power = I A = 8.2 x 103 x 2.0 x 10-4 = 1.64 W (ii) the number of photons incident per second on the surface. (N/t) hf = power N/t = 1.64 / 8.28 x10-19 = 1.98 x 1018 s-1 (iii) Hence determine the ratio number of electrons emitted per second number of photons incident per second = 1.31 x 1013/ 1.98 x 1018 = 6.62 x 10-6

ratio =…..……………. [1]

(f) Comment on your answer to (e) (iii).

Very few photons successfully emit an electron.

(g) When the wavelength of the radiation is gradually increased to 310 nm, the reading in the

microammeter just drops to zero. Explain this phenomenon and calculate the maximum kinetic energy of the electrons emitted from the metal surface when the wavelength of the radiation remains at 240 nm.

The wavelength 310 nm is the threshold wavelength [1], above which the energy of the

photon is not enough to remove an electron to the surface of the metal. [1] Hence no current is detected.


22

NYJC 2010 8866/02/PRELIM/10

For Examiner’s

Use hf = hfo + ½ mvmax2

½ mvmax

2 = 8.28 x10-19 - hc/λo = 8.28 x10-19 - 6.63 x 10-34 x 3.00 x 108 / 310 x 10-9 = 8.28 x10-19 – 6.40 x10-19 = 1.87 x10-19 J (h) (i) Calculate the momentum of the photon given in (d). [1] p = h / λ = 6.63 x 10-34 / 240 x 10-9 = 2.76 x 10-27

N s

(ii) If there are altogether 1.5 x 1018 photons striking onto the metal surface per second and are

all absorbed, determine the force exerting on the metal surface. Show your working clearly.

By Newton’s 2nd law, force on photon

18 27

91.5 10 (0 2.76 10 ) 4.14 101.0

N p x x xF x Nt

−−Δ −

= = = −Δ

By Newton’s 3rd law, force on metal surface = 4.14 x10-9 N

READ THESE INSTRUCTIONS FIRST Write in soft pencil. Do not use staples, paper clips, highlighters, glue or correction fluid. Write your name, class and index number on the Answer Sheet in the spaces provided. There are thirty questions on this paper. Answer all questions. For each question there are four possible answers A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet. Read the instructions on the Answer Sheet very carefully. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet.

PIONEER JUNIOR COLLEGE Preliminary Examination

PHYSICS 8866/01Higher 1 Paper 1 Multiple Choice 23 September 2010 1 hour Additional Materials: Multiple Choice Answer Sheet


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2

Data speed of light in free space, ms–1 81000.3 ×=c elementary charge, C 191060.1 −×=e the Planck constant, Js 341063.6 −×=h unified atomic mass constant, kg 271066.1 −×=u rest mass of electron, kg 311011.9 −×=em rest mass of proton, kg 271067.1 −×=pm acceleration of free fall, 81.9=g ms–2 Formulae

uniformly accelerated motion, 2

21 atuts +=

asuv 222 += work done on/by a gas, VpW Δ= hydrostatic pressure, ghp ρ=

electric potential, r

QVoπε4

=

resistors in series, ...21 ++= RRR resistors in parallel, .../1/1/1 21 ++= RRR

3

1 Forces of 3 N, 4 N, and 5 N are in equilibrium. What is the angle between the 3 N and 5 N forces?

A 37 o B 53 o C 127 o D 143 o

2 Which estimate is unrealistic? A The power of a hair dryer is 150 W. B The kinetic energy of a running man is 2000 J.

C The weight of a can of soft drink is 4 N. D The density of ice is 900 kg m3. 3 A radio aerial of length L, when the current is I, emits a signal of wavelength λ and power P. These quantities are related by

22 ⎟

⎠⎞

⎜⎝⎛=λ

Ι LkP

where k is a constant. What unit, if any, should be used for the constant k? A no unit B volt C watt D ohm 4 An object is projected at an angle to the horizontal in a gravitational field and it follows a parabolic path, PQRST. These points are positions of the object after successive equal time intervals, T being the highest height reached. The displacements PQ, QR, RS and ST A are equal. B decrease at a constant rate. C have equal horizontal components. D increase at a constant rate.

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4

5 A stone slides across an icy surface and travels a distance x in time t while undergoing uniform deceleration. Which of the following pairs of quantities would give a straight line graph when plotted to represent the motion of the stone?

A x and 21t

B x and t1

C tx and t

D 2tx and t

6 An aeroplane, flying in a straight line at a constant height of 500 m with a speed of 200 m s-1, drops an object. The object takes a time t to reach the ground and travels a horizontal distance d in doing so. Taking g as 10 m s-2 and ignoring air resistance, which one of the following gives the values of t and d? t d A 25 s 10 km B 25 s 5 km C 10 s 5 km D 10 s 2 km 7 What is a suitable unit for the impulse of a force? A N B C D N m N s 1N s−

5

8 A small mass moving at a velocity of u1 collides head-on with a large mass moving at a velocity of u 2 in the opposite direction.

The collision is elastic. After the collision, both masses move to the left. The small mass has a velocity of 11

and the large mass has a velocity of 1 1m s− 1m s− . Which pair of values of u1 and u 2 is possible?

u1 u 2 A 2 1m s− 12 1m s−

B 4 1m s− 6 1m s−

C 9 1m s− 3 1m s−

D 11 1m s− 1 1m s−

9 A mass accelerates uniformly when the resultant force acting on it A is zero. B is constant but not zero. C increases uniformly with respect to time. D is proportional to the rate of change of momentum of the mass.

u1 u2 large mass small mass

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6

10 The tension in a spring of natural length is first increased from zero to , causing the length to increase to . The tension is then reduced to , causing length to decrease to as shown in the diagram.

ol 1T

1l 2T

2l Which area of the graph represents the work done by the spring during this reduction in

length? A MLP B MNQP C MNSR D MPLU 11 A proton is projected horizontally into the vertical electric field in the space between two

horizontal charged plates. The proton follows a curved path as shown.

There are changes to the proton’s electric potential energy and to its gravitational potential energy.

Which row correctly identifies these changes?

electric potential energy

gravitational potential energy

A decreases decreases

B decreases increases

C increases decreases

D increases increases

tension

0

1T

length

2T

ol 2l 1lL

N

M

P Q

S

R U

V

+

−

electric field

proton path

7

12 A uniform ladder of weight 100 N rests against a smooth wall at X and a rough ground at Z. N is the normal contact force of the wall at X and R is the total force at the ground at Z. The height XY is 8.0 m and length ZY is 6.0 m.

Z

X N

8.0 m

6.0 m

R What is the value of R? A 37.5 N B 50.0 N C 107 N D 154 N 13 An object of mass m passes a point X with a velocity v and slides up a frictionless incline to stop at a point Y which is at a height h above X.

Y

A second object of mass m21 passes X with a velocity of v

21 . To what height will it rise?

A h41

B h21

C 21 h

D h

X

v h

100 N Y

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14 A spring stretches 0.015 m when a force of 10 N acts on it. Calculate the elastic potential energy stored in the spring when a force of 0.40 N is exerted on the spring.

(Assume that the spring obeys Hooke’s Law.) A 0.9 x 10-4 J B 1.2 x 10-4 J C 2.0 x 10-4 J D 2.2 x 10-4 J 15 The graph below shows how the potential energy, U varies with displacement, x for a body in a uniform field. What is the force experienced by the body in this field? A 6.0 × 10–6 N B 1.5 × 10–2 N C 3.0 × 103 N D 6.0 × 108 N 16 A plane wave of amplitude A is incident on a surface area S placed so that it is

perpendicular to the direction of travel of the wave. The energy per unit time intercepted by the surface is E.

The amplitude of the wave is reduced to A/2 and the area of the surface is increased to

2S. How much energy per unit time is intercepted by this surface? A 4E B E C 2E D E/2

U / 10–4 J

x / m

9.0

0 0.060

9

17 The length l of an air column is slowly increased from zero while a note of constant frequency is produced by a tuning fork placed in front of it. Air Column When l reaches 20 cm the sound increases greatly in volume. What is the wavelength of the sound wave produced by the tuning fork? A 20 cm B 40 cm C 80 cm D 100 cm 18 Sound waves can be detected behind an obstacle rather than light waves because A sound is a pressure wave whereas light is an electromagnetic wave. B sound travels much more slowly than light. C sound waves are longitudinal whereas light waves are transverse. D sound waves have a much longer wavelength than light waves. 19 Light of wavelength 630 nm falls on a pair of slits, forming fringes 3.00 mm apart on a

screen. What would the fringe spacing become if the wavelength were 420 nm? A 2.00 mm B 3.00 mm C 3.75 mm D 4.50 mm 20 The resistance of a piece of pure silicon falls rapidly as the temperature rises because A the ratio of positive to negative charge carriers increases. B the ratio of positive to negative charge carriers decreases. C the total number of charge carriers increases with temperature. D the charge carriers can move more easily at higher temperatures.

Tuning Fork

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l

piston

10

21 The resistance of a certain circuit element is directly proportional to the current passing through it. When the current is 1.0 A the power dissipated in the element is 6.0 W. What is the power dissipated when the current is raised to 2.0 A?

A 12 W B 24 W C 48 W D 72 W 22 Three identical cells each having an e.m.f. of 1.5 V and internal resistance of 2.0 Ω are

connected in series with a 4.0 Ω resistor R, firstly as in circuit (i), and secondly as in circuit (ii).

R R

Circuit (i) Circuit (ii)

What is the ratio power in in circuit (i)

power in in circuit (ii)RR

?

A 3.0 B 5.4 C 7.2 D 9.0

11

23 In the diagram below, the variable resistor R can be adjusted over its full range from zero to 107 Ω.

0 to 107 Ω

104 Ω

Q P

R

10 Ω What are the approximate limits for the resistance between P and Q? A 10 Ω and 104 Ω B 10 Ω and 107 Ω C 10 Ω and 1011 Ω D 104 Ω and 107 Ω 24 Three resistors are connected as shown below. The points X and Y are connected to a

source of direct current. I2 R2

X R1

I3

I1 R3

Y

The ratio 1

3

II

is

A 3 1

1

R RR+

.

B 2 1

1

R RR+

.

C 2 3

1 2 3( )R R

R R R+.

D independent of . 1R

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25 A cell of e.m.f. 2.0 V and negligible internal resistance is connected to the network of resistors shown.

V1 is the potential difference between S and P. V2 is the potential difference between S

and Q. What is the value of V1 − V2? A +0.50 V B +0.20 V C −0.20 V D −0.50 V 26 A small coil lies in a large coil coaxially. Both coils are horizontal and carry the same amount of current flowing in a clockwise direction as shown below. Which of the following statements is true as applied to the outer coil? A The outer coil will be stretched outwards. B The outer coil will be compressed inwards. C The outer coil experiences a torque about the horizontal axis. D The outer coil experiences a downward force along the plane of the coil.

5.0 kΩ

2.0 V P

5.0 kΩ

S

Q

2.0 kΩ

3.0 kΩ

13

27 The diagram below shows a solenoid carrying a current.

X

axis

Y In what direction should a straight conductor be placed within solenoid such that the magnetic force acting on it is out of the plane of the paper? A in the XY direction, current flowing from X to Y B in the XY direction, current flowing from Y to X C along the axis, current flowing from left to right D along the axis, current flowing from right to left 28 A straight conductor rests in the space between two arms of a ferromagnetic core

(presently unmagnetized). After the switch has been closed for a while, in what direction is the magnetic force acting on the conductor?

C

A D

B

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14

29 The figure below shows the first four energy levels of an electron in a certain atom. The transition from E3 to E1 produces a green line. Which transition could give rise to a blue line? A E2 to E1 B E3 to E2 C E4 to E1 D E4 to E2 30 When a metal is irradiated with monochromatic radiation, electrons are emitted. Which of

the following will increase if the frequency of the radiation is increased? A The threshold frequency of the metal. B The rate of emission of electrons. C The stopping potential of the electrons. D The maximum speed of the photons.

E4 E3

E2

E1

End of paper

1

PIONEER JUNIOR COLLEGE Preliminary Examination

PHYSICS 8866/02Higher 1 Paper 2 Structured questions 16 September 2010 2 hoursCandidates answer on the Question Paper. No additional materials are required.

READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Section A Answer all questions. Section B Answer any two questions.


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Name Class Index Number


Section A 1 At the end of the examination, fasten all your work

securely together. The number of marks is given in brackets [ ] at the end of each question or part question.

2 3 4 5 6 Section B 7 8 9

Total

2

Data speed of light in free space, ms–1 81000.3 ×=c permeability of free space, Hm–1 7

0 104 −×π=μ elementary charge, C 191060.1 −×=e the Planck constant, Js 341063.6 −×=h unified atomic mass constant, kg 271066.1 −×=u rest mass of electron, kg 311011.9 −×=em rest mass of proton, kg 271067.1 −×=pm the Avogadro constant, mol–1 231002.6 ×=AN gravitational constant, Nm2 kg–2 111067.6 −×=G acceleration of free fall, 81.9=g ms–2 Formulae


21 atuts +=

asuv 222 += work done on/by a gas, VpW Δ= hydrostatic pressure, ghp ρ= resistors in series, ...21 ++= RRR resistors in parallel, .../1/1/1 21 ++= RRR

3

Section A

Answer all the questions in this section. 1 When a solid is heated, the energy required is given by the expression gain in energy = mass × c × temperature rise, where c is a constant. (a) Name the quantities in the expression that are SI base quantities. ....................................................................................................................................... ................................................................................................................................. [2] (b) Express, in terms of SI base units, the units of (i) energy, units of energy = ........................................ [2] (ii) the constant c. units of c = ........................................ [2]

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4

2 (a) Explain the meaning of the term wavelength and frequency in a progressive wave.

....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ................................................................................................................................. [2]

(b) State two differences between a progressive wave and a stationary wave.

....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ................................................................................................................................. [2]

(c) The power of a household torchlight is 8.0 W. Assuming that the light is a point

source, calculate the intensity of the light at a distance of 1.5 m away from the torch. intensity = ........................................ W m-2 [1]

5

3 (a) Define magnetic flux density.

....................................................................................................................................... ....................................................................................................................................... ................................................................................................................................. [2] (b) Fig 3.1 shows the simplest motor in the world called the homopolar motor, which was

first invented by Michael Faraday. The disc is a conducting magnet, pivoted at its centre. The disc rotates when a current is passed through it.

Conducting Magnetic disc

Fig. 3.1

(i) State the direction of the magnetic force on the disc.

direction = ........................................ [1]

(ii) Suggest two methods in which the disc can be made to move faster. .................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [2]

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4 Fig 4.1 shows the momentum against time graphs for two colliding lorries A and B.

30 B momentum/

103 kg m s–1

20

A

10

0 0

1.0 2.0 3.0 4.0 5.0 time/ s

Fig. 4.1 The masses of lorries A and B are 2000 kg and 4000 kg respectively. (a) Explain why the gradients of the graphs during the collision have opposite signs. ....................................................................................................................................... ................................................................................................................................. [1]

(b) Calculate the force acting on lorry B during the collision. force = ........................................ N [2]

(c) Calculate the change in the kinetic energy of the system and hence deduce the type of collision.

change in kinetic energy = ........................................ J [3] type of collision: ……………..................................................................................... [1]

7

BLANK PAGE

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8

5 A microwave transmitter emits waves which are reflected from a metal plate, as shown in Fig. 5.1. A receiving aerial is placed between XY to detect the stationary waves formed.

receiving aerialX Y

45 cm

metal plate

transmitter

Fig. 5.1 (a) Explain how the stationary waves are formed.

....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ................................................................................................................................. [2]

(b) The receiving aerial is moved from one node at X through 6 antinodes to another

node at Y, a distance of 45 cm.

(i) Sketch the stationary wave pattern formed between X and Y.

X Y [1] (ii) On your diagram in (b)(i), label two points P and Q which are in phase with each

other, where the amplitude at P is larger than that at Q. [1] (iii) On the same diagram, label a point R which is in antiphase with point Q, and has

the same amplitude as that at Q. [1]

9

(iv) Determine the frequency of the waves. frequency = ........................................ Hz [2] (v) The receiving aerial moves along XY with a speed of 5.0 cms−1. Calculate the

rate at which nodes in this standing wave are passed by the moving receiver. rate = ........................................ s−1 [2]

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10

6 The wavelength λ of a series of lines in an emission spectrum of lithium are listed in Table 6.1.

n λ / nm ( )2041.0n

1−

1m/1 −

λ

2 670.8

3 323.3

4 274.2

5 256.2

6 247.6

Table 6.1 According to theory, the wavelengths are given by the equation:

( ) ( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡

−−

+= 22 0.041n

1s1

1Rλ1 ,

where n = 2, 3, 4, 5, 6 … … as shown in Table. 6.1. R is 1.097 x 107 m-1, and s is a constant. (a) Complete the last two columns in Table. 6.1. [2]

(b) Rearrange the equation so that it may be used to plot a straight line graph to find the constant s. Write down expressions for the gradient and y-intercept of the straight line graph.

gradient = ........................................ [1] y-intercept = ........................................ [1]

11

(c) Plot a straight graph on Fig. 6.2 using the values from Table 6.1.

Fig. 6.2 [1] (d)(i) Calculate the gradient of the graph in Fig. 6.2. gradient = ........................................ [1]

(ii) Discuss how well the experimental results in Table 6.1 fit the theory.

.................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [2]

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12

Section B

Answer two questions from this section. 7. (a) A car accelerates uniformly from rest along a straight line. (i) On Fig. 7.1, sketch a graph showing how the displacement of the body varies

with time. [1]

Fig. 7.1 (ii) Explain how the instantaneous velocity of the car is obtained from a graph of

displacement against time. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [2]

(iii) The average power delivered by the engine of the car of mass 1200 kg is 90 kW. Calculate the time in which the car could accelerate from rest to 30 m s-1.

time = ........................................ s [2]

Displacement

Time

13

(b) When the car is travelling at 30 m s-1, the car driver drops a ball from the car window, 1.0 m vertically from the ground.

Assuming no air resistance, calculate

(i) the time taken for the ball to reach the ground,

time taken = ........................................ s [2]

(ii) the horizontal distance travelled by the ball before it hits ground.

horizontal distance = ........................................ m [2] (iii) the vertical component of velocity at the instant the ball hits the ground.

vertical component of velocity = ........................................ m [2]

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14

(iv) On Fig 7.2 and Fig 7.3 sketch graphs to show how the vertical component (vy) and horizontal component (vx) the ball’s velocity vary with time t until it reaches the ground. [2]

vy vx

0 0 t

t Fig. 7.2 Fig. 7.3 (v) Explain how your answer to (b)(i) would change, if the driver throw the ball

horizontally from the car window, instead of dropping it.

.................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [2]

(c) Fig. 7.4 shows a person doing a bungee jump.

Fig. 7.4

15

The bungee rope has negligible mass and it is assumed to obey Hooke’s law. The bungee rope is secured to the feet of the person. The person leans over a bridge and drops vertically downwards. You may assume that air resistance is negligible.

(i) Describe the energy changes taking place from the instant the person leaves the bridge until the bungee rope is fully extended.

.................................................................................................................................. ..................................................................................................................................

.................................................................................................................................. ..................................................................................................................................

.................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [3]

(ii) Explain why it would be extremely dangerous to have a bungee rope that is much

stiffer.

.................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [2]

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16

8 (a) Electromotive force (e.m.f.) and potential difference (p.d.) may both have the volt as a unit.

(i) Define the volt.

...................................................................................................................................

............................................................................................................................ [1]

(ii) By reference to energy transfers, distinguish between e.m.f. and p.d.

e.m.f. .........................................................................................................................

................................................................................................................................... p.d. ......................................................................................................................... ............................................................................................................................ [2]

(b) A cell of e.m.f. E and internal resistance r is connected in series with a resistor R, as

shown in Fig. 8.1. A current I passes through R. An ideal voltmeter connected across R shows a reading V.

rE

R

V Fig. 8.1

(i) Using answers from (a)(ii), show that V is given by V E r= − I [2]

17

(ii) Hence sketch a graph showing how the potential difference across R varies with the current I passing through R.

[1] (iii) State the condition when the voltmeter reading is equal to E.

............................................................................................................................ [1] (c) A cell of e.m.f. 1.5 V and internal resistance 0.25 Ω is connected in series with a

resistor R, as shown in Fig. 8.2.

Fig. 8.2 The resistor R is made of metal wire. A current of 0.24 A passes through R for a time of 5.0 minutes. An ideal voltmeter is

connected across R. (i) Calculate

1. the total energy transferred by the cell, energy = ........................................ J [2] 2. the resistance of R, resistance = ........................................ Ω [2]

R

0.25 Ω1.5 V

V

0.24 A

V

I

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18

3. the energy transferred in the resistor R. energy = ........................................ J [2]

(ii) If the voltmeter is non-ideal, state and explain the change to the voltmeter reading.

...................................................................................................................................

...................................................................................................................................

............................................................................................................................ [2]

(d) A cell of e.m.f. 3.0 V and negligible resistance is connected in series with a fixed

resistor of resistance 2000 Ω and a thermistor, as shown in Fig. 8.3.

Fig.8.3 The thermistor has resistance 4000 Ω at 0 °C and 1800 Ω at 20 °C.

(i) Determine the potential difference across the thermistor 1. at 0 °C, potential difference = ........................................ V [1] 2. at 20 °C, potential difference = ........................................ V [1]

2000 Ω

3.0 V

19

(ii) In one particular application of the circuit of Fig. 8.3, it is desired that the potential difference across the fixed resistor should range from 1.2 V at 0 °C to 2.4 V at 20 °C.

Determine whether, by substituting a different fixed resistor in the circuit of Fig. 8.3, it is possible to achieve this range of potential differences.

[3]

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20

9 (a) State what is meant by photoelectric effect.

....................................................................................................................................... ....................................................................................................................................... ................................................................................................................................. [1]

(b) A hydrogen lamp emits light of frequency 5.8 x 1014 Hz at a rate of 0.50 W and the

light falls on the cathode of a photocell as shown in Fig. 9.1. The ammeter reads a current of 4.0 μA and the work function of the metal is 3.0 x 10-19 J. You may assume this current is due to all photoelectrons emitted from the photoelectric effect.

Fig. 9.1 (i) Calculate 1. the energy of the photon.

energy = ..................................... J [2]

2. the number of photons leaving the source per second.

photons leaving source per second = ..................................... s-1 [2]

A

V

E C

light

21

3. the percentage of photons falling on the surface that produces photoelectrons. percentage of photons = ..................................... % [3]

4. the de Broglie wavelength of the most energetic photoelectrons emitted. wavelength = ..................................... m [3]

(ii) The intensity of the photons falling on the cathode of a photocell is doubled. State and explain what will be observed on the ammeter that records the photocurrent in the external circuit.

.................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [2]

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22

(c) Fig. 9.2 shows a simplified representation of the 5 lowest energy levels of the outermost electron in an atom.

(i) State and explain which possible transitions you would expect to observe if the

atom is bombarded with 1. an electron of energy 12.3 eV.

.................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [2]

2. a photon of energy 12.3 eV. ..................................................................................................................................

.................................................................................................................................. .................................................................................................................................. ........................................................................................................................... [2]

n = 5 n = 4

n = 3

n = 2

n = 1

E / eV

-13.6

-3.4

-1.5

-0.85 -0.54

Fig. 9.2

23

(ii) Calculate the wavelengths of the light emitted due to the transitions in (c)(i). wavelengths = ............................................................................................... [3]

End of Paper

Answers to JC2 Preliminary Examination Paper 1 (H1 Physics) 1 C 9 B 17 C 25 C 2 A 10 B 18 D 26 B 3 D 11 A 19 A 27 A 4 C 12 C 20 C 28 D 5 C 13 A 21 C 29 C 6 D 14 B 22 D 30 C 7 C 15 B 23 A 8 B 16 D 24 D Suggested Solutions: 1

α

5 N 5 N

θ

4 N 3 N 3 N sin α = 4/5, α = 53.13o

But angle between 3 N and 5 N forces = θ = 180o – 53.13o = 126.86o Answer: C 2 Hair dryer: uses voltage of 240 V, if power is 150 W, current is 0.625 A (low current,

heating coils do not heat up properly) Running man: assuming average mass of 70 kg and a speed of 8 ms–1 (fastest man on

earth runs 100 m in 9.69 s), gives a KE of 2240 J. Vol. of a canned drink ~ 330 ml ~ 400 g in mass (include mass of can and additives

other than water) Weight = 0.400 x 9.81 ~ 3.9 N Ice is less dense than water (density = 1000 kg m–3) Answer: A 3 from equation,

22

2

2 2

LP k

PkL

Ιλ

λΙ

⎛ ⎞= ⎜ ⎟⎝ ⎠

=

Units of 2

2 2 2

W m WA m A

k = =

Using P , units of k = VΙ= V ΩA=

2

. Answer: D 4. Horizontal component of velocity remains constant in the parabolic motion. Hence, the horizontal displacement is the same. Ans: C 5.

at

21u

tx

at21utx 2

+=

+=

A plot of tx against t will yield a straight line graph.

Ans: C 6. Consider y-direction,

s10t

t)10(21500

gt21s

at21uts

2

2y

2y

=

=

=

+=

Consider x-direction,

km2)10(200tus xx === Ans: D 7 Impulse of a force = Ft Units of impulse = N s Answer: C 8

u1 u2 large mass small mass

Taking to the left as positive, 1

2 1 1 11 10 m sv v −− = − = − Since

(note: vector equation) 1 2 2 11

1 2 10 m s

u u v v

u u −

− = −

− = − Option A: 1

1 2 2 12 14 m su u −− = − − = −

1 1m s− 11 1m s−

3

Option B: 11 2 4 6 10 m su u −− = − − = − (correct)

Option C: 11 2 9 3 12 m su u −− = − − = −

Option D: 11 2 11 1 12 m su u −− = − − = −

Answer: B 9 An object accelerates uniformly = constant acceleration constant resultant force

applied on mass. Option D: Newton’s second law of motion. Answer: B 10 Work done by spring during reduction = area under the T-x graph from to . 1l 2l Answer: B 11 Upon entering the field, the proton experiences an electric force downwards. As it

accelerates downwards, its velocity increases, resulting in a gain in kinetic energy and a corresponding loss in electric potential energy. In addition, the proton experiences a decrease in height, and hence its gravitational potential energy decreases.

Answer: A 12 Taking moments about Z, total clockwise moment = total anti-clockwise moment 83100 ×=× N N 5.37=N Since the ladder is in equilibrium and all the forces formed a closed polygon (right-angle

triangle), we have 222 100+= NR N 107≈R . Answer: C 13 By conservation of energy, ½ mv2 = mgh

2

2

2vh

gvh

∝

=

The height is independent of mass.

Since the speed is v21 , the height will be

41 of the original height.

Answer: A

4

14 By Hooke’s law,

1mN015.010 −==

xFk

When F = 0.40 N, the new extension 10015.04.0

kFx ×==

m The elastic potential energy = ½ kx2

=

2

10015.04.0

015.010

21

⎟⎠⎞

⎜⎝⎛ ×⎟⎠⎞

⎜⎝⎛

= 1.2 x 10-4 J Answer: B 15

N015.006.0

0009.0==

ΔΔ

=rUF

Answer: B 16

2E

42EE

/2SEE/S

)2A(A

e)α(Amplitudareasurface

powerIntensityTherefore,

'

'2

2

2

==

=

=

=AreaSurface

PowerIntensity

Answer: D 17

cm80λ

vibrationofmodelFundamenta

column)airendcloseand(opencm204λ

=

=

Answer: C 18 Waves tend to bend round an obstacle more if its wavelength is longer than the size of

the obstacle. For the same corner, sound waves which have a longer wavelength tend to bend more than light waves which have a shorter wavelength. Hence, we cannot ‘see round corners’ but can ‘hear round corners’.

Answer: D

19 Since aDx λ

= , we have λ∝x with aD kept constant.

5

2

1

2

1

λλ

=xx

42063000.3

2=

x

mm 00.22 =x Answer: A 20 Answer: C 21 2 2( )P I R I kI kI= = = 3

36.0 (1)k= 3(2)P k= W 48P = Answer: C 22 For circuit (i)

22 4.5 4 0.81

10P I R ⎛ ⎞= = =⎜ ⎟

⎝ ⎠ W

For circuit (ii) 2

2 1.5 4 0.0910

P I R ⎛ ⎞= = =⎜ ⎟⎝ ⎠

W

Therefore, ratio = 9.0 Answer: D

23 If R = 0, effective resistance = 4

410(10 ) 1010 10

≈ Ω+

If R = 107 Ω, effective resistance 7 4

47 4

10 (10 ) 1010 10

≈ ≈ Ω+

Answer: A

24 31 2 3 3

2

RI I I I IR

= + = + 3

3 21

3 2

R RR+

=II

Therefore 1

3

II

is Independent of 1R

Answer: D

25 15.0 2.0 1.0

5.0 5.0V = =

+V

6

23.0 2.0 1.2

3.0 2.0V = =

+V

V 1 2 0.20V V− = − Answer: C 26 Current in the same direction attracts, therefore both coils attract each other. Answer: B 27 By right hand grip rule to first find the field in solenoid pointing towards the right. Then by fleming left hand rule to find position as well as direction of current. Answer: A 28 By fleming left hand rule. Tracing the way current flows in the DC circuit, the direction of the magnetic field is known. Answer: D 29 Blue has more energy than green => transit from greater energy level Answer: C 30 Increasing the frequency of radiation => Increase in the energy of photons => Increase the maximum KE of photoelectrons => A larger stopping potential is required to stop the more energetic photoelectrons Answer: C

1

Answers to JC2 Preliminary Examinations Paper 2 (H1 Physics) Suggested Solutions: No. Solution Remarks 1(a) Mass and temperature [1] each 1(b)(i) Units for energy = J

2 2

WD Force displacementJ N m

kg m s−

= ×= ×

=

[1] for correct definition of quantity [1] final answer

1(b)(ii)

12222

KsmKkgsmkgcofunits

riseetemperaturmassenergyingainc

−−−

==

×=

[[1] for correct definition of quantity [1] final answer

2(a) Wavelength is the distance between successive crests/compressions, or the distance between successive troughs/rarefactions, or the distance between any two successive points on the wave that are in phase. Frequency is the number of oscillations that pass through a given point per unit time. Frequency is the reciprocal of the

1fT

=

[2] 2 marks for meaning of wavelength and frequnecy

(b)(i) Stationary waves : Energy is not propagated Transverse waves: Energy is propagated. Stationary waves: particles in a stationary wave have varying amplitude between 2 nodes. Transverse wave: particles: Particles have fixed amplitude.

[1] [1]

(b)(ii) 2r4

8area

powerintensityπ

==

Intensity = 0.283 W m-2

[1]

3(a) Magnetic flux density is defined as the force acting on a conductor of unit length carrying unit current placed perpendicular to the magnetic field.

[2]

3(b)(i)

Force is directed into the paper. [1]

3(b)(ii) Increase the strength of the magnet or increase magnitude of current.

[2]

4(a) The gradient of the momentum-time graph represents the resultant force that acts on the object. The gradients for A and B are of opposite signs and they are in opposite directions (but of the same magnitude) according to Newton’s third law.

[1] for correct explanation using N3L

2

4(b)

3

gradient of graph of B

(28 22) 101.5

2666.67 N2700 N

dpFdt

= =

− ×=

=≈

[1] substitution to find gradient [1] final answer

4(c) 221

2 2pKE mvm

= =

Total final kinetic energy 2 2

2 2

2 2

12000 280002(2000) 2(4000)134 kJ

A B

A B

p pm m

= +

= +

=

Total initial kinetic energy

2 2

2 2

2 2

18000 220002(2000) 2(4000)141500J 141.5 kJ

A B

A B

p pm m

= +

= +

= =

Change in KE of the lorries

f iKE KE134000 141500

7500 J

= −

= −= −

Type of collision: inelastic as final KE is less than initial KE (KE is not conserved)

[1] for final KE [1] for initial KE [1] for change in KE (with -ve sign) [1] for correct type of collision

No. Solutions Remarks 5(a) Stationary waves are formed when the incident waves from

the transmitter interfere with the reflected waves, where both progressive waves are of equal amplitude, frequency and moving with the same speed.

[2] for stating waves moving in opposite direction, of equal amplitude, frequency, and speed interfering to form the stationary wave, with reference to the question

3

5(b)(i) 5(b)(ii) 5(b)(iii)

[1] for correct diagram [no mark if dotted lines are not drawn, or that shape is uneven] [1] for correct labelling of P and Q [1] for correct labelling of R

5(b)(iv) 453 =λ 15=λ cm

Since λfv = ,

28 1015100.3 −××=× f 9100.2 ×=f Hz

[1] for correct wavelength [1] for correct substitution and answer

5(b)(v) The distance between consecutive nodes is λ

21 ence, the

rate at which nodes are detected is

X Y P Q R

. H

λ21

detectorvf = ,

5.70.5

=f

67.0≈f s−1

[1] for correct expression and substitution [1] for correct answer

6(a)

n λ / nm ( )2041.0n

1−

1m/1 −

λ

2 670.8 0.261 1.491 x 106

3 323.3 0.114 3.093 x 106

4 274.2 0.0638 3.647 x 106

5 256.2 0.0407 3.903 x 106

6 247.6 0.0282 4.039 x 106

[2]

6(b) ( ) ( )22 s1

R041.0n

1R1+

+−

−=λ

Gradient of graph = -R

y-intercept of graph = ( )2s1

R+

4

6(c)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.05 0.1 0.15 0.2 0.25 0.3

[1]

6(d) The experimental data forms a straight-line graph. Gradient of graph = -1.10 x 107. Hence R = 1.10 x 107 m-1. This agrees well with the theoretical value R = 1.097 x 107 m-1

[1]

7(a)(i)

[1]

7(a)(ii) The instantaneous velocity can be obtained from the gradient of the graph since velocity is defined as the rate of change of displacement.

Displacement

Time

5

7(a)(iii)

s00.610x90

)30)(1200(21

t

Ptmv21

3

2

2

==

=

[1] [1]

7(b)(i) Consider vertical direction,

s452.081.9)1(2

gs2t

gt21s

at21uts

2

2

===

=

+=

[1] [1]

7(b)(ii) Sx = u t = (30) (0.45152) = 13.5 m

[1] [1]

7(b)(iii) vy=at = (9.81)(0.4515) = 4.43 m s-1

[1] [1]

7(b)(iv)

[1] Correct sharp of graphs. [1] Correct values at axes.

vy/ ms-1

t/s0

4.43

0.452

vx/ ms-1

t/s 0

30

0.452

6

7(b)(v) The answer to b(i) will remain unchanged. The ball has the same initial vertical velocity (0 ms-1) and the vertical acceleration experienced is the same as well.

[1]

7(c)(i) When the person is on the bridge, he possesses maximum gravitational potential energy. Once he falls off the bridge, he loses gravitational potential energy and gains kinetic energy. When the rope is stretched longer than the original length of the rope, there is elastic potential energy in the rope. The loss in gravitational potential energy and loss in kinetic energy at this stage is converted to a gain elastic potential energy. When the rope is fully stretched, the elastic potential energy is at its maximum, the kinetic energy is zero and the gravitational potential energy is the minimum.

[1] [1] [1]

7(c)(iii) When the rope is much stiffer, the spring constant is larger. Since Tension in rope = spring constant x extension of rope, a large tension is exerted on the person by the rope when the rope stretches. This causes a large deceleration on the person and may cause injuries. The time taken for change in momentum is shorter; therefore there is larger resultant force.

[1] [1]

8(a)(i) One volt (V) is the potential difference between two points in

a circuit in which 1 joule of energy is converted when one coulomb passes from one point to the other.

[1]

8(a)(ii) The e.m.f. of a cell (and that of other sources of electrical energy) can be defined as the energy converted into electrical energy from other forms (e.g. chemical, mechanical) when unit charge passes through the cell. OR The e.m.f. of a cell is defined as the energy transferred by a cell in driving unit charge round a complete circuit. The p.d. between two points in a circuit or across a conductor is defined as the energy converted from electrical energy to other forms of energy when unit charge passes from one point to the other.

[1] [1]

8(b)(i)

e.m.f. of cell, WEQ

=

potential difference across resistor R, '' WV

Q=

potential difference across internal resistor r, '''' WV

Q=

By conservation of energy, energy supplied by cell = energy dissipated by R + energy dissipated by r

' 'W W W= + '

[1] for showing equations of the

form WVQ

=

[1] for forming equation showing conservation of

7

' 'EQ V Q V Q= + ''

' 'E V V= +

E IR Ir= + E V Ir= + V E Ir= −

energy

8(b)(ii)

[1] for correct graph shape and y-intercept E

8(b)(iii) If the circuit is open, voltmeter reading is equal to E. OR If the cell has no internal resistance, voltmeter reading is equal to E.

[1] for correct condition

8(c)(i)1 Total energy transferred by cell = EQ = 1. 5(0.24)(5)(60) = 108 J

[1] for correct substitution [1] for correct answer

8(c)(i)2 E = I (R + r) 1.5 = 0.24 (R + 0.25) R = 6.0 Ω


8(c)(i)3 Energy transferred in resistor R = I2Rt = 0.242 (6.0)(5)(60) = 104 J


8(c)(ii) Voltmeter reading will be lesser. The effective resistance across R and the voltmeter is lesser. The p.d. across them is therefore lesser.

[1] [1]

8(d)(i)1 4000 3.0 2.02000 4000

⎛ ⎞ =⎜ ⎟+⎝ ⎠ V

[1]

8(d)(i)2 1800 3.0 1.422000 1800

⎛ ⎞ =⎜ ⎟+⎝ ⎠ V

[1]

8(d)(ii) 3.0 1.2

4000R

R⎛ ⎞ =⎜ ⎟+⎝ ⎠

R = 2670 Ω

[1] for R at 0 °C

V

E

I

8

3.0 2.41800R

R⎛ ⎞ =⎜ ⎟+⎝ ⎠

R = 7200 Ω Therefore, there is no single value of R that satisfies both conditions.

[1] for R at 20 °C [1] for conclusion

9(a) Photoelectric effect is the emission of electrons from a metal

surface when it is exposed to electromagnetic radiation of sufficiently high frequency.

[1]

(b)(i)1 E = hf = (6.63 x 10-34)(5.8 x 1014) = 3.8454 x 10-19 J = 3.8 x 10-19 J


2 E

tnP

p⎟⎠⎞

⎜⎝⎛=

19108454.350.0

−×=⎟

⎠⎞

⎜⎝⎛

ptn

118103.1 −×=⎟⎠⎞

⎜⎝⎛ s

tn

p


3 ( ) 619 100.4106.1 −− ×=×⎟⎠⎞

⎜⎝⎛

etn

13105.2 ×=⎟⎠⎞

⎜⎝⎛

etn

%100×⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

=

p

e

tntn

percentage

%100103.1105.2

18

13

×××

=

= 1.92 x 10-3 %

[1] [1] [1]

4 maxKEhf += φ

1919max 100.3108454.3 −− ×−×=KE

19max 108454.0 −×=KE

192 108454.021 −×=mv

( ) 192

108454.02

−×=m

mv

( )( )1931 108454.01011.92 −− ××=p

[1] [1]

9

ph

=λ

( )( )1931

34

108454.01011.92

1063.6−− ××

×=λ

m91069.1 −×=λ

[1]

(ii) The ammeter reading will be doubled. When the intensity of the photons falling on the cathode of a photocell is doubled, this doubles the rate of photoelectrons emitted and as a result, the photocurrent is doubled.

[1] [1]

(c)(i)1 Electron in atom absorbs 10.2 eV of energy and transits from n = 1 to n = 2 state or absorbs 12.1 eV of energy and transits from n = 1 to n = 3 state. These will lead to line spectra produced due to transitions from n = 3 to n = 1, n = 2 to n = 1 and n = 3 to n = 2. This is because electron can lose any amount of its kinetic energy to the atom.

[1] for correct transitions [1] reason

2 No transition will be observed. When a photon hits an atom, the photon can only be absorbed in full (or not at all). As such, it can only be absorbed if its energy is equal to the difference in energy levels. 12.3 eV does not correspond to the difference of any 2 particular energy levels in the atom.

[1] [1] reason

(ii) n = 3 to n = 1 ( )( )

( )( ) m719

834

1 1003.1106.15.16.131031063.6 −

−

−

×=×−××

=λ

n = 2 to n = 1 ( )( )

( )( ) m719

834

1 1022.1106.14.36.131031063.6 −

−

−

×=×−××

=λ

n = 3 to n = 2 ( )( )( )( ) m7

19

834

1 1054.6106.15.14.3

1031063.6 −−

−

×=×−

××=λ

[1] for each correct wavelength calculated

RAFFLES INSTITUTION 2010 Preliminary Examination

PHYSICS Higher 1 Paper 1 Multiple Choice

8866 / 01

24 September 2010 1 hour

Additional Materials: OMR form Soft clean eraser Soft pencil (type B or HB is recommended)

READ THESE INSTRUCTIONS FIRST Do not open this booklet until you are told to do so. Fill in your particulars on the OMR form. There are thirty questions in this paper. Answer all questions. For each question there are four possible answers A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the OMR form. Read the instructions on the OMR form very carefully. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet.

This booklet consists of 14 printed pages including the cover page.

2

Data

speed of light in free space, c = 3.00 x 108 m s−1

elementary charge, e = 1.60 x 10−19 C

the Planck constant, h = 6.63 x 10−34 J s

unified atomic mass constant u = 1.66 x 10−27 kg

rest mass of electron me = 9.11 x 10−31 kg

rest mass of proton mp = 1.67 x 10−27 kg

acceleration of free fall, g = 9.81 m s−2 Formulae

uniformly accelerated motion, s = 212ut at+

2v = 2 2u as+



resistors in series, R = R1 + R2 + …

resistors in parallel, 1/R = 1/R1 + 1/R2 + …

3

1 The coefficient of viscosity, η, for a fluid is given by:

FLη = Av

where F is the external force on the fluid, v is the relative motion of the fluid layers, L and A

are the width and area of the fluid layer respectively. The base units for η are

A N s-1 m-2 C kg m s-1

B N s m-2 D kg m-1 s-1

2 Estimate the number of atoms in 1 cm3 of a solid.

A 1010 C 1030

B 1024 D 1040

3 The period of a simple pendulum is given by 2 LTg

π= . The length of the pendulum L is

measured to be ±(20.0 0.1) cm , and the time recorded for 20 complete oscillations

is ±(17.9 0.2) s . What is the fractional uncertainty in the calculated value for the acceleration

of free fall g?

A 0.0162 C 0.159

B 0.0273 D 0.270 4 At time t = 0 s, a ball was released from rest above a floor. In the velocity-time graph shown

below, at which time does the ball reach its maximum height after bouncing from the floor?

velocity v

time t A

B

DC0

4

5 Consider a falling raindrop undergoing constant deceleration. Which pair of quantities would

yield a straight line graph when plotted to represent the motion of the raindrop?

A Velocity of the raindrop and its displacement.

B Displacement of the raindrop and its time in motion.

C Kinetic energy of the raindrop and its displacement.

D Kinetic energy of the raindrop and its time in motion. 6 In the absence of air resistance, a stone is thrown from X and follows a parabolic path in

which the highest point reached is Y.

The horizontal component of velocity of the stone is

A zero at Y C greatest at X

B greatest at Y D the same at X and Y 7 Two particles of identical masses are initially projected towards each other on a smooth

surface with speeds u1 and u2 respectively. They collide elastically with each other, and their

directions and speeds after the collision are shown in the figure below.

X

Y

u2

Before collision

u1

v2

After collision

v1

5

Which one of the following equations cannot be applied to the collision of this system?

A u1 - u2 = v2 + v1 C u12 – u2

2 = v12 + v2

2

B u1 + u2 = v2 – v1 D u1

2 + u22 = v1

2 + v22

8 A movable notice-board of mass 2.0 kg is placed on a smooth floor. What is the initial

acceleration of the notice-board when a horizontal stream of water, travelling at speed

8.0 m s-1, strikes it at a rate of 1.0 kg s-1 for a duration of 50 s.

A 0.16 m s-2 C 4.2 m s-2

B 4.0 m s-2 D 8.0 m s-2

9 A pendulum bob is suspended in a bus of mass 3000 kg undergoing constant deceleration.

The pendulum makes an angle of 18° with the vertical. What is the deceleration of the bus?

A 0.32 m s-2 C 3.2 m s-2

B 3.0 m s-2 D 9.3 m s-2

18°direction of motion

6

10 A clown on a unicycle accelerates to the left.

What is the direction of the resultant force due to the road acting on the wheel of the

unicycle?

A

C

B

D

11 Two blocks P and Q of masses 4m and m accelerate along a smooth floor when a force F is

applied to block P as shown.

What is the force exerted by block Q on block P during this acceleration?

A 5F C 4

5F

B 4F D F

P QF

direction of motion

road

7

12 A uniform rod of mass 2.0 kg is hinged to a wall as shown in the figure below. The rod is

supported at the other end by a cable. The rod makes an angle of 56o to the wall. If a load of

mass 1.5 kg is suspended from the centre of the rod, what is the tension in the cable?

56o

hinge

load

rod

cable

A 6.1 N C 16 N

B 14 N D 20 N 13 A 1.6 kg block slides down a plane that is inclined at 25° with the horizontal, at a constant

speed of 2.0 m s-1. At what rate is the frictional force doing work on the block?

A -28 W C 13 W

B -13 W D 28 W 14 A 100 kg crate is pulled from rest across a floor with a constant force of 320 N. For the first

20.0 m, the floor is frictionless and for the next 10.0 m, a constant frictional force of 30.0 N

acts on the crate. What is the final speed of the crate?

A 8.00 m s-1 C 13.6 m s-1

B 8.37 m s-1 D 13.9 m s-1

8

15 An electric motor has an efficiency of 45%. It is used to raise a bucket of rocks of mass

250 kg at constant speed through a height of 20 m. The time taken to raise the bucket of

rocks is 20 minutes. What is the power supplied to the motor?

A 11 W C 41 W

B 21 W D 91 W

16 Which of the following statements about electromagnetic waves is not true?

A They can be polarised.

B They are transverse waves.

C They always travel at the speed of light.

D They are diffracted when they pass through a small aperture. 17 Some fine sand particles are present in a long transparent tube. A speaker is placed at the

end of the tube, and the frequency of the sound emitted is varied until the fine sand settles

into a series of small heaps. The diagram below shows a section of the tube and some of the

heaps that were formed.

Which of the following statements is true?

A The air molecules are vibrating vertically.

B The wavelength of the sound is given by L.

C The air pressure where the heaps are is the lowest.

D The positions of the heaps show the positions of the displacement nodes. 18 Which of the following gives three regions of the electromagnetic spectrum in order of

decreasing wavelength?

A radiowaves, ultraviolet, X-rays

B ultraviolet, infra-red, microwaves

C visible spectrum, gamma rays, radiowaves

D gamma rays, microwaves, visible spectrum

L

9

19 A horizontal steel wire is fixed at one end and is kept under tension by means of weights

suspended over a pulley. The length of wire between the fixed end and the pulley is 1.0 m.

Magnets are placed near the centre of the wire, and an alternating voltage supply is

connected to the wire between the fixed end and the pulley. Standing waves are formed when

the voltage supply is turned on. Five antinodes are observed on the wire.

Given that the speed of the wave on the wire is 24 m s-1, what is the frequency of the voltage

supply?

A 48 Hz C 96 Hz

B 60 Hz D 120 Hz 20 In the figure below, A and B are two loudspeakers which are π radians out of phase with each

other and emit sound waves of wavelength 4.0 m with equal amplitude X. The waves from A

and B arrive at point C.

A B

C

18 m

If AC is 18 m and BC is 10 m, what is the amplitude of the resultant wave at C?

A 0 C 2X B X D 4X

N

S

1.0 m

Fixed end

pulley

weights

10

21 Eight small conductors of charge Q are placed on the edge of an insulating disc of diameter

D. Given the angular frequency of rotation of the disc is2Tπω = , where T is the period of

rotation.

What is the equivalent electric current at the edge of the disc?

A 4Qωπ

C 8Qω

B 8QDω

π D 16Qπ

ω

22 A car battery of e.m.f. 12 V and internal resistance 0.020 Ω is connected to a load of 4.0 Ω. If

the potential difference across the load is 10 V, what is the power lost in the connecting

wires?

A 0.13 W C 4.9 W

B 1.0 W D 5.0 W

D

QQ

QQ

QQ

Q

Q

11

23 Five resistors of equal resistance are connected as shown.

Which two points would give the maximum combination resistance?

A PQ C PS

B PR D QS 24 The resistance of a certain element is directly proportional to the current passing through it.

When the current is 1.0 A the power dissipated in the element is 3.0 W. What is the power

dissipated when the current is raised to 2.0 A?

A 1.5 W C 12 W

B 6.0 W D 24 W

P

R

QS

12

25 A battery is connected to a uniform resistance wire XYZ, where Y is at the midpoint between

points X and Z. Point Y is earthed as shown in the figure below.

Which one of the following graphs show how the potential varies across XYZ?

A

C

B

D

26 In the figure below, Y is a circular coil carrying an anti - clockwise current. X is a long, straight

wire carrying a current perpendicularly out of the plane of the paper through the centre of the coil.

Each part of the coil Y experiences

A a force towards X C no force in any direction

B a force away from X D a force into or out of the plane of the paper

X Y Z

V

X Y Z

V

X Y Z

V

X Y Z

V

X ZY

13

27 One end of a flat rectangular coil of negligible mass is placed at the centre of a 1000-turn

circular coil of diameter 25 cm as shown in the figure below. A current of 5.0 A is passed

through the rectangular coil and when a 5.0 g paper rider is placed at 2.0 cm to the right of

the pivot, the rectangular coil is balanced horizontally.

4.0 cm 5.0 A

15 cm 2.0 cmpaper rider

1000-turn coil of diameter 25 cm

The magnetic flux density at the centre of a flat circular coil of N turns and radius r is given by

oNBr2

μ=

I where I is the current carried in the coil and μo is the permeability of free space.

What is the magnitude of the current in terms of μo that the 1000-turn circular coil must carry

in order for the rectangular coil to remain horizontal?

A 60.83 10 A

oμ

−× C 68.2 10 A

oμ

−×

B 61.2 10 A

oμ

−× D 616 10 A

oμ

−×

28 Four identical wires A, B, C and D carry equal currents but in the directions as shown in the

figure below. What is the direction of the resultant magnetic force experienced by wire C?

14

A

C

B

D

29 In a photoelectric emission experiment, a metal is irradiated with photons of wavelength λ.

The minimum frequency to cause photoelectric emission is f0. If c is the speed of light, what

fraction of the photon energy is converted to kinetic energy in the electron travelling with the

greatest speed?

A 0f c

λλ −

C 01 f cλ

−

B 0

cc f λ−

D 01fcλ

−

30 The work function of a metal is 3.00 eV. White light, with frequencies ranging from

4.00 x 1014 Hz to 7.90 x 1014 Hz is incident on the surface of the metal. What is the maximum

kinetic energy of the electrons ejected from the surface of the metal?

A 4.38 x 10-20 J C 4.38 x 10-19 J

B 8.55 x 10-20 J D 8.55 x 10-19 J

END OF PAPER

Centre Number Index Number Name Class

RAFFLES INSTITUTION 2010 Preliminary Examination

PHYSICS Higher 1

Paper 2

8866 / 02

21 September 2010 2 hours

Candidates answer on the Question Paper.


READ THESE INSTRUCTIONS FIRST Write your Centre number, index number, name and class in the spaces provided at the top of this page. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid.

For Examiner’s Use 1 / 5 2 / 9 3 / 8 4 / 8

Section A

5 / 10 6 / 20

7 / 20 Section B 8 / 20

Section A Answer all questions. Section B Answer two questions. Write your answers in the spaces provided in this booklet. At the end of the examination, circle the Section B questions you have answered in the grid. The number of marks is given in brackets [ ] at the end of each question or part question. Total / 80

This booklet consists of 23 printed pages including the cover page.

2 DATA AND FORMULAE

Data speed of light in free space, c = 3.00 x 108 m s−1

elementary charge, e = 1.60 x 10−19 C

the Planck constant, h = 6.63 x 10−34 J s

unified atomic mass constant , u = 1.66 x 10−27 kg

rest mass of electron, me = 9.11 x 10−31 kg

rest mass of proton, mp = 1.67 x 10−27 kg

acceleration of free fall, g = 9.81 m s−2

Formulae

uniformly accelerated motion, 212s ut at= +

2 2 2v u as= + work done on/by a gas, W = pΔV hydrostatic pressure, p = ρgh

electric potential, 04

QVrπε

= −

resistors in series, R = R1 + R2 + . . . . resistors in parallel, 1/R = 1/R1 + 1/R2 + . . . .

3

SECTION A

Answer all questions in this section.

1 A cylindrical thermos flask is used to store hot water. The internal diameter and depth of the thermos flask are measured to be (8.50 ± 0.01) cm and (21.0 ± 0.1) cm respectively.

(a) State the instrument used to measure its diameter and a systematic error that can occur with the use of this instrument.

[2]

(b) Calculate the capacity of the thermos flask and its associated uncertainty.

Volume = cm3 [3]

4

2 (a) A mass hanging from a spring balance in air gives a reading of 50 N. When the mass is completely immersed in water, the reading on the balance is 40 N. It is now completely immersed in another liquid, giving a reading of 34 N. Calculate the density of this liquid. Assume that the density of water is 1000 kg m-3.

Density = kg m-3 [2]

(b) In Fig. 2 below, a uniform beam of length 10.0 m and weight 500 N is hinged to a wall at point O. Its far end is supported by a cable that makes an angle of 53.0° with the horizontal. A 70.0 kg worker stands on the beam.

(i) Draw a labelled diagram showing the forces acting on the beam. [2]

O beam

cable

53.0°

s Fig. 2

5

(ii) The worker walks towards the far end of the beam from O. Calculate the furthest distance s he can travel if the maximum possible tension in the cable is 1000 N.

s = m [2]

(iii) Calculate the magnitude of the force exerted by the hinge on the beam when the tension in the cable is 1000 N.

Force exerted by the hinge = N [3]

6

3 (a) Define magnetic flux density.

[2]

(b) A long, thin wire is in a region of uniform magnetic flux density B. The wire carries a current of 5.8 A and is oriented at an angle of 12o to the direction of the magnetic field as shown in Fig 3.

Fig. 3

(i) Calculate the magnetic flux density B given that the magnetic force exerted per unit length on the wire is 0.045 N m-1.

B = T [3]

7

(ii) Determine the angle at which the wire must be oriented with respect to the magnetic field if the force per unit length acting on the wire is now 0.015 N m-1.

angle = o [2]

(iii) State the direction of the magnetic force on the wire.

[1]

8

4 A hydrogen lamp emits light of frequency 7.0 x 1014 Hz at a rate of 0.25 W. Only 0.40 % of all the photons given out fall on the cathode of a photocell. The current registered in the external circuit is 8.5 μA. It can be assumed that this current consists of all the photoelectrons emitted.

(a) Calculate

(i) the energy of a photon

Energy of a photon = J [2]

(ii) the number of photons leaving the lamp in one second

Number of photons in one second = [2]

(b) Calculate the percentage of the photons that fall on the cathode which produces photoelectrons.

Percentage = % [3]

(c) State the effect on the current registered in the external circuit when the power of the lamp is increased.

9

[1]

10

5 Radiation is a significant component of heat transfer in buildings, especially for sun-exposed surfaces and regions of large temperature differences. Most countries have building regulations that contain instructions about limiting heat transfer in order to reduce the amount of heating or air-conditioning required. In order to calculate heat transfer, a thermal transmittance coefficient or U-value is

measured for each type of building material. Mathematically, PU

A TΔ= where P is the

rate of heat transfer in watts, A is the surface area of the structure and TΔ is the air temperature difference between each side of the structure in kelvins. The U-values of three construction components are given below:

Component U-value / W m-2 K-1

Single-glazed window 5.6

Double-glazed window 3.2

Uninsulated roof 1.9

A house has windows of total area 24 m2 and a roof of area 60 m2. On average, the owner heats the house for 3000 hours per year to a temperature that is 14 K above that of the air outside.

(a) (i) Calculate the amount of energy lost in a year through single-glazed windows.

Energy Loss = kWh [3]

(ii) By installing double-glazed windows, calculate the owner’s annual savings if electricity costs $0.25 per kWh.

11

Savings = $ [3]

(b) The roof is now insulated with two 50 mm thick layers of thermal insulation on each side to reduce heat transfer, as shown in Fig. 5 below.

Fig. 5 U-value for thermal insulation 50 mm thick = 1.4 W m-2 K-1 To calculate the rate of heat transfer P through such a roof, a composite U-value, Uc, has to be used. Uc can be expressed in terms of the U-values of the individual materials by the equation

1 2

1 1 1 .....CU U U= + +

(i) Using the above equation, show that the rate of heat transfer P through the roof with thickness of thermal insulation on each side t = 50 mm is 430 W. [1]

t

12

(ii) The table below shows the values of P for their respective t values.

t / mm P / W

50 430

100 250

150 170

200 130

Using the data from the table, plot a graph of P against t. [2]

(iii) Explain why the rate of heat transfer for a thickness of 250 mm thermal insulation on each side cannot be accurately determined from the above graph.

[1]

200

300

400

100

t /mm

13

SECTION B

Answer two questions from this section.

6 A group of students built a catapult to test its capability as a launcher. In one of their test launches, a ball was successfully projected over a 5.0 m wall. The ball was released 1.0 m above the ground with an initial velocity u at an angle θ to the horizontal. At the highest part of the trajectory, the ball managed to just go over the wall with a horizontal speed of 10 m s−1. Assume that air resistance is negligible.

5.0 m

Fig. 6.1

(a) Describe the shape of the trajectory (labelled A) of the ball.

[1]

(b) Calculate

(i) the vertical component of the initial velocity u,

Vertical component of u = m s-1 [2]

A

1.0 m

14

(ii) the angle of projection θ,

θ = 0 [2]

(iii) the time taken for the ball to reach top of the wall, and

time taken =

s [2]

(iv) the horizontal distance between the wall and the point of projection.

horizontal distance =

m [2]

15

(c) If air resistance was significant, sketch the path of the trajectory on Fig. 6.1 and label it B. State two differences between trajectories A and B.

[3]

(d) The estimated normal contact force acting on the ball upon hitting the floor is shown in Fig. 6.2. Assume that the floor is frictionless.

0 Time/s 0.250

Fig. 6.2

(i) Sketch on Fig.6.2 the normal contact force exerted by the ball on the floor. [1]

(ii) Define impulse.

[1]

300

0.250

Normal contact force / N

16

(iii) Determine the impulse delivered to the ball in the vertical direction.

Vertical component of impulse =

N s [2]

(iv) Hence find the average normal contact force acting on the ball.

Average normal contact force =

N [2]

(v) Describe the energy changes during the collision of the ball with the floor.

[2]

17

7 (a) State the Principle of Superposition of waves.

[2]

(b) Fig. 7.1 shows two waves P and Q. They are superimposed on each other at the instant shown. Draw the resultant waveform in Fig.7.1 on page 17.

18

.

Fig. 7.1

[4]

Y

Y

Y

X

X

X

Wave P

Wave Q

A

‐A

‐A

A

A

‐A

Resultant wave

19

(c) A 0.60 m horizontal piece of string is attached to two fixed points and made to vibrate with a small amplitude.

(i) For a particular frequency of the vibrating string, a stationary wave pattern with three nodes is observed. Sketch the waveform.

[1]

(ii) A stationary wave pattern with five nodes is obtained when the string vibrates at a frequency of 160 Hz. Calculate the speed of propagation of the wave in the string.

Speed =

m s-1 [3]

20

(d) Fig. 7.2 shows an arrangement to demonstrate double-slit experiment using microwaves of wavelength 3.00 cm. The slit separation is 9.00 cm and the microwave emitter is placed along the perpendicular bisector of the slits A and B.

Fig. 7.2

(i) For observable interference patterns, the sources must be coherent. Explain what is meant by coherent.

[1]

(ii) A detector travelling along AX detects a series of maxima and minima. Explain.

[4]

21

22

(iii) Find the greatest distance from A, along the line AX, for which destructive interference occurs.

Greatest distance from A = m [3]

(iv) Describe the intensity detected along AX at distance beyond that calculated in (iii).

[2]

23

8 (a) Define the terms resistance and resistivity.

[2]

(b) Use energy considerations to distinguish between electromotive force (e.m.f.) and potential difference (p.d.).

[2]

(c) A cell of e.m.f. 2.50 V and internal resistance r is connected to two resistive wires in series as shown in Fig. 8.1. The wires are made of the same material but have different lengths and diameters. Wire AB is 50.0 cm long and has a diameter d, whereas wire BC is 30.0 cm long and has a diameter 0.30 d. The connecting wires are assumed to have no resistance.

Fig. 8.1

Show that 0.15AB

BC

RR

= [2]

r

2.50 V

A B C

24

(d) An ammeter is added to the circuit in part (c), along with a voltmeter connected across wire BC as shown in Fig 8.2. If the ammeter shows a reading of 0.400 A and the voltmeter gives a reading of 2.00 V, determine

Fig 8.2

(i) the terminal p.d. of the 2.50 V cell

V = V [3]

(ii) the internal resistance r of the 2.50 V cell

r = Ω [2]

(iii) the efficiency of the circuit, given that Power OutputEfficiency 100%Power Input

= ×

r

2.50 V

A B

A

C

V

25

Efficiency = % [2]

(iv) the resistivity of the wires AB and BC, given that d is 2 mm.

Resistivity = Ω m [2]

(e) Suggest and explain whether your answer in part (d)(ii) is an overestimate or underestimate if the ammeter cannot be considered to be ideal.

[2]

(f) The wires AB and BC are now connected in parallel. State and explain how this will affect the efficiency of the system as calculated in part (d)(iii), assuming that both the ammeter and voltmeter are ideal.

[3]

26

END OF PAPER

Question Answer 1 D 2 B 3 B 4 D 5 C 6 D 7 C 8 B 9 C

10 B 11 A 12 B 13 B 14 C 15 D 16 C 17 D 18 A 19 B 20 A 21 A 22 C 23 B 24 C 25 C 26 C 27 C 28 A 29 D 30 A

H1 Physics Prelim Paper Suggested Solutions

1 (a) Vernier callipers, zero error.

(b)

( )

23

3

3

1191.645 cm4

2

2 0.01 0.1 1191.6458.50 21.0

8 cm (1 s.f.) 1192 8 cm

dV h

V d hV d h

V

V

π⎛ ⎞

= =⎜ ⎟⎝ ⎠

Δ Δ Δ= +

×⎛ ⎞Δ = + ×⎜ ⎟⎝ ⎠

=

∴ = ±

2 (a)

1 1

1

3 3

2

2

32 3

50 40 10N

10 1.02 10 m1000 9.81

50 34 16N

16 1600kg m1.02 10 9.81

U W TVg

V

UVg

ρ

ρ

ρ

−

−−

= − = − =

=

∴ = = ××

= − =

=

∴ = =× ×

(b) (i)

(ii) Taking moments about O,

( )5.00 500 (70 9.81 ) 1000sin 53.0 10.07.99 m

ss

× + × × = ° ×=

(iii) At equilibrium, the net vertical and horizontal forces must be zero.

2 2

cos53.0 602N500 (70 9.81) sin53.0 388N

602 388 716

x

y

R TR T

R N

= ° =

= + × − ° =

= + =

tension

weight of beam

weight of worker

reaction force


3 (a) It is the force per unit length per unit current on a straight conductor oriented

perpendicularly to the direction of the magnetic field. B2

(b) (i)

( )

sin1 10.045

sin 5.8sin120.037 T

F B LFBL I

B

θ

θ

=

⎛ ⎞⎛ ⎞ ⎛ ⎞= =⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠

∴ =

I

(ii) ( )1 1sin 0.015

0.0373 5.84.0o

FL B

θ

θ

⎛ ⎞ ⎛ ⎞= =⎜ ⎟ ⎜ ⎟×⎝ ⎠ ⎝ ⎠∴ =

I

(iii) Into the paper 4 (a) (i) 34 14 196.63 10 7.0 10 4.641 10 JE − −= × × × = ×

(ii)

17 119

0.25 5.39 10 s4.641 10

nhfPt

n Pt E

−−

=

⇒ = = = ××

(b) No. of photons that fall on cathode = 0.0040 x 5.39 x 1017 = 2.155 x 1015

613

198.5 10 5.313 101.6 10

e

e

Q t n e tnt e

−

−

= ⇒ × =

×∴ = = = ×

×

I I

I

This is the amount of photons per second that cause photocurrent. ∴ the percentage of photons causing photocurrent

= 13

17

5.313 10 100 0.0099%5.39 10

×× =

×

(c) Decrease. With a greater work function, for the same no. of photons that fall on the cathode, less no. of electrons are ejected per unit time.


5 (a) (i)

4

6

4

5.6 24 14 1881.61881.6 3000 60 60 2.0321 10 MJ

1kWh 1000 60 60 3.60 10 J2.0321 10 MJ 5644.7 kWh

P UA TE Pt

Δ= = × × =

= = × × × = ×

= × × = ×

∴ × =

(ii) 1 2

9

( ) (5.6 3.2) 24 14 806.4

806.4 3000 60 60 8.7091 10 J 2419.2 kWhSavings 2419.2 0.25 $604.80

P U U A T

E Pt

Δ Δ

Δ Δ

= − = − × × =

= = × × × = × =

= × =

(b) (i) 1 2 3

1

1 1 1 1 1 1 11.4 1.9 1.4

1 1 10.51154

1.4 1.9 1.40.51154 60 14 430

C

C

C

U U U U

U

P U A T WΔ

−

= + + = + +

= + + =

= = × × =

⎛ ⎞⎜ ⎟⎝ ⎠

(ii)

Heat transfer via conduction dominates and relationship between rate of heat

transfer and thickness of thermal insulation is given to be kA T

RLΔ

= where k

is the thermal conductivity of the medium, A is the surface area normal to

direction of heat transfer and L is the thickness of the insulation. This

relationship is inversely proportional, thus graph should be a curve.

(iii) A curve needs at least 8 plotted points to be accurate. There are only 3


plotted points in this graph, thus the curve may not be accurate.

6 (a) The shape of the trajectory is parabolic.

(b) (i)

( ) ( ) −

= +

= + − − ⇒ =

2 2

2 1

2

0 2 9.81 5.0 1.0 8.9 m sY Y Y Y

Y Y

v u a s

u u

(ii)

θ θ= = ⇒ = 08.86tan 41.510

Y

X

uu

(iii)

( ) ( )= +

= + − ⇒ =0 8.86 9.81 0.90 sY Y Yv u a t

t t

(iv) ( ) ( )= = =10 0.903 9.0 mX Xs u t

(c) • B is non-parabolic or asymmetrical.

• Maximum height for B is lower than A. • Range for B would be shorter than A.

• B will reach maximum height earlier than A.

(d) (i)

(ii) Impulse of a force acting on an object is the change in momentum of the object.

(iii) Impulse

( ) ( )

area under - graph1 0.250 300 37.5 Ns2

F t=

= =

300

0.250

Normal contact force / N

Time / s


(iv) Average normal contact force = impulse 37.5

time 0.250= = = 150 N

(v) During collision, the KE of the ball is converted into sound energy, thermal

energy and elastic PE as the ball deforms. Part of the elastic PE is returned to the ball as KE on rebound.


7 (a) When two or more waves meet at a point, the resultant displacement at that point is

the vector sum of the individual displacements due to each wave.

(b)

(c) (i)

(ii) ( )

( )( )

-1

4 0.602

40.60

2 160

48 m s

v

v

λ=

=

=

(d) (i) Sources must have a constant phase difference. (ii) As detector moves along A X, the path difference decreases from 9.00 cm (at

A) to 0.00 cm (at infinity). Since path difference nλΔ = , n decreases from 3 (at A) to 0 (at infinity). When n is an integer, maxima is obtained; when n is a half-integer, minima is obtained.

(iii) For destructive interference, path difference 1

2 λΔ =

( )

( )

2 2

2

22

2

19 3.002

81 1.5

81 1.5

3 2.253 78.75

26.3 cm

x x

x x

x x

x xxx

+ − =

+ = +

+ = +

= + +==

(iv) Beyond 26.3 cm, the intensity increases to a maximum then decreases again as distance increases.


8 (a) The electrical resistance, R of a conductor is defined as the ratio of the p.d., V across it to the current, I through it.

The electrical resistivity ρ of a material is the constant of proportionality relating the electrical resistance R to the dimensions of the material (length and area). Also accept if there is a statement relating dependence of R on dimensions and ρ as a material characteristic/property.

(b) The potential difference V between two points in a circuit is the amount of electric

energy that is converted to other forms of energy when a unit charge passes from one point to the other.

The e.m.f. of a source is defined as the amount of converted from other forms to electrical energy when the source drives a unit charge round a complete circuit.

(c)

( )

( )

22

2 2

2 2

2

2

4

4

OR

0.350.0 0.1530.0

BC BCAB AB AB

BC BC BCAB AB

L L LRA dd

d dR L LR L Ld d

dd

ρρ ρππ

= = =

= × ×

= × =

(d) (i) ( )0.400 2.00 V5.00

BC BC

BC

V RR

= =

= Ω

From part (c)

( ) ( )0.15 0.75 0.400 0.75 0.300 V

AB BC

AB

R RV

= = Ω

= =

2.00 0.300 2.30 VACV = + =

(ii)

( ) ( )2.50 2.00 0.300 0.4000.500

ACE V Irr

r

= +

= + +

= Ω

(iii)

Efficiency 100%

2.30 100% 92.0%2.50

ACIVIE

= ×

= × =

(iv) From part (c)(i)


( ) ( )23

62

5.00

0.30 2 105.00

4 4.71 10 m30 10

BCLRA

ρ

π

ρ

−

−−

= Ω =

× ×

= = × Ω×

(e) Over-estimate. 0.20 V is actually the p.d. across R as well as that of the ammeter.

( )0.500 0.500

AC A

A

E V I R RR R R− = +

+ = Ω ⇒ < Ω There must be some statement relating the resistance of the ammeter to either

- pd calculated for R actually includes the pd across the ammeter

- resistance calculated of R actually includes the resistance of the ammeter

to show that the calculated value of R is actually an overestimate.

(f) Efficiency will decrease.

The combined resistance of the load (wires) is now much lower (≈0.652 Ω) and comparable to internal resistance R which results in the terminal p.d. dropping quite substantially as well.

This means that the power dissipated across the load is now comparable to the power loss due to the internal resistance R which implies that efficiency will be < 92%.

RIVER VALLEY HIGH SCHOOLYEAR 6 PRELIMINARY EXAMINATION

H1 PHYSICS 8866 PAPER 1

20 SEP 2010

1 HOUR

CANDIDATE NAME


NUMBER INSTRUCTIONS TO CANDIDATES DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. Read these notes carefully. Write your name, class and index number in the spaces above. There are thirty questions in this paper. Answer all questions. For each question, there are four possible answers, A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet. Read the instructions on the Answer Sheet very carefully. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Anyrough working should be done on the Question Paper. The total number of marks for this paper is 30. ____________________________________________________________________________

This Question Paper consists of 15 printed pages. River Valley High School Pg 1 of 15 Year 6 H1 Physics 8866Preliminary Examination 2010

Data speed of light in free space, c = 3.00 × 108 m s–1

elementary charge, e = 1.60 × 10–19 C

the Planck constant, h = 6.63 × 10–34 J s

unified atomic mass constant, u = 1.66 × 10–27 kg

rest mass of electron, me = 9.11 × 10–31 kg

rest mass of proton, mp = 1.67 × 10–27 kg

acceleration of free fall, g = 9.81 m s–2

Formulae


s ut at= +

2 2 2v u a= + s

work done on/by a gas, W p V= Δ hydrostatic pressure, p ghρ= resistors in series, 1 2R R R= + +K resistors in parallel, 1 21/ 1/ 1/R R R= + +K

River Valley High School Pg 2 of 15 Year 6 H1 Physics 8866Preliminary Examination 2010

For each question there are four possible answers, A, B, C and D. Choose the one you consider to be correct.

1 Which of the following could be the correct expression for the speed v of sound in

a gas of density ρ and at a pressure P?

(γ is a dimensionless constant.)

A v P

γρ

= B v Pγρ= C Pv γ

ρ= D v Pγρ=

2 When a drop of oil of mass m and density ρ is put on a water surface it spreads over a circular area of diameter d. Assuming that this area consists of a monomolecular layer which one of the following gives the approximate diameter of a molecule?

A

mdπρ

B dmρ

π C

mdπ ρ3

34

D m

dπ ρ24

3 The figure below shows a graph of an object’s motion. Which sentence is a correct interpretation?

A The object slides along a flat surface. Then it slides forward down a smooth

incline plane, and then finally stops. B The object is moving at constant velocity. Then it slows down and stops. C The object is initially stationary. Then it moves backwards and then finally

stops.

D The object moves along a flat area, moves backwards down a smooth incline plane, and then it keeps moving.

0

disp

lace

men

t

time


4 An object has an initial velocity u. It is subjected to a constant acceleration a. The force is not in the same direction as the initial velocity. A vector diagram is drawn to find the final velocity v.

What is the length of side X of the vector diagram?

A v – u B v + u C at D u + at

5 The diagram shows two trolleys X and Y held stationary and connected by an

extended elastic cord. The mass of X is twice that of Y.

The trolleys are released at the same instant. They move towards each other and stick together on impact. Just before the collision, the speed of X is 20 cm s–1. What is the speed of Y after the collision?

A zero B 5.0 cm s–1 C 7.0 cm s–1 D 10 cm s–1


6 The graph shows the variation with time of the momentum of a ball as it is kicked in a straight line.

Initially, the momentum is p1 at time t1. At time t2 the momentum is p2. What is the magnitude of the average force acting on the ball between times t1 and t2?

A

2

12

tpp − B

12

12

ttpp

−− C

2

2

tp D

12

12

ttpp

−+

7 A 2.0 kg object moving at 10 m s−1 collides normally with a wall and bounces off

with half of its original kinetic energy. What is the magnitude of the impulse applied by the wall?

A 5.9 N s B 14 N s C 34 N s D 50 N s

8 A car with front-wheel drive accelerates in the direction shown.

Which diagram best shows the direction of the total force exerted by the road on the front wheels?

A

B C D


9 A ball falls vertically and bounces on the ground.

Which of the following statements is true when the ball is in contact with the ground? A The force that the ball exerts on the ground is always less than the weight of

the ball. B The force that the ball exerts on the ground is always equal to the weight of

the ball. C The weight of the ball is always equal in magnitude and opposite in direction

to the force that the ground exerts on the ball.

D The force that the ball exerts on the ground is always equal in magnitude and opposite in direction to the force the ground exerts on the ball.

10 A solid has density 4.0 g cm−3. What is the density of a liquid in which the solid

would float with one-fifth of its total volume above the liquid surface?

A 4.0 g cm−3 B 5.0 g cm−3 C 7.5 g cm−3 D 8.5 g cm−3

11 Two 20 g flatworms climb over a very thin wall, 10 cm high. One of the worms is

20 cm long, the other is wider and only 10 cm long. Determine the ratio of work done against gravity by the longer worm to the shorter one when half of their bodies are over the top of the wall.

A

23

B 1 C 32

D 2

thin wall Me too!

I am a flatworm.

12 A body moving along a straight-line has mass 3.0 kg and kinetic energy 24 J. The

motion is then opposed by a resultant force of 4.0 N. The body will come to rest after travelling a distance of

A 2.0 m B 6.0 m C 8.0 m D 12 m


13 A cannon of mass 3000 kg fires a cannonball of mass 50 kg with a horizontal

velocity of 85 m s−1. Determine the kinetic energy of the cannon.

A 1.1 × 107 J B 1.8 × 105 J C 3.0 × 103 J D 50 J

14 In a ripple tank experiment, parallel water waves of wavelength 0.80 m strikes the

hypotenuse of a triangular barrier as shown.

What is the phase difference, in radian, at any instant between the waves at two points 0.50 m apart along the barrier as shown?

A 0.80π B 0.96π C 1.0π D 1.3π


15 The figure shows the shape at a particular instant of part of a transverse wave travelling from left to right along a string.

Which statement about the motion of elements of the string at this instant is correct? A The speed of Q is higher than S. B Both Q and R are moving upwards. C The energy of P and S is entirely kinetic.

D The acceleration of P and R is a maximum.

16 A stationary wave in a gas in a resonance tube can be described in terms of the amplitude xΔ of oscillation of the particles of the gas from their mean positions. Which one of the following correctly describes the situation at resonance in a tube which is closed at one end? (Neglect end correction at the open end.)

at closed end at open end

xΔ xΔ

A zero zero

B zero maximum

C maximum maximum

D maximum zero


17 A source of sound of frequency 2300 Hz is placed several metres from a vertical reflecting board. A microphone, connected to a cathode-ray oscilloscope, is moved from A to B which are both positions of maximum intensity through ten minimum intensity positions as shown.

If L is 0.75 m, what is the speed of sound in air?

A 310 m s–1 B 330 m s–1 C 350 m s–1 D 380 m s–1

18 A student sets up the apparatus shown to determine a two-slit interference pattern on the screen.

He wishes to increase the fringe spacing. Which of the following changes to the apparatus will increase the fringe spacing? A Increase the distance p. B Increase the distance q. C Increase the distance r.

D Immerse the whole setup in water.


19 Two cubes, X and Y are cut from the same block of metal. The linear dimension

of X is 2 times that of Y. What is the ratio X

Y

RR

of the resistances between the

opposite faces of X and of Y?

A

12

B 1 C 2 D 4

20 The electrical characteristic of a component is shown below.

Which graph below shows the way the resistance of the component varies with applied voltage?

A B

C D

I


21 A battery of e.m.f. E and internal resistance r is connected to a 4.0 Ω resistor. A p.d. of 5.2 V is measured across the terminals of the battery. When the 4.0 Ω resistor is replaced with one of resistance 12.0 Ω, the p.d. across the battery becomes 6.0 V. What are the values of E and r?

E/V r/Ω

A 6.5 1.0 B 7.5 1.8 C 7.6 0.63 D 12 6.0

22 The battery in the circuit below has negligible internal resistance.

The current I is

A 1.0 A B 2.0 A C 4.5 A D 9.0 A

2.0 Ω2.0 Ω2.0 Ω

I6.0 V


23 In the diagram below shows an electrical circuit in which the internal resistance of the cell is negligible. It may be assumed that the voltmeter has infinite resistance and the resistance of the ammeter is negligible.

What is the voltmeter reading when switch S is opened and when switch S is closed?

S opened S closed A 0 V 0 V B 1.0 V 1.0 V C 2.0 V 0 V D 2.0 V 2.0 V

2.0 V

100 Ω

V

AS

24 Two long current carrying conductors are placed perpendicular to each other.

The current flowing through one of the wires is 4.0 A upwards, while the current through the other wire is 2.0 A towards the left. What is the magnitude and direction of the resultant magnetic field at a point X, which is 3.0 m perpendicularly away from both wires? Ignore the Earth's magnetic field. (Magnetic flux density at a distance d from a long straight conductor carrying

current I is I2

oBd

μπ

= .)

A 1.33 x 10−7 T out of the plane of the page B 4.00 x 10−7 T into the plane of the page C 4.00 x 10−7 T out of the plane of the page

D 2.67 x 10−7 T into the plane of the page

3.0 m

X 3.0 m

2.0 A

4.0 A


25 A horizontal wire PQ of length 0.50 m and weight 0.50 N is placed at an angle 30° to the magnetic field as shown below. The wire is balanced by the magnetic force of the magnetic field of magnetic flux density of 1.0 T.

Top view

What is the magnitude and direction of the current in the wire?

magnitude direction A 1.2 A P to Q

B 2.0 A P to Q C 1.2 A Q to P

D 2.0 A Q to P

P

30°

Q

26 The diagram shows a simple current balance. The rectangular metallic frame

WXYZ carries a current I in a magnetic field B as shown. WX and YZ have length p while XY and WZ have breadth q. The counterbalancing rod is of length r. Weights of mass m are placed on the pan until the rectangular frame is horizontal. When equilibrium has been established,

A Bqpmgr

=I B Bqmg

=I C 2Bqmgr

=I D Bqrmgp

=I


27 When electromagnetic radiation falls on a particular metal surface, photoelectrons

may be emitted. The variation of the maximum kinetic energy E of these electrons with the frequency f of the radiation is shown in the figure below.

When the experiment is repeated using another metal with a smaller work function, which graph best represent the variation of E with f of this metal (solid line)?

A B

C D

28 The intensity of a beam of monochromatic light is doubled. Which of the following

about the photons is correct? A The speed of the photon is doubled. B The frequency of the photon is doubled. C The kinetic energy of the photon is doubled.

D The number of photons arriving per unit are per unit time is doubled.


29 An ultraviolet radiation source causes the emission of photoelectrons from a zinc

plate. How would the maximum kinetic energy EK of the photoelectrons and the photocurrent be affected by changing to a more intense source with the same wavelength?

EK photocurrent A unchanged decreased

B increased decreased C unchanged increased

D increased increased

30 A beam of light of wavelength λ is incident normal to a surface of area S and is

completely absorbed by the surface. The rate of photons arriving at the surface is n. The pressure exerted on the surface by the light is

A nhλ

S B nh

λS C 2nhλ

S D 2nh

λS

END OF PAPER


RIVER VALLEY HIGH SCHOOLYEAR 6 PRELIMINARY EXAMINATION

H1 PHYSICS 8866 PAPER 2

13 SEP 2010

2 HOUR CANDIDATE NAME


NUMBER INSTRUCTIONS TO CANDIDATES DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. Read these notes carefully. Write your name, centre and index number and class in the spaces above.

FOR EXAMINERS’ USE Section A

1 /52 /83 /94 /85 /10

Section B

6 /207 /208 /20

Candidates answer on the Question Paper. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use paper clips, highlighters, glue or correction fluid. Section A Answer all questions. Section B Answer any two questions.

TOTAL /80The number of marks is given in brackets [ ] at the end of each question or part question. ____________________________________________________________________________

This Question Paper consists of 21 printed pages. River Valley High School Pg 1 of 21 Year 6 H1 Physics 8866Preliminary Examination 2010

Data speed of light in free space, c = 3.00 × 108 m s–1







Formulae


s ut at= +

2 2 2v u a= + s

work done on/by a gas, W p V= Δ hydrostatic pressure, p ghρ= resistors in series, 1 2R R R= + +K resistors in parallel, 1 21/ 1/ 1/R R R= + +K


Section A

Answer all questions in this section.

1 The resistive force F that acts on an object moving at speed v in a stationary fluid of

constant density is given by the expression

F = kv2 where k is a constant.

(a) State the base units of (i) force F,

[1] (ii) speed v.

[1] (b) Use your answers in (a) to determine the base units of k.

base units of k = ………………………… [1] (c) Explain why it is technically incorrect to define speed as distance travelled per

second. Include in your answer the correct statement defining speed. …………………………………………………………………………………………… …………………………………………………………………………………………… ……………………………………………………………………………………… [2]


2 Jane, whose mass is 50.0 kg, needs to swing across a river (having width D) filled

with man-eating crocodiles to save Tarzan from danger. She must swing on a vine into a wind exerting a constant horizontal force F. The vine has a length L and initially makes an angle θ with the vertical (Fig. 2.1). Take D = 50.0 m, F = 110 N, L = 40.0 m, and θ = 50.0°.

Fig 2.1 (a) (i) Show that the angle φ is 28.9°.

[2] (ii) Hence, or otherwise, determine h.

h = ………………………… m [2]

D

F

Wind Jane

θ

Lφ

Tarzan

h


(b) Calculate the minimum speed Jane needs to begin her swing in order for her to

just reach Tarzan.

minimum speed of Jane = ………………………… m s–1 [2] (c) Once the rescue is complete, Tarzan and Jane must swing back across the

river. With what minimum speed must they begin their swing if Tarzan has a mass of 80.0 kg?

minimum speed = ………………………… m s–1 [2]


3 Fig. 3 shows a pair of identical loudspeakers A and B placed 2.00 m apart and

emitting coherent sound waves of frequency 470 Hz. An observer walks from X to Y. The perpendicular distance between the sources and XY is 12.0 m. As he walks, he hears sound of maximum intensity at P, minimum intensity at Q and maximum intensity at R. R is 4.50 m away from P.

Fig. 3 (a) Explain why the observer hears sound of maximum and minimum intensity as

he walks from X to Y. …………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………………………………………………… ……………………………………………………………………………………… [2] (b) It can be shown using Pythagoras’ theorem that AR is 12.5 m and BR is

13.2 m. (i) Determine the wavelength of the sound.

wavelength = ………………………… m [2]


(ii) Determine the speed of the sound.

speed of sound = ………………………… m s–1 [2] (c) The power of the loudspeakers A and B are identical. Suggest why the

intensity at Q is not zero. …………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………………………………………………………………... ……………………………………………………………………………………… [3]


4 (a) Distinguish between electromotive force and potential difference. …………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………………………………………………… ……………………………………………………………………………………… [2] (b) An electric hotplate is designed to operate on a power supply of 240 V has two

coils of wire of resistivity of 9.8 × 10–7 Ω m. Each coil of wire has a length of 16 m of cross-sectional area 0.20 mm2.

(i) For one of the coils, calculate 1. its resistance,

resistance = ………………………… Ω 2. the power dissipation when a 240 V supply is connected across it.

power = ………………………… W [4]


(ii) Fig. 4.1 shows how the two coils can be connected to operate at

different powers.

Fig. 4.1 On Fig. 4.2, fill up the table with “ON” or “OFF” to obtain the lowest and highest levels of operating power.

switch A switch B switch C

Lowest

Highest

Fig. 4.2

[2]

240 V

A

B C


5 The Geiger-Nuttall theory of α-particle emission relates the half-life of the α-particle

emitter to the energy E of the α-particle. One form of this relationship is

L = 166E

– 53.5.

L is a number calculated from the half-life of the α-particle emitting nuclide and E is measured in MeV. Values of E and L for different nuclides are given Fig. 5.1.

Nuclide V L E / Me1E

/ 12(Me ) V

238U 4.20 5 8 17.1 0.48236U 9 7 2 4.4 14.8 0.472 U 2 9 5 34 4.8 12.8 0.45

228 h 2 8 T 5.4 7.7208 n 4 6 4 R 6.1 3.1 0.40212 o 9 5 8 P 7.3 –2.7 0.36

Fig. 5.1

(a) Complete the table above by calculating, using the value of E provided, the

value of 1E

for the nuclide 228 . Give your answer to three significant

figures. [1]

Th


Fig. 5.2 shows the variation with 1

E of the quantity L.

20

16

12

8

4

0

–4

0.2 0.3 0.4 0.5

L

/ MeV121

2– 1

E

Fig. 5.2

(b) (i) Identify the data point for the nuclide 208 . Label this point R. [1]Rn (ii) On Fig. 5.2, mark the point for the nuclide 228 . Label this point T. [1]Th (iii) Draw the best-fit straight line for all the data points. [1] (c) (i) Determine the gradient of the line you have drawn in (b)(iii).

[2]

L

1E

/ 12(MeV)


(ii) Suggest why the graph does not agree with the stated relationship for

the Geiger-Nuttall theory.

[2] (d) On Fig. 5.2, draw the line that would be expected if the relationship for the

Geiger-Nuttall theory were correct. No further calculation is required. [2]


Section B

Answer two questions from this section.

6 (a) Define moment of a force. ………………………………………………………………………………………….... …………………………………………………………………………………….... [2] (b) A person supports a load of 20 N in his hand as shown in Fig 6.1. The system

of the hand and load is represented by Fig 6.2. The rod represents the forearm and T represents the tension exerted in the biceps. The forearm weighs 65 N.

(i) Show that the tension T in the biceps is 410 N.

[2]


(ii) Determine the magnitude and direction of the force acting at the elbow.

force acting at the elbow = ………………………… N direction of the force: ………………………… [4] (c) (i) State Newton’s laws of motion. ………………………………………………………………………………….... ………………………………………………………………………………….... ………………………………………………………………………………….... ………………………………………………………………………………….... ………………………………………………………………………………….... ……………………………………………………………………………… [3] (ii) A karate expert can split a stack of bricks by bringing her arm and hand

swiftly against the bricks with considerable speed. Using Newton’s laws of motion, explain why she has to execute the karate strike very quickly.

………………………………………………………………………………….... ………………………………………………………………………………….... ………………………………………………………………………………….... ………………………………………………………………………………….... ………………………………………………………………………………….... ……………………………………………………………………………… [3]River Valley High School Pg 14 of 21 Year 6 H1 Physics 8866Preliminary Examination 2010

(d) Part of an arch made of stone is shown in Fig. 6.3.

The central stone is known as a keystone and has a weight of 600 N. The keystone is supporting a load of 4600 N. The sides of the keystone make an angle of 10° to the vertical. The two stones P and Q, which are next to the keystone, exert forces at right angles to the sides of the keystone.

(i) On Fig. 6.3, draw and label arrows on the keystone to show the

following four forces. W, the weight of the keystone L, the force the load exerts on the keystone FP, the force stone P exerts on the keystone FQ, the force stone Q exerts on the keystone [4]

(ii) Determine the value of the force FP.

FP = ………………………… N [2]

P

Q

load

10° 10°

keystone

Fig. 6.3


7 (a) Define magnetic flux density and the tesla. …………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………………………………………………… ……………………………………………………………………………………... [3] (b) A metal wire of length 0.57 m and cross-sectional area 1.0 × 10–6 m2 is situated

at right angles to a uniform magnetic field of flux density 1.8 × 10–3 T, as illustrated in Fig. 7.1. × × × × × × × × × × × × × × ×× × × × × × × × × × × × × × ×× × × × × × × × × × × × × × ×× × × × × × ×× × × × × × × × × × × × × × × ×× × × × × × × × × × × × × × × ×× × × × × × × × × × × × × × × ×

Fig. 7.1

The metal has density 7.9 × 103 kg m–3 and resistivity 8.8 × 10–8 Ω m. A potential difference is applied between the ends of the wire so that there is an electromagnetic force acting on the wire.

(i) On Fig. 7.1, mark the direction of the current in the wire. [1] (ii) For the wire, calculate 1. its weight

weight = ………………………… N

electromagnetic force on wire

magnetic field directed into

plane of paper


2. its resistance.

resistance = ………………………… Ω [5] (iii) Calculate the potential difference required between the ends of the wire

for the electromagnetic force on the wire to equal its weight.

potential difference = ………………………… V [3] (iv) The horizontal component of the Earth’s magnetic field is 1.8 × 10–5 T.

State and explain why, in practice, current-carrying conductor wires are not seen to lift off the ground

................................................................................................................... ................................................................................................................... ……………………………………………………………………………... [2]


(c) (i) Two long straight parallel wires are separated by a distance x. Each

carries current I in the same direction. Explain, with the aid of diagrams, the forces which exist between the two wires.

…………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… ……………………………………………………………………………... [5] (ii) The ampere is defined as the constant current which, if maintained in

two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 × 10–7 N m–1 of length. Suggest why this definition of ampere may pose a problem in determining one ampere experimentally.

................................................................................................................... ……………………………………………………………………………... [1]


8 (a) Explain what is meant by the following terms photon, photoelectric effect,

threshold frequency, stopping potential and ionisation energy. photon: …………………………………………………………………………………. …………………………………………………………………………………………… photoelectric effect: …………………………………………………………………… …………………………………………………………………………………………… threshold frequency: ………………………………………………………………….. …………………………………………………………………………………………… stopping potential: …………………………………………………………………….. …………………………………………………………………………………………… ionisation energy: ……………………………………………………………………... ……………………………………………………………………………………... [6] (b) Fig. 8.1 shows a simplified representation of the 5 lowest energy levels of

doubly ionised lithium ( ) that has only one electron. 2+Li

Fig. 8.1


(i) Explain how emission spectral lines provide the evidence for the

existence of discrete energy levels in an atom. …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… ……………………………………………………………………………… [3] (ii) Explain why the ionised lithium vapour must be heated in order to

produce an emission spectrum. …………………………………………………………………………………… ……………………………………………………………………………… [1] (iii) Considering transitions between only these levels, 1.

determine the wavelengths of the spectral transition that produce the shortest and longest wavelength,

shortest wavelength = ………………………… m longest wavelength = ………………………… m [2] 2. state the number of emission spectral lines that is produced by

transitions among these levels, ………………………………………………………………………... [1]


3. sketch the emission spectrum of a gas consisting of these ions on

Fig. 7.2. Use vertical lines to denote the relative positions of the spectral lines.

Fig. 8.2 [4] (c) The electronic configuration of a lithium atom ( ) is as shown in Fig. 8.3. 3

7Li

Fig. 8.3

The ionisation energies of a lithium atom are: • first ionisation energy – 5.42 eV • second ionisation energy – 76.0 eV

(i) State the value of the third ionisation energy. ……………………………………………………………………………... [1] (ii) The work function of lithium metal is less than 3 eV. Explain why the

ionisation energies of an atom are always higher than the work function of the metal of the same element.

…………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… ……………………………………………………………………………… [2]

END OF PAPER


CONFIDENTIAL

River Valley High School 2010 Year 6 Preliminary Examination

H1 Physics

Answer Key and Solutions Paper 1 No. Answer Key No. Answer Key No. Answer Key 1 C 11 A 21 A 2 D 12 B 22 D 3 C 13 C 23 C 4 C 14 B 24 A 5 A 15 D 25 B 6 D 16 B 26 A 7 C 17 C 27 C 8 B 18 C 28 D 9 D 19 A 29 C 10 B 20 B 30 B

CONFIDENTIAL 1

CONFIDENTIAL

River Valley High School 2010 Year 6 Preliminary Examination

H2 Physics Paper 2 Section A Qn No.

1(a) (i) [Force] = kg m s−2 (ii) [speed] = m s−1

(b) [k] = (kg m s−2)/( m s−1)2 = kg m−1

(c) To define a quantity, in this case speed, it has to be defined in terms of quantities only and not in terms of units (e.g. second). Speed should be defined as distance travelled per unit time.

2(a) (i) Lsin θ + Lsin φ = D

(40.0 sin 50.0° + 40.0 sin φ) = 50.0 φ = 28.9° (Shown)

(ii) Vertical height Jane is above Tarzan, h = 40.0 cos φ − 40.0 cos 50.0° = 9.307 m

(b) By conservation of energy,

12

MJvJ2 + MJgh = F × D (work done against friction)

Therefore, vJ = 6.12 m s−1

(c) By conservation of energy,

12

(MJ + MT)v2 + F × D = (MJ + MT)gh

Therefore, v = 9.90 m s−1

3(a) The distances of a point on XY from the two sources are different.

When the difference in distance is integer multiples of wavelength apart, the wave meet in phase and constructive interference occurs. This results in maximum intensity. When the difference in distance is half-integer multiples of wavelength apart, the wave meet out-of-phase and destructive interference occurs. This results in minimum intensity.

(b) (i) Since a maximum is detected at P and next at Q, the path difference from A

and B is one wavelength. [Explanation must be shown to obtain 1 mark]

CONFIDENTIAL 2

CONFIDENTIAL

BR AR 13.2 12.5 0.700 mλ = − = − = (ii) 470 0.700v fλ= = ×

1329 m sv −=

(c) Distances of Q from A and B are different. Since intensity at a position from a point source is inversely proportional to the square of the distance between them, the intensities of the waves arriving at Q from A and B are different. Since intensity is proportional to the square of the amplitude, the amplitude of the waves arriving from A and B will be different. Q is a position with destructive interference without complete cancellation of the waves occurs. Hence the intensity at Q is not zero.

4(a) Electromotive force of a source is the amount of energy converted from

non-electrical forms to electrical energy when unit charge passes through the source. The potential difference between two points in a circuit is one volt if one joule of electrical energy is converted to other forms when one coulomb of charge moves from one point to the other.

(b) (i)

1. ( )( )

723

169.8 100.20 10

R −

−= ×

×

Ω 78.4R =

2. ( )224078.4

P =

W 735P = (ii)

switch A switch B switch C

Lowest OFF ON OFF

Highest ON OFF ON

5(a) 0.430

(b) (i) correct point identified;

(ii) plot correct to ±

21 square;

(iii) straight-line with acceptable fit;

(c) (i) some indication that large triangle used; (points separated by at least half-length of line) correct value from candidate’s graph;

(ii) intercept identified; should be 0.32, not 0.38 so graph does not agree;

(d) straight-line with same gradient;

CONFIDENTIAL 3

CONFIDENTIAL

having intercept of 0.32;

CONFIDENTIAL 4

CONFIDENTIAL

Section B

6(a) Moment of a force acts on a rigid body about an axis is the product of the force and the perpendicular distance between the line of action of the force and the axis.

(b) (i) Taking moments about the elbow,

Ty x 3.5 = 65 x 10 + 20 x 35 Ty = 385.7 N T = Ty / cos 20° = 410 N

(ii) Tx = 385.7 / tan 20° = 140.4 N ∑ Fx = 0 Tx = Rx = 140.4 N ∑ Fy = 0 Ty = Ry + 65 + 20 Ry = 385.7 -65 – 20 = 300.7 N Resultant force acting at elbow (pivot) = 2

xR R+ 2y = 332 N

State direction

(c) (i) Newton’s second law states that the rate of change of momentum of an

object is directly proportional to the resultant force acting on that object and has the same direction as the force.

Impulse-momentum theorem states that the impulse imparted to an object is equal to the change in its momentum.

(ii) Larger change in momentum (higher speed) Shorter time interval force exerted on hand equal in magnitude and opposite in direction to the force on wood

(d) (i) 1 mark for each correct direction

(ii) 0F∑ =

4600 600 2 sin10PF+ = 15PF = kN

7(a) The magnetic flux density is defined as the force per unit length per unit current acting on an infinitely long current carrying conductor placed perpendicularly to the magnetic field.

CONFIDENTIAL 5

CONFIDENTIAL

The magnetic flux density of a magnetic field is said to be 1 tesla, if the force acting per unit length on an infinitely long conductor carrying a current of 1 A and placed perpendicularly to the magnetic field is 1 N m−1.

(b) (i) From left to right

(ii) 1. W m g= ( )DAL gρ=

( )( )( )( )3 67.9 10 1.0 10 0.57 9.81−= × ×

N 24.42 10−= ×

2. RLRAρ

=

( ) ( )( )

86

0.578.8 10

1.0 10−

−= ×

×

Ω 25.02 10−= × (iii) F BIL W= =

VW B LR

=

2.16WRVBL

= = V

(iv) B-field is very weak. Moreover W and R is higher in practice (wires are longer), F required is larger.

(c) (i) correct diagram (directions of B-field and forces)

current in one wire sets-up concentric B-field around itself second wire is placed with current flowing perpendicularly to the B-field set-up by first wire, a force is experienced by the second wire By N3L, the first wire will experience and equal and opposite force to that of the second wire Hence the forces on the wires are attractive

(ii) • Infinitely long wire is not possible in practice • Geometrical arrangement is difficult to maintain (i.e., wires are 1 m apart)

8(a) Photon is a quantum of electromagnetic energy

Photoelectric effect is the emission of electrons … … when electromagnetic radiation of frequency greater than the threshold frequency is incident on the surface of a metal. Threshold frequency is the minimum em radiation frequency that can cause photoelectric emission on a particular metal. Stopping potential is the highest negative potential at the collecting plate that stop even the most energetic photoelectrons.

CONFIDENTIAL 6

CONFIDENTIAL

The energy needed to remove the outermost electron.

(b) (i) Electromagnetic radiation is emitted as photons when electrons losses energy in the atom. The energy of the photons is hf, f is the frequency of the radiation. Spectral lines are discrete with well-defined frequency. Therefore electrons loss energy in discrete amount in atoms. This is only possible if electrons in an atom transit between discrete energy level.

(ii) Heating causes the sizable number of ions to be excited, i.e., electrons are at higher energy levels. Heating causes the sizable number of ions to be excited, i.e., electrons are at higher energy levels.

(iii) 1. emission

hc hc hcEE E

λ λλ

= ⇒ = ⇒ =Δ

Shortest wavelength ( )

10.6 nm (3 s.f.)121.9 4.9

hce

= =−

Longest wavelength ( )

460 nm (3 s.f.)7.6 4.9

hce

= =−

2. Number of spectral lines occurs between two levels, number of ways to produce spectral lines is 5

2C Number of spectral lines is 10. 3.

Approx. correct position for spectral lines (5 → 1) and (5 → 4) at 10 nm and

460 nm. Approx. correct relative position for spectral lines (5 → 2) and (5 → 3). 3 other lines very close and to the right of (5 → 1) spectral line. 2 other lines slightly further and increasing wavelength to the right of (5 → 2) spectral line.

(c) (i) 122 eV

(ii) Work function is the energy to remove delocalised electrons in the conduction

band. Ionisation energy is the energy to remove electrons in an energy level of an atom. The conduction band occupies energies higher than the discrete energy levels in an atom. Therefore less energy is required to remove delocalised electrons.

CONFIDENTIAL 7

CONFIDENTIAL

CONFIDENTIAL 8

1

SAJC 2010 Prelims/8866/01 [Turn Over

ST. ANDREW’S JUNIOR COLLEGE JC2 2010

Preliminary Examinations PHYSICS, Higher 1 8866/01 Paper 1 22nd September 2010 1 hour (1400 Hrs – 1500 Hrs) Additional Materials: Optical Mark Sheet (OMS) READ THESE INSTRUCTIONS FIRST Write in soft pencil. Do not use staples, paper clips, highlighters, glue or correction fluid. Write your name, Civic Group and index number on the separate Optical Mark Sheet (OMS). There are thirty questions in this paper. Answer all the questions. For each question there are four possible answers A, B, C, D. Choose the one you consider correct and record your choice in soft pencil on the separate Optical Mark Sheet (OMS). Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet.

Instructions for using the Optical Mark Sheet (OMS)

1. Fill in your class number (e.g. 09A01 = "01", 09S22 = “22”) in the first two rows. 2. Fill in your class register number in the next two rows. (e.g. register number 1 is filled in as

"01"). 3. Write your class and register numbers into the column on the left (ie. 0101)

For Official Use

Paper 1 / 30 Paper 2 / 80

Total / 110 Percentage / 100 Grade

This Question Paper consists of 12 printed pages

Class no.

Register no.

Write your numbers here

2


Data


elementary charge, e = -1.60 x 10-19 C






Formulae

uniformly accelerated motion, s = u t + ½ a t2

v2 = u2 + 2 a s

work done on/by a gas, W = p ΔV

hydrostatic pressure, p = ρ g h


resistors in parallel, 1 / R = 1 / R1 + 1 / R2 + ..

3


1 A quantity x is measured many times and the number N of measurements is plotted against x. The true value of the quantity is x0. Which graph best represents precise measurements with poor accuracy?

2 A stationary rocket is fired horizontally and travels a distance of (100 ± 1) m. If the

acceleration of the rocket is constant at (23.1 ± 0.5) m s-2, what would be its final velocity at the end of the distance covered?

A (68 ± 1) m s-1 B (67.9 ± 1.0) m s-1 C (68.0 ± 1.1) m s-1 D (67.97 ± 1.08) m s-1

3 Frankie throws a small rubber ball vertically downwards at a speed of 3.0 m s-1. It hits

the ground and rebounds vertically. The graph below shows the velocity-time graph for the first 1.7 s of the motion of the rubber ball.

Fig. 3 What is the displacement of the ball between the point at which it was first thrown and the highest point of the motion?

A zero B 1.8 m C 3.6 m D 7.2 m

A B C D

time / s

v / ms-1

0.6

- 3

- 9

8

0 1.5 1.7

4


4 A device launches two identical balls, x and y, simultaneously in a horizontal direction from the same height, as shown in the diagram below. The results are as indicated.

Fig. 4 (not to scale) Which statement correctly describes what happens? A x hits the ground before y as it is closer to the launch site. B y hits the ground before x as it has a higher launch velocity. C x and y hit the ground simultaneously with the same velocity. D x and y hit the ground simultaneously with different velocities. 5 Three balls A, B and C, each move in different directions, as indicated by the vector v.

They then experience the same acceleration in the upward direction. Which of the following is true about their respective speeds?

Ball A Ball B Ball C

Fig. 5

Ball A Ball B Ball C

A increases increases increases

B increases increases decreases

C no change increases increases

D no change no change decreases

v

v

v

a a a

A B C

x y

Launch device

5


6 A force F is applied to a body of mass m on a smooth inclined plane as shown. The body moves up along the inclined plane with uniform acceleration. The magnitude of the resultant force acting on the body upwards along the incline is

Fig. 6

A F sin φ – mg sin θ B F cos φ – mg sin θ C mg cos θ – mg sin θ D - F cos φ + mg sin θ 7 Which of the following statement concerning momentum is correct?

A Momentum is a scalar quantity. B Momentum is proportional to the rate of change of force. C Newton’s third law can be used to derive the principle of conservation of

momentum. D When a small mass collide with a large mass and they coalesce, momentum

is not conserved. 8 In which of the following situations can a person experience weightlessness?

A A parachutist descending at terminal velocity with the parachute fully open. B An astronaut propelled vertically in the initial stage of his journey, with the

rocket engines burning. C An athlete clearing the bar in a high jump event. D A Naval Diver equipped so that he remains at a constant depth below the

water surface without any effort on his part. 9 What is not true of two forces that give rise to a couple?

A They act in opposite directions. B They both act at the same point. C They both act on the same body. D They both have the same magnitude.

φ F

mg θ

6


10 The diagram shows the force against extension for a wire. When the force is 60 N, the extension of wire is 3.4 mm. The energy stored when the wire is extended by 1 mm from its initial length is

A 0.0088 J C 29.9 J B 0.102 J D 102 J

11 A man drives along a straight road from right to left with a constant speed and tosses

a coin vertically upwards. If effects of air resistance are significant, which diagram best represents the trajectory of the coin seen by a stationary observer?

A B

C D

60

3.4 extension/ mm

force/ N

Fig. 10

7


12 A boat moving at constant speed v through still water experiences both water drag force, F1 and force of air resistance, F2. What power does the boat engine supply?

A (F1 + F2) v C (F1 + F2) v2 B (F1 − F2) v D

21

(F1 + F2) v

13 A body moves from X to Y along a track. Its kinetic energy at Y is 25 J, and its

potential energy is 30 J more than at X. If the work done by friction on the body along XY is 10 J, what is the original kinetic energy of the body at X?

Fig. 13

A 35 J B 45 J C 55 J D 65 J 14 A block of mass 4 kg is released at point P on a curved frictionless track as shown.

The block slides down a vertical distance of 80 cm and strikes a spring at the end of the track. If the elastic constant of the spring is 350 N m-1, find the maximum compression of the spring.

Fig. 14

A 8.97 cm B 17.9 cm C 29.9 cm D 42.4 cm 15 The diagram shows a transverse wave on a rope. The wave is travelling from left to

right. The phase difference between P and Q is

Fig. 15

A 4π

B 2π

C π D π2

P Q

Y

X

P wall

spring 80 cm

8


16 The energy carried by a wave is proportional to

A the square of the wave’s amplitude. B the square of the wave’s intensity. C the square root of the wave’s intensity. D the wave’s amplitude.

17 A cylindrical glass tube with both ends open is closed at one end by covering it with a

thick metal sheet as shown below. The fundamental resonant frequency is found to be 280 Hz.

Fig. 17 If the metal sheet is now removed, what is the new fundamental frequency of the

resulting open tube? A 140 Hz B 280 Hz C 420 Hz D 560 Hz 18 Wave generators S1 and S2 generate waves of equal wavelength which then arrive at

a point P. At P, S1 by itself produces an oscillation of amplitude a and S2 produces an oscillation of amplitude 2a, and there is a phase difference of 2π radians between the oscillations.

Which of the following graphs best represents the resultant oscillation at P when both generators are switched on?

a

−atime

displacement

A

a

−atime

displacement

C

a

−atime

displacement

B

3a

−3a

time

displacement

D

Metal sheet

Glass tube

9


19 A standing wave is set up on a stretched string PS as shown in the diagram.

Fig. 19

The vibrations of the two points Q and R, shown on the string have A different amplitude and are in anti-phase. B different amplitude and are in phase. C the same amplitude and are in anti-phase. D the same amplitude and are in phase.

20 Fig. 20a shows a circuit with battery of EMF, E connected to identical bulbs of

resistance, R. An additional identical bulb, D, was added to the circuit as shown in Fig. 20b. Which bulbs will become brighter or dimmer?

Bulb A Bulbs B & C

A Brighter Brighter B Brighter Dimmer

C Dimmer Dimmer D Dimmer Brighter

21 The diagram shows two resistors connected in a circuit in which a current of 1.5 A is

flowing. What is the current in the 1.8 Ω resistor?

Fig. 21

A 0.15 A B 1.35 A C 1.5 A D 2.7 A

1.8 Ω

0.2 Ω

1.5 A

D C B

A

Fig. 20b

C B

A

Fig. 20a

Q R P

x

S

antinodex

10


22 A 24-ohm resistor radiates 12 W. A 16-ohm resistor in parallel with it will radiate

A 8 W B 12 W C 18 W D 24 W 23 A resistor is made from two equal lengths of wire of the same resistivity joined in

series. The first wire X has twice the diameter of the second wire Y. When a current flows through the resistor, what is the potential difference across X as a fraction of the total potential difference across the resistor?

A 51

B 41

C 54

D 21

24 A 10 Ω resistor is connected across three identical cells each having an e.m.f. of

1.5 V and internal resistance of 3 Ω.

Fig. 24

What is the current flowing through the resistor? A 0.079 A B 0.12 A C 0.14 A D 1.7 A 25 The figure shows the path taken by an electron as it enters a region of magnetic field

directed downwards into the plane of the paper. Which of the indicated paths is the one taken by the electron in the magnetic field?

Fig. 25

10 Ω

× × × × ×

× × × × ×

× × × × ×

× × × × ×

× × × × ×

A B

D

C

Electron entering

magnetic field

11


26 Two long straight wires, X and Y, are placed perpendicularly to each other at a small distance apart. The current in wire X is flowing into the page and the current in wire Y is flowing to the right.

Fig. 26

What is the direction of the force acting on wire Y at point P due to the magnetic field produced by wire X? A out of the page B into the page C upwards D downward

27 Two long straight and parallel wires carrying currents in the same direction separate

the surrounding space into three regions 1, 2 and 3. In which region(s) can there be a neutral point (i.e. a point of zero magnetic field)?

Fig. 27

A Region 2 only. B Both regions 1 and 3. C Either region 1 or region 3 but not both. D There are no neutral points.

28 A student connects a photocell to a supply and finds that when the cell is exposed to

monochromatic radiation a current flows only when the potential difference across the cell is less than 1.6 V. What is the maximum energy of the emitted electrons?

A 1.0 x 10–19 J B 2.6 x 10–19 J C 4.8 x 10–11 J D 1.6 J

29 Which of the following statements, referring to photoelectric emission, is always true?

A No emission of electrons occurs for very low intensity illumination. B For a given metal there is a minimum frequency of radiation below which no

emission occurs. C The velocity of the emitted electrons is proportional to the intensity of the

incident radiation. D The number of electrons emitted per second is independent of the intensity of

incident radiation.

I1

I2

Region 1

Region 2

Region 3

Wire X

PWire Y

x

12


30 The diagram shows the energy levels of a gas atom.

____________________ 0 J ____________________ -2.4 x 10-19 J ____________________ -5.4 x 10-19 J ____________________ -21.8 x 10-19 J

Fig. 30

A free electron of kinetic energy of 20.0 x 10-19 J collides with the cool gas atoms. What is the kinetic energy of the free electron after the collision? A 1.8 x 10-19 J B 3.6 x 10-19 J C 5.4 x 10-19 J D 16.4 x 10-19 J

- End of Paper -

1


Class Index Number Name 09

ST. ANDREW’S JUNIOR COLLEGE

JC 2 2010 Preliminary Examinations

PHYSICS, Higher 1 8866/02 Paper 2 Structured Questions 20th September 2010 2 hours (1400 Hrs – 1600 Hrs) Candidates answer all questions on the Question Paper. No additional materials are required. READ THESE INSTRUCTIONS FIRST Write your name, index number and Civics Group on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Section A Answer all questions. Section B Answer any two questions. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.



Section A / 40

Section B / 40

Total / 80

2


Data


elementary charge, e = -1.60 x 10-19 C






Formulae

uniformly accelerated motion, s = u t + ½ a t2

v2 = u2 + 2 a s

work done on/by a gas, W = p ΔV



resistors in parallel, 1 / R = 1 / R1 + 1 / R2 + ..

3


Section A Answer all the questions in the space provided.

1 A boom is used to enable a person to move heavy loads. A typical arrangement is as shown.

Fig. 1.1 A steel cable is attached to the top of the boom and the floor, a certain distance behind the boom, such that the cable makes an angle of 45º to the horizontal, as shown in Fig. 1.1. The uniform boom has a mass of 45 kg and length 3 m. A human operator exerts a force F of 120 N horizontally at a distance of 0.75 m away from the hinge, as measured along the boom. The system is in equilibrium. (a) State the conditions for a body to be in equilibrium. [ 2 ]

…………………………………………………………………………………………………... …………………………………………………………………………………………………...

(b) Show that the tension, T, in the cable connecting the top of the boom to the floor is 4.1 kN. [ 2 ]

cable

rope

4


(c) Determine the magnitude of the force exerted on the hinge by the boom.

Force = ………………………. N [ 3 ]

2 (a) In a YOG cross-country cycling event, a competitor cycles up a slope inclined at 37o

at a steady speed of 13 m s-1. The total mass of the bicycle and the rider is 80 kg.

The total resistive force acting on the bicycle and the rider is 75 N. Find the power

required to sustain this speed.

Power = ……………………….. W [ 3 ]

(b) Discuss the energy changes of the rider as he travels up the slope mentioned in (a). [ 3 ]

…………………………………………………………………………………………………...

…………………………………………………………………………………………………...

…………………………………………………………………………………………………...

5


3 For a hypothetical electronic device, the potential difference V, measured across the device, is related to the current I by

V = 355 I 2 (a) (i) Explain whether the device obeys Ohm’s Law. [ 1 ]

…………………………………………………………………………………………..

…………………………………………………………………………………………..

(ii) Determine the resistance of the device when the current is 240 mA.

Resistance = ………………….. Ω [ 2 ] (b) When the lights of a car are switched on, an ideal ammeter in series with them reads

10.0 A and an ideal voltmeter connected across them reads 12.0 V. (See Fig. 3.1) The internal resistance of the battery is 50.0 mΩ.

Fig. 3.1

(i) Show that the EMF of the battery is 12.5 V. [ 1 ]

50.0 mΩ

6


(ii) With both switches turned on, the ammeter reading now drops to 8.00 A and the voltmeter reading decreases to 9.6 V. Calculate the current through the starting motor when the lights are on.

Current = ……..……………..A [ 3 ] 4 A uniform wire of length 62.0 cm and mass 13.0 g is suspended by a pair of flexible leads in

a magnetic field B of 440 mT. A current is passed through the wire such that the tension T in the supporting leads is zero.

Fig. 4.1

(a) (i) Draw in Fig. 4.1 the direction of the current in the wire. [ 1 ]

(ii) Determine the magnitude of the current through the wire.

Current = ……………..……. mA [ 2 ]

x x x x x

x x x x x

x x x x x

x x x x x

x x x x x

62 cm

B Flexible leads

wire

TT

7


(b) “If a current-carrying conductor does not experience any magnetic force when placed stationary in a region of space, there is no magnetic field in that region.” Discuss the validity of the above conclusion that there is no magnetic field in that region of space. [ 2 ]

………..………………………………………………………………………………………… ………..………………………………………………………………………………………… ………..…………………………………………………………………………………………

5 (a) De Broglie discovered that when he passed fast-moving electrons through a crystalline

solid, diffraction images obtained were similar to those found in diffraction experiments using X-rays ( =λ 10 – 10 m) through crystalline solids. Explain what can be deduced from this experiment concerning

1. the nature of electrons. [ 1 ]

……………………………………………………………………………………………… ………………………………………………………………………………………………

2. separation of the atoms of the crystalline solid. [ 1 ]

……………………………………………………………………………………………… ………………………………………………………………………………………………

(b) One such electron has a kinetic energy of 1 x 10-18 J. Calculate

(i) the speed of the electron,

Speed = ……………………. m s -1 [ 1 ]

(ii) the wavelength of the electron.

Wavelength = ………………………….. m [ 2 ]

8


6 A mass M is moving at 5.00 ms-1 along a horizontal frictionless guide which bends into a vertical circle of radius r, as shown in Fig. 6.1. Fig. 6.2 and Fig. 6.3 show the velocity-time graphs for the vertical and horizontal components respectively of the velocity along the section ABC of the curve.

Fig.6.2

M

Fig. 6.1 A

B

C

r

9


Fig. 6.3

(a) With the aid of Fig. 6.2, determine an appropriate value for the height of the vertical

circle.

height of vertical circle = ……………………….. m [ 2 ]

10


(b) (i) From Fig. 6.2 and Fig. 6.3, determine the vertical and horizontal components of the acceleration of the mass M at B, 200 ms after it passes the point A.

vertical component of the acceleration = ……………………….. ms-2 [ 1 ]

horizontal component of the acceleration = ……………………….. ms-2 [ 2 ]

(ii) Hence, determine the magnitude and the direction of the resultant acceleration of the mass M at B.

magnitude of acceleration = ……………………….. ms-2 [ 1 ]

direction of acceleration = ………………………………………… [ 2 ] (c) Without detailed mathematical calculations, deduce the total area between the curve

and the time axis of Fig. 6.3. Explain your answer. [ 2 ]

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

11


Section B Answer any two questions from this section.

7 (a) Frankie released a 15.0 g rubber ball from a height of 10.0 m from a classroom block above a flat ground. Assume that air resistance is negligible.

(i) How long does it take for the ball to reach the ground?

time = ………..………… s [ 2 ]

(ii) Assuming that the ball does not lose any energy during the bounce, sketch and label the acceleration versus time graph of the ball, starting from the release of the ball to the third time that the ball hits the ground. [ 3 ]

(iii) State one change in the a-t graph above if the ball loses some energy as it bounces off the ground. [ 1 ]

…..……………………….…………………………………………………………………..

…..……………………….…………………………………………………………………..

a /m s-2

t / s

12


(iv) Calculate the speed of the ball just before it hits the ground.

Speed = …………………………. m s-1 [ 2 ] (b) Fig. 7.1 shows how the force F on the rubber ball in (a) varies with time t when the ball

first hits the hard ground and rebounds. The kinetic energy of the ball after the collision is the same as it was before the collision.

(i) State the quantity that is obtained by determining the area under the graph in Fig. 7.1. [ 1 ]

……………………………………………………………………………………………..

(ii) Using Fig. 7.1 and your answer in (a)(iv), determine the maximum force F1 that was applied by the ground on the ball during its rebound.

F1 = ………………………… N [ 3 ]

F / N

t / ms

0.8 1.6 0

F1

Fig. 7.1

13


(c) Frankie decides to throw the same rubber ball at a velocity of 22 m s-1 at an angle of 35o below the horizontal, aiming at a 450.0 g toy truck placed 9.9 m below him on the ground, as shown in Fig. 7.2 below.

Fig. 7.2

(i) State the principle of conservation of momentum. [ 2 ] ………………………………………………………………………………………………. ……………………………………………………………………………………………….

……………………………………………………………………………………………….

(ii) Calculate the vertical velocity of the ball just before it hits the toy truck.

Vertical velocity = ……………………… m s-1 [ 2 ]

Classroom block

truck

35o

9.9 m

tray

14


(iii) If the ball hits the base of the tray on top of the toy truck, determine their common velocity when they move off together after the impact. (Assume that there is no friction acting on the truck initially).

Velocity = ……………………… m s-1 [ 2 ]

(iv) How should Frankie hit the truck with his rubber ball so that the truck moves off with a higher velocity than the one calculated in (c)(iii) ? [ 2 ]

……………………………………………………………………………………………….

……………………………………………………………………………………………….

……………………………………………………………………………………………….

15


8 (a) State and explain two differences between sound waves and electro-magnetic (EM) radiation. [ 4 ]

………..………………………………………………………………………………………… ………..………………………………………………………………………………………… ………..………………………………………………………………………………………… ………..…………………………………………………………………………………………

………..………………………………………………………………………………………… ………..…………………………………………………………………………………………

………..………………………………………………………………………………………… ………..………………………………………………………………………………………… (b) Fig. 8.1 shows Graph A, which is the displacement-distance graph at time t = 0 s of

a progressive wave. Graph B represents the displacement-distance graph of the same wave at t = 0.1 s.

Fig. 8.1

P

16


(i) State the amplitude of Graph A at t = 0 s.

Amplitude = …………….……. cm [ 1 ]

(ii) State the wavelength of the progressive wave.

Wavelength = ..………….………. cm [ 1 ]

(iii) On Graph B, draw a dot (labelling it Q), to represent the position of P when t = 0.1 s. [ 1 ]

(iv) Determine the phase difference between Graph A and Graph B, and hence compute the period of the wave.

Phase difference = ……..……………… [ 1 ]

Period = ……….…….…..…. s [ 2 ]

(v) Hence or otherwise, sketch displacement-time graph of particle P, starting from t = 0 s for one complete cycle. Indicate Q on your sketch.

[ 4 ]

Displacement /cm

Time/ s

17


(c) A long freight train on a straight track can be treated as a line source emitting a cylindrical expanding sound wave. Assuming that the air absorbs no energy, show that the amplitude, A of the wave is dependent on the distance from the source, r in

the relationship, 1 Ar

α [ 2 ]

(d) A spherical sound source is placed at P1 near a reflecting wall AB and a microphone

is located at point P2, as shown in Fig. 8.2. The frequency of the sound source is variable. When the sound reflects off the wall, there is no phase change on reflection; the angle of incidence equals the angle of reflection.

Fig. 8.2

(i) Show that the length of the dashed path from P1 to P2 travelled by sound

waves reflected off AB is 34.08 m. [ 1 ]

18


(ii) Determine the lowest frequency for which the sound intensity, as observed at P2, will be a maximum.

Frequency = ……..….……….. Hz [ 3 ]

19


9 (a) The figure below represents the lowest energy levels of the mercury atom with the corresponding quantum number, n, and energy measured in eV.

Fig. 9.1

Considering transitions between only these 5 levels, state

(i) The total number of possible emission transitions that can be produced.

Number = .………..………….. [ 1 ]

(ii) The spectral transition that has the shortest wavelength.

From level ……… to level ……… [ 1 ]

(b) Cool mercury vapour (with energy levels like that of Fig. 9.1) at low pressure is

bombarded with electrons of kinetic energy E. State the transition(s), if any, that would be observed if E has the value of

(i) 4.00 eV : …………………………………………………………………………. [ 1 ]

(ii) 7.00 eV : …………………………………………………………………………. [ 1 ]

(iii) Instead of an electron, a photon of energy 7.00 eV is incident on the mercury atom in the ground state. Which transitions, if any, would be made by the electron in the ground state? Explain your answer. [ 2 ]

…………………………………………………………………………………………..

…………………………………………………………………………………………..

n54 3 2 1

Energy– 1.56 eV – 2.48 eV – 3.71 eV – 5.52 eV – 10.4 eV

20


(c) A student commented that ionization energy and work function are the same since both involve the removal of electrons. Discuss whether you agree with the statement. [ 2 ]

…………….……………………………………………………………………………………

…………….……………………………………………………………………………………

…………….……………………………………………………………………………………

(d) A monochromatic light source with a power output of 0.50 W and a wavelength of

480 nm is incident on a cold metal surface in a vacuum tube. The light is incident on a metal surface which has a work function of 4.7 eV.

(i) Calculate the rate of emission of photons from the light source.

Rate of emission = …..………………….. [ 2 ]

(ii) Explain whether photoelectrons are emitted. [ 2 ]

…………………………………………………………………………………………..

…………………………………………………………………………………………..

…………………………………………………………………………………………..

21


(iii) Assuming that the radiation is incident normally to the metal surface of area 4.13 × 10 – 7 m2, calculate the radiation pressure on the surface.

Radiation pressure = …………………. N m-2 [ 4 ]

(e) The emitted photoelectrons in a photoelectric experiment are collected at the

adjacent electrode of the same metal. The photoelectric current I depends on the frequency f of the incident light, the potential difference V between collector and emitter, and the incident power P. Draw sketch graphs to show

(i) How I varies with V, with P and f remaining constant. [ 2 ]

(ii) Suggest and explain what will happen to the graph if the metal is replaced by another metal with a higher work function. [ 2 ]

………………………………………………………………………………………….

………………………………………………………………………………………….

………………………………………………………………………………………….

[End of Paper]

1

SAJC 2010 H1 Prelims solutions

SAJC JC2 Preliminary Exams (H1 Physics) 2010 Suggested Solutions Paper 1 (MCQs)

1 2 3 4 5 6 7 8 9 10 B A A D B B C C B A

11 12 13 14 15 16 17 18 19 20 D A D D C A D D D B

21 22 23 24 25 26 27 28 29 30 A C A C C B A B B B

Paper 2 (Structured) Section A

1 (a) Net force in all directions is zero. [ 1 ] Net moment about any axis or point is zero. [ 1 ]

(b)

Taking moments about the hinge, (T sin 15º × 3) + (120 × 0.75 sin 60º) [ 1 ]

= (45 × 9.81 × 1.5 sin 30º) + (200 × 9.81 × 3 sin 30o) [ 1 ] T = 4.1 kN (shown)

(c) Consider vertical equilibrium,

Hy = (45 × 9.81) + (200 × 9.81) + T cos 45o , where T = 4.1 kN [ 1 ] Hy = 5.3 kN (upwards) Consider horizontal equilibrium Hx = 120 + T sin 45 º = 3.0 kN (rightwards) [ 1 ]

22yx HHH += = 6.1 kN [ 1 ]

Magnitude of the force the hinge exerts on the boom is 6.1 kN

45 x 9.81

200 x 9.81

T sin 15O

F sin 60O

2


2 (a) ΣF = 0 (steady speed) Fmotor – FR – mg sin 370 = 0 Fmotor – 75 – 80(9.81)(sin 370) = 0 [ 1 ] Fmotor = 547.3 N [ 1 ] ∴P = Fv = (547.3)(13) = 7110 W [ 1 ] (b) Chemical energy in cyclist is converted into gravitational PE of the cyclist system, while remaining energy is to do work against resistive force (to maintain the

speed). [ 3 ]

3 (a) (i) The device does not obey Ohm’s Law, which states that for a conductor at constant temperature, the current in the conductor is directly proportional to the potential difference across it. For this device, I is not directly proportional to V [ 1 ]

(ii) When I = 0.240 A,

V = 355(0.240)2 = 20.448 V [ 1 ]

R = V/I = 20.448 / 0.240 = 85.2 Ω [ 1 ] (b) (i) E = Ir + V = (10.0)(0.05) + 12 [ 1 ] = 12.5 V

(ii) E = Ir + V 12.5 = Itotal (0.05) + 9.6 [ 1 ] Itotal = 58 A Itotal = Imotor + Ilights [ 1 ] Imotor = 58 – 8

= 50 A [ 1 ]

4 (a) (i) left-to-right [ 1 ]

(ii) F = B I L sin θ mg = B I L I = (0.013)(9.81) / [(0.440)(0.620)] [ 1 ] = 0.467 A = 467 mA [ 1 ] (b) A stationary current-carrying conductor placed parallel to a magnetic field will not

experience a magnetic force. Hence, the conclusion is not valid. [ 2 ]

3


5 (a) 1. Electrons exhibit wave-like nature as diffraction is a wave property. [ 1 ]

2. Significant diffraction occurs when the wavelength is similar in the order of magnitude as the separation between the crystal atoms. Since wavelength of x-ray is of the order of 10 – 10m, hence the separation of atoms in the crystalline solid is of the order 10 – 10m. [ 1 ]

(b) (i) KE = ½ mv2 ( )

31

18

1011.910122

−

−

××

==mKEv

v = 1.5 x 106 m s-1 [ 1 ]

(ii) ( )( )631

34

105.11011.91063.6

×××

==−

−

mvhλ [ 1 ]

m10109.4 −×=λ [ 1 ]

6 (a) From Fig. 6.2, area under the graph = vertical displacement traveled from A to C

= height of circle = 32 x (0.5 x 50x10-3) [ 1 ] = 0.800 m (3 sf) [ 1 ]

(b) (i)

ay = (3.5 – 0.4) / (170 – 300)x10-3 = - 23.8 ms-2 (3 sf) [ 1 ] ax = (0 – (-4)) / (100 – 305)x10-3- = - 19.5 ms-2 (3 sf) [ 2 ]

4


(ii)

[ 1 ]

[ 1 ] The direction of the acceleration is 39.3o south of west. [ 1 ] (c) The total area between the curve and the time axis is zero. [ 1 ]

This is because the net horizontal displacement traveled by the mass from A to C is zero. [ 1 ]

Section B

7 (a) (i) Using s = ut + 1

2at2

10.0 = 1

2(9.81)t2 [ 1 ]

t =1.43 s [ 1 ]

(ii)

a

t

9.81 ms-2

1.43 s

For correct shape [ 1 ] For correct number of bounces [ 1 ] For correct labeling of timing at first bounce [ 1 ]

5


(iii) The horizontal part of the graph will get shorter with each consecutive bounce. OR The peak negative acceleration gets smaller. [ 1 ]

(iv) From v2 = u2 + 2 a s, v2 = 0 + 2 (9.81)(10.0) v = 14.0 m s-1

(b) (i) Impulse or change in momentum. [ 1 ]

(ii) total change in momentum = area under F-t graph

Since total change in momentum = final momentum – initial momentum and final momentum is equal in magnitude but opposite in direction to initial momentum, hence | total change in momentum | = 2 (initial momentum) = 2 (15.0 x 10-3)(14.0) [ 1 ]

2 (15.0 x 10-3)(14.0) = ½ (1.6 x 10-3)(F1) [ 1 ]

F1 = 525 N (3 sf) [ 1 ]

(c) (i) For a system of interacting objects, the total momentum of the bodies (ie. momentum of the system) remains constant, [ 1 ]

provided no external resultant force acts on the system. [ 1 ] (ii) Taking downwards as positive, v2 = u2 + 2 a s = (22 sin 35o)2 + 2 (9.81)(9.9) [ 1 ] v = 18.8 m s-1 [ 1 ]

(ii) By conservation of momentum, m1 u1 + m2 u2 = (m1 + m2) v (0.015)(22 cos 35o) + 0 = (0.465)(v) [ 1 ] v = 0.581 m s-1 [ 1 ]

(iv) To impact a greater momentum to the truck so that it moves off with a higher velocity, the ball should strike the truck and rebound off the truck (i.e. should not be collected in the tray of the truck). [ 2 ]

Q8 (a) Sound waves are longitudinal waves; EM waves are transverse waves. [ 1 ]

The particles of longitudinal waves oscillate parallel to the direction of the propagation of the waves while the particles of transverse waves oscillate perpendicular to the direction of the propagation of the waves. [ 1 ]

Sound waves are mechanical waves while EM waves are electromagnetic waves. [ 1 ]

Mechanical waves require a material medium for their propagation while EM waves do not require a material medium for their propagation. [ 1 ]

6


(b) (i) 1 cm [ 1 ]

(ii) 2 cm [ 1 ]

(iii) Q directly below P [ 1 ]

(iv) Phase difference = (0.25/2) X 2π = π/4 [ 1 ] 0.1 / Period = (π/4) / 2π [ 1 ] Period = 0.8 s [ 1 ]

(v) Labelling of vertical axis – Amplitude = 1 cm [ 1 ]

Labelling of horizontal axis – Period = 0.8 s [ 1 ]

Drawing of y = cos ωt for one cycle [ 1 ] Correct position of Q at t = 0.1 s, y = 0.7 cm [ 1 ] (c) Intensity = Power / Curved Area of Cylinder = Power / 2πrL , where L is the length of the train [ 1 ]

Since Power and L is constant, and Intensity α A2, A2 α 1/r [ 1 ] 1 Ar

α

(d) (i) Reflected Path = √ [ (24.4 + 3.05 + 3.05)2 + (15.2)2 ] = 34.08 m [ 1 ]

(ii) Direct path = √ [ (24.4)2 + (15.2)2 ] = 28.75 m [ 1 ]

Lowest frequency occurs when path difference = n x (max wavelength) (34.08 – 28.75) = 1 x (max wavelength)

max wavelength = 5.33 [ 1 ] Lowest frequency = 330 / 5.33 = 61.9 Hz [ 1 ]

7


9 (a) (i) 10 transitions [ 1 ]

(ii) shortest wavelength implies largest frequency. Transition which emits photon of highest frequency is from level 5 1. [ 1 ]

(b) (i) No transition will be observed. [ 1 ] (ii) from 3 1 , 3 2 , 2 1 [ 1 ]

(No marks given if student gives any transition for absorption , e.g. 1 3)

(iii) No transitions will be made. [ 1 ] The incoming photon must be absorbed entirely or not at all. However, no energy transition is exactly 7.00 eV. [ 1 ]

(c) Ionisation energy is the energy needed to free an outermost electron from the atom, [ 1 ] whereas work function is the energy needed to free the free electrons from the metal surface. [ 1 ]

(d) (i)

)103(1063.6)10480(50.0

)(

834

9

×××

==

==

−

−

hcP

tn

hctn

tnhfP

λλ

181021.1 ×= [ 1 ]

(ii) Photoelectrons will be emitted if f > fo

Frequency of the radiation is = 149

8

1025.610480

103×=

××

= −λc

Hz

Threshold frequency, fo = 4.7eV × 1.6 × 10 -19 ÷ 6.63 × 10 – 34 = 1.13 × 10 – 15 [ 1 ] Since f < fo, no photoelectrons will be emitted. [ 1 ]

[ 1 ]

8


(iii)

PaAFP

NFtnhF

hp

tpn

tTotalF

379

9

9

3418

1009.81013.410343.3

10343.310480

)1063.6)(1021.1(22

)2(

−−−

−

−

−

×=×÷×==

×=×

××==

=

==

λ

λ

momentum in change

(e) (i)

shape of graph: [ 1 ] ; labelling: [ 1 ]

(ii) With a lower stopping potential, [ 1 ]

graph will shift right [ 1 ]

‐ End of solutions ‐

[ 1 ]

[ 1 ]

[ 1 ]

[ 1 ]

1

SRJC 2010 8866/Prelim/2010

SERANGOON JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 1

PHYSICS 8866

Preliminary Examination 26 August 2010 Paper 1 Multiple Choice 1 hour

Additional Materials: Optical Mark Sheet (OMS) READ THIS INSTRUCTIONS FIRST

Write your name, civics group and index number in the spaces at the top of this page. There are thirty questions on this paper. Answer all questions. For each question, there are four possible answers labeled A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the OMS. Read the instructions on the OMS very carefully. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this question paper.

This document consist of 14 printed pages and no blank page


Section A

Total / 30

NAME

CG INDEX NO.

SRJC 2010 8866/Prelim/2010

DATA AND FORMULAE

Data

speed of light in free space, c = 3.00 x 108 m s1

elementary charge, e = 1.60 x 1019 C

the Planck constant, h = 6.63 x 1034 J s

unified atomic mass constant, u = 1.66 x 1027 kg

rest mass of electron, me = 9.11 x 1031 kg

rest mass of proton, mp = 1.67 x 1027 kg

acceleration of free fall, g = 9.81 m s2

Formulae


v2 = u2 + 2as

work done on/by a gas, W = pV

hydrostatic pressure, p = gh resistors in series, R = R1 + R2 + … resistors in parallel, 1/R = 1/R1 + 1/R2 + …

1

SRJC 2010 8866/Prelim/2010

1 In a speed test, an engineer has determined the top speed of an automobile to be

240.57 km h-1. The accuracy of his equipment is ±5%.

Which of the following is the correct representation of his results?

A (241 ± 2) km h-1 B (240 ± 10) km h-1

C (241 ± 12) km h-1 D (240.57 ± 12.03) km h-1

Ans: B

V/V = 0.05

V = 0.05 x 240.57

= 10 km h-1

V = (240 ± 10) km h-1

2 A precision engineering company specialises in making small ball bearings which are used in

many office equipment. Each ball bearing is 1.0 mg with an uncertainty of 0.1 mg. Its

diameter is 0.60 cm with an uncertainty of 0.01 cm.

What is the percentage error in the calculated value of its density?

A 12% B 15% C 23% D 29%

Ans: B

= M/V

= 3M/(4r3)

= 6M/(D3)

/ x 100%

= [M/M + 3D/D] x 100% = [0.1/1 + 3(0.01/0.60)] x 100% = 15%

2

SRJC 2010 8866/Prelim/2010 [Turn Over

3 The diagram shows a velocity-time graph. What is the change in displacement during the last 2 seconds of the motion? A 6 m B 24 m C 40 m D 60 m Ans: C Area of trapezium = 0.5 (24+16)(2) = 40 m. 4 A stone is thrown upwards and follows a curved path. Air resistance is negligible. Why does the path have this shape? A The stone has a constant horizontal velocity and constant vertical acceleration. B The stone has a constant horizontal acceleration and constant vertical velocity. C The stone has a constant upward acceleration followed by a constant downward

acceleration. D The stone has a constant upward velocity followed by a constant downward velocity. Ans: A Any object travelling in free fall without the presence of air resistance would experience

only the force of gravity acting on it. This results in a constant acceleration downwards hence vertical velocity is not a constant. While the horizontal velocity remains constant as no net force acts in the horizontal direction.

v / m s-1

t / s

0 1 2 3 4 5

4

8

12

20

24

16

3

SRJC 2010 8866/Prelim/2010

5 Which graph represents the motion of a car that is travelling along a straight road with a speed that increases uniformly with time?

Ans: A For an object to travel with speed constantly increasing it must have constant acceleration. 6 A 1500 kg car and a 6000 kg lorry travel toward each other and collide head on. Both the

car and the lorry continue to move together in the original direction of the lorry with a speed of 0.2 m s-1. The car and the lorry each exert forces on the other vehicle during the impact.

Which of the following statements is correct regarding the magnitude of the forces each

vehicle exerts on the other? A The force exerted by the car is greater. B The force exerted by the lorry is greater. C The force exerted by both vehicles are the same. D Not enough information is given to determine which force is greater. Ans C By Newton’s third law, the force by lorry on car is equal in magnitude to the force by car on

lorry.

acceleration

time

acceleration

time

displacement

time

displacement

time

A B

C D

0 0

0 0

0 0

0 0

4


7 As shown below, a helicopter has a load slung at the bottom by means of a cable. The helicopter is flying horizontally and accelerating in the forward direction.

Which of the following diagrams illustrates the resultant force acting on the load correctly?

A B C D

Ans D

As the load is moving horizontally and accelerating to the left with the Helicopter, by Newton’s 2nd Law, the acceleration is towards the left. (For those who need more visual representations, the Vertical component of the Tension is equal in magnitude to the weight of the load. The only remaining force left is the horizontal component of the Tension towards the left.)

load

load

load load

load

load

Tension

Weight

5

SRJC 2010 8866/Prelim/2010

8 What is the total pressure at the bottom of a long narrow tube inclined at 30° to the horizontal, and filled with water to a slant height of 80 cm, in the school science laboratory? The density of water is 1000 kg m-3.

A 4.0 x 103 Pa B 7.8 x 103 Pa

C 1.05 x 105 Pa D 1.09 x 105 Pa

Ans: C P = pressure due to water + atmospheric pressure

= water g (0.800 sin 30°) + 1.01 x 105 = 1000 x 9.81 (0.800 sin 30°) + 1.01 x 105

= 1.05 x 105 Pa

9 Which of the following describes the centre of gravity of a rigid body?

A The centre of the volume of the object.

B The single point through which the weight of the object acts.

C The point at which all forces must act on the body.

D The single point through which the weight of the object appears to act.

Ans: D 10 What are the conditions for equilibrium, for forces acting on an extended rigid body?

A The algebraic sum of all forces acting on a rigid body must be zero.

B The forces acting on the object must have the same line of action of force.

C The vector sum of all forces acting on a rigid body must be zero.

D None of the above

Ans: D (the second necessary condition is that the vector sum of all external torques acting on the body must be zero)

11 0.20 m3 of water is pumped up 10 m vertically in 4 minutes by a motor that is 30% efficient.

Taking the density of water to be 1000 kg m-3, what is the input power to the motor? A 82 W

B 273 W

C 389 W

D 1635 W

Ans: B

0.3P = mgh

t

= Vgh

t

= 1000 0.20 9.81 10

4 60

P = 273 W

6


12 An engine accelerates a train carriage along a track by a constant force. Taking friction to be negligible, which of the graphs below show the variation of the engine power with time?

A

B

C

D

Ans: A

F = ma (Newton’s 2nd law if mass is constant)

Since F is constant, a is also constant

P = Fv

v = u + at

P = mav

P = mau + ma2t

Since m, a and u are constant, so P is proportional to t, so option A has to be the answer.

P/W

0 t/ms

P/W

0 t/ms

P/W

0 t/ms

P/W

0 t/ms

7

SRJC 2010 8866/Prelim/2010

13 A ball with a initial speed u is projected up along a smooth inclined plane. The plane is tilted at an angle θ off the horizontal and is of length h. If the ball manages to clear the plane, during its flight, what is its minimum speed?

A (2u2 – 2gh sin θ)½

B (2gh sin θ – 2u2)½

C cos θ (u2 – 2gh sin θ)½

D can’t be determined, not enough information

Ans: C

Let v be the speed of the ball just after clearing the inclined plane.

By conservation of energy,

Change in K.E. + Change in P.E = 0

½ mv2 – ½ mu2 + mgh sin θ = 0

v2 – u2 + 2gh sin θ = 0

v = (u2 – 2gh sin θ)½

Component of horizontal velocity of v = v cos θ

= cos θ (u2 – 2gh sin θ)½

14 The diagram shows two waves X and Y.

Wave Y has amplitude 8 cm and frequency 150 Hz.

What are the possible amplitude and frequency of wave X?

amplitude / cm frequency / Hz

A 4 50

B 4 450

C 16 50

D 16 450

Ans: C

Since there are three complete cycle of wave Y in wave X for the same time duration, hence

frequency of wave X is one third that of wave Y, i.e. 150/3 = 50 Hz.

And its amplitude is twice that of wave Y so wave X amplitude

= 8 x 2 = 16 cm.

displacement

0

Wave X Wave Y

time

8


15 Light can exhibit all of the phenomena listed.

Which phenomenon can sound not exhibit?

A interference B polarisation

C refraction D total internal reflection

Ans: B

Sound waves are longitudinal waves. Hence polarisation is not evident in sound waves.

16 The diagram shows a standing wave on a string. The standing wave has three nodes N1, N2

and N3.

Which statement is correct?

A All points on the string vibrate in phase.

B All points on the string vibrate with the same amplitude.

C Points equidistant from N2 vibrate with the same frequency and in phase.

D Points equidistant from N2 vibrate with the same frequency and the same amplitude.

Ans: D

A standing wave will have particles in phase with each other in a loop and in anti phase with

particles in the adjacent loop. Hence the particles equidistant from N2 would only have equal

amplitude and not similar phase.

N1 N2 N3

9

SRJC 2010 8866/Prelim/2010

17 T is a microwave transmitter placed at a fixed distance from a flat reflecting surface S. A small microwave receiver, R, is moved from T towards S along the dotted line and

receives signals of alternate maxima and minima of intensity. The distance between one maxima and the subsequent minima is 15 mm.

What is the frequency of the microwaves? A 1.0 × 107 Hz B 1.0 × 1010 Hz C 5.0 × 107 Hz D 5.0 × 109 Hz Ans: D 0.25 λ = 15 x 10-3 m λ = 60 x 10-3 m

f = v

λ=

8

-3

3 x 10

60 x 10= 5.0 x 109 Hz

18 The diagram shows two loudspeakers producing sound waves that are in phase. As a student moves from X to Y, the intensity of the note she hears is alternately loud and

soft. The distance between adjacent loud and quiet regions may be reduced by A decreasing distance d. B increasing distance L. C decreasing the amplitude. D increasing the frequency. Ans: D Using the equation for Young’s double slit experiment, the distance between adjacent maximum and minimum intensity is given by the variable x.

d

X

Y

L loud

soft

soft

loud

loud

S

T

R

10


λL

x = d

= vL

fd

Hence it can be seen that increasing the frequency of the source would reduce the distance between adjacent loud and soft sounds.

19 Four identical lamps are powered by an e.m.f source. The lamps are brightest when they are A all arranged in parallel.

B all arranged in series.

C arranged in combination of series and parallel.

D arranged such that there are an equal number of lamps arranged in series and parallel.

Ans: A. The lamps will be brightest when they are all arranged in parallel. 20 Which of the following statements is true about the e.m.f. of a cell? A It is the electrical force required to move a unit charge within a circuit.

. B It is the electrical power changed into other forms per unit charge within the cell.

C It is the electrical energy supplied per unit current by the cell.

D It is the electrical energy supplied per unit charge by the cell.

Ans: D. It is the electrical energy supplied per unit charge by the cell.

21 A 12 V cell with internal resistance is connected in series with five identical 500 resistors. Focusing on a charge Q moving in the circuit, which of the following statements is correct?

A The energy dissipated in the five resistors is less than 12Q.

B The energy dissipated in the five resistors is equal to 12Q.

C The energy dissipated in the cell is equal to 12Q.

D The energy dissipated in the cell is more than 12Q.

Ans: A Energy dissipated in the cell and resistors equal to 12Q. Thus, energy dissipated in the resistors less than 12Q.

22 The effective resistance of resistors arranged in parallel A increases when one resistor is removed.

B decreases when one resistor is removed.

C may increase or decrease when one resistor is removed, depending on the maximum

resistance value of the resistors.

D may increase or decrease when one resistor is removed, depending on the minimum

resistance value of the resistors.

Ans: A. The effective resistance of resistors arranged in parallel increases when one resistor is removed.

11

SRJC 2010 8866/Prelim/2010

23 Which of the following statements describes the correct property of a thermistor? A The resistance of a thermistor changes with temperature of the surroundings.

B The resistance of a thermistor changes with light intensity of the surroundings.

C The resistance of a thermistor changes depending whether it is connected in series or

parallel.

D A thermistor allows electric current to flow in one direction only.

Ans: A. The resistance of a thermistor changes with temperature of the surroundings.

24 Three parallel conductors X, Y and Z carrying equal current are placed at the corners of an

equilateral triangle as shown below. A fourth wire P carrying two times the current of the other wires is placed midway between the straight line joining A to C. What is the most probable direction of the resultant magnetic field passing through the fourth wire due to X, Y and Z? Ans: C The resultant magnetic field of X and Z points perpendicular to the line XZ and the resultant field due to Y points at a small angle anticlockwise from line XZ. The resultant field due to Y is weaker than the combined field of X and Z as it is further away from P. Hence, resultant field is most likely to be C.

25 A positively charged sphere hanged from the ceiling by an insulating spring as shown.

A magnetic field was then passed through the sphere. The magnetic field alternates between going perpendicularly into and out of the paper at a rate of 1 cycle per second. What is the subsequent motion of the sphere? A Sphere oscillates left and right. B Sphere oscillates into and out of the plane of the paper. C Sphere remains stationary. D Sphere oscillates up and down. Ans: C Force acts on moving charge only.

X

P

Z Y

A

B C

D

Spring

Positively charged sphere

12


26 3 parallel straight conductors X, Y and Z carrying currents of I, 2I and I respectively are

placed in the position shown below. Which of the following is a correct description of the forces acting on the wires?

A Forces acting on wire Y due to X and Z are equal and opposite and therefore considered as action-reaction forces.

B Wire Y exerts a larger force on X than Wire X on Y because Wire Y has a larger current.

C Wire X exerts a larger force on Y than Wire Y on X because Wire Y has a larger current.

D Wire Y and Z exerts forces equal and opposite on each other. Ans: D Forces acting on parallel conductors must be acting on different bodies and are action-

reaction forces and therefore must be of equal magnitude.

27 A piece of cool clean metal is irradiated with U-V light such that photoelectrons are emitted. How would the maximum kinetic energy, EK, of the photoelectrons emitted and the photocurrent i change, when a lower intensity of light with the same wavelength is irradiated?

EK i

A decreases decreases B unchanged decreases C decreases unchanged D unchanged unchanged

Ans B As wavelength of light is not changed, the energy of each photon is the same, hence Ek of the electrons is unchanged. As intensity of light source is proportional to the rate of emission of electrons, when intensity decreases, the photocurrent also decreases.

Wire X Wire Y Wire Z

10 cm 10 cm

13

SRJC 2010 8866/Prelim/2010

28 In a typical photoelectric effect experiment, monochromatic light is irradiated onto a metal surface. The graphs below shows the results of how y varies with x.

What is y and x? y x A p.d across emitter and collector frequency of radiation B Intensity of source frequency of radiation C photocurrent intensity of source D photocurrent p.d across emitter and collector

Ans D

29 The intensity of a beam of monochromatic light is doubled. Which one of the following represents the corresponding change if any in the momentum of each photon of the radiation?

A increased fourfold B doubled C the same D halved

Ans C By de Broglie’s equation

p = h

.

However, changing the intensity of the light source does not change any of the variables in the equation, therefore the momentum of the photon is unchanged.

30 When a parallel beam of white light passes through a cool vapour of mercury, dark lines appear in the spectrum of the emergent light. This is principally because the energy is absorbed and

A is not re-radiated at all. B is re-radiated as ultra-violet radiation. C is re-radiated gradually over a long period of time. D is re-radiated uniformly in all directions. Ans D

x

y

0

1


SERANGOON JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 1

PHYSICS 8866 Preliminary Examination 20 August 2010 Paper 2 Structured Questions 2 hours Candidates answer on the Question Paper. No additional Materials are required. READ THIS INSTRUCTIONS FIRST

Write your name, civics group and index number in the spaces at the top of this page. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Section A Answer all questions. Section B Answer any two questions. At the end of the examination, fasten all your work securely together. The number of marks is given in bracket [ ] at the end of each question or part question.

This document consist of 22 printed pages and no blank page


Section A

1

2

3

4

Section B

5

6

7

Total

NAME

CG INDEX NO.

2

SRJC 2010 8866/Prelim/2010

For

Examiner’s

Use

DATA AND FORMULAE

Data

speed of light in free space, c = 3.00 x 108 m s1

elementary charge, e = 1.60 x 1019 C

the Planck constant, h = 6.63 x 1034 J s

unified atomic mass constant, u = 1.66 x 1027 kg

rest mass of electron, me = 9.11 x 1031 kg

rest mass of proton, mp = 1.67 x 1027 kg

acceleration of free fall, g = 9.81 m s2

Formulae


v2 = u2 + 2as

work done on/by a gas, W = pV

hydrostatic pressure, p = gh resistors in series, R = R1 + R2 + … resistors in parallel, 1/R = 1/R1 + 1/R2 + …

1


For

Examiner’s

Use

Section A


1 Romeo has devised a method to find out how much force a bouncing ball experiences when

it is in contact with the surface from which it bounces. The method consists of dropping the

ball on to the scale pan of a top pan balance as shown in Fig. 1.1. The balance is calibrated

in newtons and Romeo records the maximum reading on the scale, the height from which the

ball is dropped and the height to which it bounces.

Romeo obtains the following information.

Height from which the ball is dropped = 0.70 m

Height to which the ball bounces = 0.55 m

Maximum reading on the balance scale = 40.0 N

The mass of the ball is 0.20 kg

(a) Show that

(i) the speed of the ball when it strikes the scale pan is 3.71 m s-1. [1]


Loss in GPE = Gain in KE

mgh = ½ mv2

gh = = ½ v2

v ( )( . )( . ) .2gh 2 9 81 0 70 3 71 m s-1

(ii) the speed of the ball when it leaves the scale pan is 3.28 m s-1. [1]


Gain in GPE = Loss in KE

Bouncing ball

Metre-rule

top pan balance

Fig. 1.1

2

SRJC 2010 8866/Prelim/2010

For

Examiner’s

Use

mgh = ½ mv2

gh = = ½ v2

v ( )( . )( . ) .2gh 2 9 81 0 55 3 28 m s-1

(b) Calculate the total change in momentum of the ball between striking and leaving the

scale pan.

change in momentum = ………………….. N s [2]

Taking upward to be positive

Change in momentum = m(vf – vi ) = (0.20)(3.28 – (-3.71))

= 1.40 N s

(c) Romeo assumes that the contact force between the ball and the scale pan F varies

with time t as shown in Fig. 1.2.

Determine the contact time Δt.

contact time Δt = ……………… s [2]

Area under F-t graph = change in momentum

½ (Δt)(50) = 1.40

Δt = 0.0559 s

(d) Romeo now drops another ball from the same height on to the scale pan. This ball is

the same mass as the first ball but is made of a harder material. Sketch in Fig. 1.2, the

shape of the graph Romeo might expect to get for this ball. [1]

Award mark when graph has larger maximum F and shorter contact time

Fig. 1.2

F / N

t / s

50

Δt

3


For

Examiner’s

Use

(e) In practice, while Romeo was carrying out the experiment, the results of the height of

the ball was determined using the metre-rule and his naked eye.

(i) Suggest a method in which Romeo could reduce the errors in his results.

……………………………………………………………………………………………………...

……………………………………………………………………………………………………...

……………………………………………………………………………………………………...

…………………………………………………………………………………………………..[1]

Romeo could use a video camera to film the entire fall of the ball and play it in slow

motion to determine the time when the ball instantaneously comes to a stop.

(Other answers may be acceptable)

(ii) Precision, accuracy, systematic, random

Fill in the blanks in the following passage with the some of the words above.

When testing with the same ball, Romeo did not take into account the

compression of the pan when measuring the height of the ball on the rebound.

This introduces a ____________ error which affects the ____________ of his

reading. [2]

4

SRJC 2010 8866/Prelim/2010

For

Examiner’s

Use

2 (a) State what is meant by a progressive wave.

……………………………………………………………………………………………………...

……………………………………………………………………………………………………...

……………………………………………………………………………………………………...

…………………………………………………………………………………………………..[2]

A progressive wave is one which energy can be transferred.

Its particles does not propagate in the direction of the wave but vibrates either perpendicular

or parallel to the direction of wave propagation.

(b) Two speakers S1 and S2 produce waves of the same frequency.

(i) State three conditions that must be satisfied for waves from the two sources to

produce audible interference pattern.

1. ………………………………………………………………………………………...………..

……………………………………………………………………………....................................

2. ………………………………………………………………………………………...………..

……………………………………………………………………………....................................

3. ………………………………………………………………………………………...………..

……………………………………………………………………………................................[3]

1. Sources must be coherent.

2. Waves must interfere.

3. Waves must have roughly the same amplitude.

5


For

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(ii) One of the speakers, S1, is connected to a signal generator. It is then oriented to

face a wall.

Sound waves are produced between the speaker and the wall to form a

stationary wave.

1. Outline how you would use this apparatus to obtain the speed of sound

waves in air.

………………………………………………………………………..……………………..

………………………………………………………………………..……………………..

………………………………………………………………………..……………………..

………………………………………………………………………..……………………..

………………………………………………………………………..……………………..

………………………………………………………………………..……………………..

………………………………………………………………………..……………………..

………………………………………………………………………..…………………..[3]

Measure separation between (adjacent) nodes / antinodes and double to get

λ/this is ½λ [not between peaks and troughs]

Frequency known from/produced by signal generator OR measured on CRO / by

digital frequency meter.

Detail on measurement of wavelength OR frequency e.g. measure several [if a

number is specified then ≥3] node spacings and divide by the number [not one

several times]

OR measure several (≥3) periods on CRO and divide by the number

OR adjust CRO so only one full wave on screen

Use v = fλ

Signal generator wall

6

SRJC 2010 8866/Prelim/2010

For

Examiner’s

Use

2. In principle stationary waves produced in this way could cause problems for

listeners in a concert hall. Explain why.

………………………………………………………………………..……………………..

………………………………………………………………………..…………………..[1]

Little or no sound /amplitude OR you may be sat at a node

3. In practice this problem is not serious. Suggest a reason why.

………………………………………………………………………..……………………..

………………………………………………………………………..…………………..[1]

Reflected wave not as strong as incident wave.

OR walls are covered to reduce reflections/Absorbs incident waves.

OR waves arrive from elsewhere [reflections/different speakers].

OR such positions depend on wavelength / frequency.

7


For

Examiner’s

Use

3 (a) Photoelectric effect is the phenomenon where electrons are emitted from the surface of

a metal when a suitable source of electromagnetic radiation is irradiated on the surface.

(i) Explain the term suitable in the sentence above.

………………………………………………………………………..…………………………..

………………………………………………………………………..………………………..[1]

Suitable refers to the fact that the electromagnetic radiation must have a frequency

above the threshold frequency.

(ii) The variation with frequency f of the maximum kinetic energy Ek of the emitted

electrons is shown in Fig. 3.1.

(iii) Use Fig. 3.1 to determine the threshold wavelength of the radiation required for

photoemission.

threshold wavelength = …………………….. nm [2]

From graph,

Threshold frequency, f = 7.6 x 1014

Threshold wavelength = .

.f

8

14

c 3 00 10

7 6 10

= 395 nm

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Fig. 3.1

Ek / 10-19 J

f / 1014 Hz 0 4 8 12 16 20

0

2

4

6

8

SRJC 2010 8866/Prelim/2010

For

Examiner’s

Use

(iv) Draw in Fig. 3.1 a line to show the variation with frequency f of the maximum

kinetic energy Ek of the emitted electrons for a second metal which has a higher

work function than that in what is originally shown. [1]

Award marks only if gradient of two lines are the same and the new line appears on the

right of the original line.

(b) Explain how lines in the emission spectrum of gases at low pressure provide evidence

for discrete electron energy levels in atoms.

………………………………………………………………………..……………………………..

………………………………………………………………………..……………………………..

………………………………………………………………………..……………………………..

………………………………………………………………………..………………………….[2]

Only radiation of fixed wavelengths are detected in the emission spectrum implying that only

photons of fixed energies are emitted.

These photons emitted correspond to the energy lost by electrons when they de-excite from

a higher energy state to a lower energy state. Hence implying that there are discrete electron

energy levels in atoms.

(c) Three electron energy levels in atomic hydrogen are represented in Fig. 3.2.

The wavelengths of the emission spectral lines produced by electron transitions

between these three energy levels are 486 nm, 656 nm and 1880 nm.

(i) On Fig. 3.2, draw arrows to show the electron transitions between the energy

levels that would give rise to these wavelengths. Label each arrow with the

wavelength of the emitted photon. [2]

Award 2 marks when all arrows and labels are correct.

Deduct 1 mark for each wrong label or direction.

Increasing energy

Fig. 3.2

486 nm

656 nm

1880 nm

9


For

Examiner’s

Use

(ii) Calculate the minimum change in energy of an electron when making transitions

between these levels.

Minimum change in energy corresponds to the emission of photon with the longest

wavelength.

Using E = hc

,

E = . .34 8

9

6 63 10 3 00 10

1880 10

E = 1.06 x 10-19 J

10

SRJC 2010 8866/Prelim/2010

For

Examiner’s

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4 Statistics for road traffic accidents are sometimes interpreted as showing that many occur as

a result of speeding or tiredness of the driver. As a result, some countries have introduced

laws to limit the speed at which vehicles may travel and also the length of time a person may

drive without a rest.

In order to enforce these laws, some types of vehicle are fitted with tachographs. A

tachograph records, on a circular chart, amongst other information, the times at which the

vehicle is being driven together with its speed. One such chart from a lorry tachograph is

illustrated in Fig. 4.1.

The time of day, using the 24 hour clock, is shown on the inner scale. Each concentric circle

represents a speed measured in kilometers per hour (km h-1). For example, at time 12.15,

the lorry was travelling at 40 km h-1.

(a) Use Fig. 4.1 to determine

(i) the speed of the lorry at 10.40.

speed = …………………. km h-1 [1]

80 km h-1

(ii) the length of time for which the lorry was in motion between 08.00 to 11.00.

time = …………………. h [1]

1.75 h or 1 hr 45 min

Fig. 4.1

11


For

Examiner’s

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(b) Suggest what evidence is provided between the times 08.00 and 13.00 on Fig. 4.1 that

some device on the lorry limits its maximum speed.

………………………………………………………………………..……………………………..

………………………………………………………………………..……………………………..

………………………………………………………………………..……………………………..

………………………………………………………………………..………………………….[2]

Between 10.15 and 10.30, the lorry accelerates quickly / steeply from rest and seems to

reach a maximum of 80 km h-1 beyond which it is unable to exceed.

Between 10.30 to 12.00, the lorry’s also seems to plateau at 80 km h-1.

Whenever there is a slight reduction of speed from 80 km h-1 the speed of the lorry

immediately spikes upwards suggesting that the lorry driver must have accelerated the lorry

quickly but it was limited only to 80 km h-1 by the device.

(c) Fig. 4.2 shows data for a particular journey.

time of day activity

1800 – 1900 moving at constant speed of 30 km h-1

1900 stop

1930 accelerate to 60 km h-1

1930 – 2120 continue at 60 km h-1

2120 decelerate to 40 km h-1

2120 – 2230 continue at 40 km h-1

Indicate in Fig. 4.1 the journey represented by the information in Fig. 4.2. [3]

12

SRJC 2010 8866/Prelim/2010

For

Examiner’s

Use

(d) When the tachograph was switched off, the chart stops rotating and the speed

recorded is the maximum for the chart.

(i) Use Fig 4.1 to determine the time at which the tachogrpah was switched off.

time = …………………. [1]

14.12 – 14.15

(ii) Suggest why, when the tachograph is switched off, it is desirable for the speed

recorded to be the maximum, rather than zero.

………………………………………………………………………..……………………………..

………………………………………………………………………..……………………………..

………………………………………………………………………..……………………………..

………………………………………………………………………..………………………….[2]

This is to distinguish the time the lorry is switched off from the time the lorry stops due

to jams or traffic lights.

The maximum speed of 100 km h-1 is used to indicate this since the lorry is only able to

move at a maximum speed of 80 km h-1.

Hence it could only mean that the lorry is swiched off.

13


For

Examiner’s

Use

Section B

Answer two questions in this section

5 (a) State the principle of conservation of energy.

…………………………………………………………………………………………..…………

..……………………………………………………………………………………………………

…..…………………………………………………………………………………………………

…………………………………………………………………………………………………. [2]

Energy can neither be destroyed nor created in any process.

It can be transformed from one form to another, and transferred from one body to

another but the total amount remains constant.

(b) Comment, with a short explanation, the validity of the following statements:

(i) “The work done by a person lowering a weight in his hand at constant speed is

negative.”

…..…………………………………………………………………………………………………

…………………………………………………………………………………………………. [2]

True.

The force by the person on the weight is upwards, whereas the displacement is

downwards.

Thus, work done, which is the force multiplied by the displacement in the direction of

the force, is negative.

(ii) “Work is a scalar quantity and therefore has no direction associated with it.”

…..…………………………………………………………………………………………………

…………………………………………………………………………………………………. [1]

True. Work is the scalar product of two vector components, force and displacement.

Therefore, work is a scalar.

(c) Derive, from the equations of motion, the formula, Ek = ½ mv2 [4]

Consider a body of mass m which moves a displacement s under the action of a

constant force F, starting with initial velocity 0 m s-1 and having a final velocity v m s-1.

It possesses kinetic energy Ek equal to the work done by the force F.

14

SRJC 2010 8866/Prelim/2010

For

Examiner’s

Use

The total work done, W = Fs

By Newton’s 2nd Law, F = ma, W = mas

The body has been uniformly accelerated from rest to some velocity v, thus

v2 = 02 + 2as

Rearranging as = v2 /2

Substituting above into W = mas:

W = ½ mv2

Hence, Ek = ½ mv2

(d) In Fig. 5.1, Object X, which has a mass of 600 g, with an attached Spring A, is pushed

against Spring B (Both springs are of negligible mass and Object X is not attached to

Spring B), compressing Spring B by 10 cm. Object X is then released. Spring A has a

spring constant of 2.5 x 104 N m-1. Spring B has a spring constant of 3.0 x 104 N m-1.

(i) Show that the energy stored in Spring B when Object X is released is 150 J.

energy = ……………… J [1]

E = ½ k x2 = ½ (3.0 x 104) (0.10)2 = 150 J

(ii) Object X continues travelling. It goes up a rough plane inclined at 25° at is 1.5 m

long. The frictional force is 0.3 N.

Calculate the kinetic energy of the object at the end of the rough inclined plane.

kinetic energy = ……………… J [2]

flat smooth ground continues for 1 km

Rough inclined plane

75 cm

350 cm

Spring A

Spring B

Object X

Point C

Fig. 5.1

15


For

Examiner’s

Use

Final K.E = 150 – (0.6)(9.81)(1.5 sin 25°) – (0.3)(1.5)

= 145.81 m s-1

(iii) The object continues travelling. The rest of the path is smooth. Calculate Object X’s velocity at point C.

velocity = ………………m s-1 [2]

Loss of G.P.E = Gain in K.E.

(0.6)(9.81)(1.5 sin 25° + 3.5) = Final K.E – 146.3

(0.6)(9.81)(1.5 sin 25° + 3.5) = ½ (0.6)(v2) – 146.3

v = 23.8 m s-1

OR

150 + (3.5)(0.6)(9.81) = ½ (0.6) v2 + (0.3)(1.5)

v = 23.82 m s-1

(iv) 5 cm after passing point C, Object X has a head on collision with Object B which

is moving at 3 m s-1 in the opposite direction. Object B has a mass of 500 g.

Spring A becomes maximally compressed during the collision

Calculate the maximal compression of the Spring A

velocity = ………………m s-1 [3]

By principle of conservation of momentum

mAuA + mB uB = (mA + mB) v

(0.6)(23.8) + (0.5)(-3) = (0.6 + 0.5) v

v = 10.6 m s-1

Energy stored in spring = loss in K.E.

½ k x2 = ½ (0.6)(23.8)2 + ½ (0.5)(3)2 – ½ (1.1)(10.6)2

½ (2.5 x 104)(x2) = ½ (0.6)(23.8)2 + ½ (0.5)(3)2 – ½ (1.1)(10.6)2

x = 0.0940 m

(c) A simplified way to derive the Bernoulli equation is to start from the fact that the change

in the work done on a fluid is equal to the change in the kinetic energy of the fluid.

Constant pressure is applied while work is being done on the fluid.

16

SRJC 2010 8866/Prelim/2010

For

Examiner’s

Use

Bernoulli’s equation shows p1 + ½ ρ v12 = p2 + ½ ρ v2

2, where p1 is the initial pressure,

p2 is the final pressure, v1 is the initial velocity of the fluid, v2 is the final velocity of the

fluid, ρ is the density of the fluid. Note that gas is a fluid.

(i) Derive an expression for the change in the work done on a fluid. [1]

Change in the work done on a fluid = (p1 - p2) ΔV

(ii) Derive Bernoulli’s equation. [2]

Change in the work done on a fluid = Change in the kinetic energy of the fluid

(p1 - p2) ΔV = ½ Δm (v22 - v1

2)

ρ = m

V

p 1 - p2 = ½ ρ (v22 - v1

2)

p1 + ½ ρ v12 = p2 + ½ ρ v2

2 (shown)

17


For

Examiner’s

Use

6 (a) Fig. 6.1 shows a circuit consisting of seven resistors and an 18 V e.m.f. source.

(i) Calculate the potential difference across AB.

potential difference = ……………………. V [4]

Effective resistance

= 1/1/[1/(1/6 + 1/6) + 8] +1/10 + 5

= 10.24

current = V/R = 18/10.24 = 1.76 A

VAB = IR = 1.76 x 5.23 = 9.22 V

(ii) Calculate the power dissipated in the 8 resistor.

power = ……………………. W [2]

Ans:

current = V/R = 9.22/11 = 0.838 A

P = I2R =0.8382(8) = 5.62 W

D

5

3

2

6

4

10

A

B

C

E

F

8

18 V

Fig. 6.1

18

SRJC 2010 8866/Prelim/2010

For

Examiner’s

Use

(iii) Describe the change in your answers in part (a)(i) and (a)(ii) when the wire CE is

removed from the circuit.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

…………………………………………………………………………..…………………….[2]

The potential difference across AB will be larger.

The power dissipated in the resistor will be smaller.

(b) A student wants to design a circuit to automatically turn on a 16 V lamp when the

ambient light is low. He is unsure what to do with a 500 resistor and a light

dependent resistor (LDR). The resistance of the LDR varies from 500 to 2500 .

Explain, with clear workings, how he should connect the two components to terminals

AB and CD in Fig. 6.2 for the 16 V lamp to be operating normally.

……..........................………………………………………………............................………………

……..........................………………………………………………............................………………

……..........................………………………………………………............................………………

……..........................………………………………………………............................………………

……..........................………………………………………………............................………………

……..........................………………………………………………............................………………

……..........................………………………………………………............................………………

……..........................………………………………………………..............................………… [4]

20 V

0 V

A B C D

Fig. 6.2

19


For

Examiner’s

Use

When ambient light is low, resistance of LDR = 2500

If LDR at terminals CD,

VCD = 2500/(500+2500) x 20

= 16.7 V

Thus, connect LDR to terminals CD and 500 resistor to terminal AB.

(c) A student finds an unlabelled conductor and conducts an experiment to discover the

variation in voltage and current with time, as shown in Fig 6.3 and Fig. 6.4.

(i) Calculate the total amount of charges that flow through the conductor from

time = 0 s to time = 20.0 s.

charges = ……………………. C [2]

Q = current x time

= area under current vs time graph

= [0.75 x 2.0 + 1.25 x 8.0 + 0.5(1.25+0.5)(10.0) ] x 10-3

= 2.03 x 10-2 C

15.0

Voltage/ V

Time / s

12

20

8

2.0 10.0 15.0

Fig. 6.3

Current/ mA

Time / s

0.75

1.25

0.50

2.0 10.0 20.0

Fig. 6.4

20

SRJC 2010 8866/Prelim/2010

For

Examiner’s

Use

(ii) The student claims that the conductor is non-ohmic. Explain whether he is correct

or not.

……..........................………………………………………………............................………

……..........................………………………………………………............................………

……..........................………………………………………………............................………

……..........................………………………………………………............................………

……..........................………………………………………………............................………

……..........................………………………………………………............................………

……..........................………………………………………………............................………

……..........................………………………………………………..............................…..[4]

Time = 0 to 2.0 s,

Resistance = 12/(0.75 x 10-3) = 16 x 103

Time = 0 to 2.0 s,

Resistance = 12/(0.75 x 10-3) = 16 x 103

At time = 15.0 s,

If resistance is still 16 x 103 , then current = V/R = 8/16 x 103

= 0.5 mA

However, from Fig. 6.4 the current at time = 15.0 s is higher than 0.5 mA. Thus,

resistance is not equal to 16 x 103 from time = 10.0 s onwards.

Therefore, this conductor is non-ohmic.

(iii) Determine the maximum power consumed by the conductor.

maximum power = ……………………. W [2]

Maximum power

= I2R

= (1.25 x 10-3)2 x 16 x 103

= 0.0250 W

21


For Examiner’s

Use

7 (a) Define magnetic flux density and tesla.

……..........................………………………………………………............................………

……..........................………………………………………………............................………

……..........................………………………………………………............................………

……..........................………………………………………………..............................…[2]

Magnetic field strength (flux density): the force exerted per unit length per unit current

on a conductor placed perpendicularly to the magnetic field.

One tesla is the magnetic flux density of a magnetic field that results in a force of 1 N

on a conductor of length 1 m carrying a current of 1 A, placed perpendicularly in the

field.

(b) Fig. 7.1 shows a wire carrying 0.50 mA current passing through a region

consisting of a uniform magnetic field and Earth’s magnetic field.

Determine the resultant force per unit length acting on the wire due to the

magnetic fields.

resultant force per unit length = ………………… N m-1 [3]

where is the resultant flux density perpendicular to the wireR RF B L B I

I

9

9 3 12

cos10 sin67 5.99 10 T

5.99 10 0.50 10 3.00 10 N

R E P

R

B B B

F= B

L

Direction is perpendicularly out of the plane of the paper.

wire

Direction of uniform magnetic field, Bp = 6 x 10

-5 mT

Direction of Earth’s magnetic field, BE = 5 x 10

-5 mT

Direction of current of 0.50 mA

67o

100o

Fig. 7.1

22

SRJC 2010 8866/Prelim/2010

For Examiner’s

Use

(c) A current balance hinged at BE can be used to determine the magnetic field

strength of a magnetic field. The setup shown in Fig. 7.2a and Fig. 7.2b consists

of a wire frame of negligible mass in a uniform horizontal magnetic field of

unknown field strength Bu.

The total resistance along section BCD is 70 Ω. Section AF is an insulator.

The wire frame was initially horizontal before being placed in the magnetic field.

After being placed in the magnetic field, the balance tilted in a way such that AF

is lower than CD.

A spring of spring constant 10 N m-1 was then attached to AF to pull AF vertically

upwards such that the wire frame is horizontal again.

A B C

E D F

Direction of horizontal magnetic field Bu

20o

Plan view

Fig. 7.2b

A B C

E D F

5.0 cm

10.0 cm 30.0 cm

6.0 V 30 Ω

Fig. 7.2a

23


For Examiner’s

Use

The extension of the spring was 0.40 cm.

(i) Determine the spring force acting on AF.

spring force = .............. N [1]

0.40

10 0.040 N 100

sF

(ii) Determine the current flowing through BCD and state the direction of the

current flow.

current = ................ A

direction ................................................[2]

I

6.00.060 A

30 70

V

R

Current flows from D to C to B.

(iii) Determine Bu.

Bv = …………….. T [3]

By principle of moments,

I

I

30 5.0 10.0

sin20 0.06 10.0

cos20 0.06 5.0

0.312 T

s BC CD

BC BC BC u

CD CD CD u

u

F F F

F B L B

F B L B

B

(d) Three parallel wires A, B and C, carrying currents of 6.0 A, 4.0 A and 8.0 A

respectively are placed as shown in Fig. 7.3.

The magnetic field strength created by a current-carrying wire at a distance r

away can be determined by the equation 0

2B

r

I.

6.0 A

4.0 A

8.0 A

10.0 cm 5.0 cm

Wire A Wire B Wire C

Fig. 7.3

24

SRJC 2010 8866/Prelim/2010

For Examiner’s

Use

(i) State the direction of the resultant force acting on wire A, due to wire B and

C.

.............................................................................................................................[1]

To the right

(ii) Explain your answer in part (i).

……..........................………………………………………………............................

……..........................………………………………………………............................

……..........................………………………………………………............................

……..........................………………………………………………............................

……..........................………………………………………………............................

……..........................………………………………………………............................

……..........................………………………………………………............................

……..........................………………………………………………...........................[4]

To the left of wire A:

BA > BC >BB

The magnetic field strength due to A and C are in the same direction and

opposite to that of B. Resultant field strength is BA + BC -BB.

To the right of wire A:

BA > BC >BB

The magnetic field strength due to A and B are in the same direction and

opposite to that of C. Resultant field strength is BA - BC + BB.

Hence, field strength to the left of A is stronger than that to the right of A.

Wire A experiences a force towards the right.

25


For Examiner’s

Use

(iii) Sketch the flux patterns due to wire A and B only in Fig. 7.4. [2]

(e) Two charged particles A and B moved in a uniform magnetic field pointing

perpendicularly out of the plane of the paper as shown in Fig. 7.5.

State whether the charges of A and B are positive or negative.

........................................................................................................................[2]

Both charges are positive.

Fig. 7.4

A B

Direction of movement of particle A

Direction of movement of particle B

Fig. 7.5


Write in soft pencil. Do not use staples, paper clips, highlighters, glue or correction fluid. Write your name and Civics group on the Answer Sheet in the spaces provided. There are thirty questions in this paper. Answer all questions. For each question there are four possible answers, A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet. Read the instructions on the Answer Sheet very carefully. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet.

This booklet consists of 14 printed pages.

[Turn over

TEMASEK JUNIOR COLLEGE 2010 Preliminary Examination Higher 1

PHYSICS Paper 1 Multiple Choice

8866/01 24 September 2010

1 hour


2

Data








Formulae


v2 = u2 + 2as





3

1 Which of the following list contains only scalar quantities?

A mass, volume, torque, potential energy

B density, electric potential, momentum, magnetic flux

C acceleration, kinetic energy, area, displacement

D gravitational potential, pressure, electric charge, temperature

2 Which list of SI units contains only base units?

A kilogram, newton, meter, ampere, ohm

B kelvin, meter, second, ohm, mole

C kelvin. meter, mole, ampere, kilogram

D newton, kelvin, second, volt, mole

3 A student measures the dimensions of a cylindrical metal rod with an uncertainty of 2 %.

Its diameter is 14.8 mm and its length is 40.2 mm. The metal rod has a resistivity of 8105.1 m.

The percentage uncertainty in the value of the resistance of the rod is

A 2 % B 4 % C 6 % D 8 %

4 A student takes five readings of the diameter of a rod:

0.77 mm 0.78 mm 0.75 mm 0.76 mm 0.78 mm

The actual length of the rod is 0.90 mm. Which of the following best describes the errors in the readings?

Random Error Systematic Error

A small small

B small large

C large small

D large large

5 A body is thrown vertically upwards in a medium in which the viscous drag cannot be

neglected. If the times of flight for the upward motion tu and the downward motion td (to return to the same level) are compared, then

A td > tu because the body moves faster on its downward flight and therefore the viscous force is greater.

B td = tu because the effect of the viscous force is the same whether the body is moving upwards or downwards.

C td < tu because at a given speed the net accelerating force when the body is moving downwards is greater than the retarding force when it is moving upwards.

D td > tu because at a given speed the net accelerating force when the body is moving downwards is smaller than the retarding force when it is moving upwards.

4

6 A linear accelerator sends a charged particle along the axis of a set of coaxial hollow metal cylinders as shown in the diagram.

The particles travel at constant speed inside each cylinder. The particle crosses the gap between the cylinders at equal time intervals, and at each gap its kinetic energy increases by a fixed amount. Which of the graphs best represents the way in which v, the velocity of the particle varies with d, the distance along its track?

7 A ball is projected horizontally from the top of a cliff on the surface of the Earth with a

speed of 40 m s-1. Assuming that there is no air resistance, what will its speed be 3.0 s later? Take g as 10

m s2.

A 30 m s1 B 40 m s1 C 50 m s1 D 60 m s1

d

A

d

v

B

d

v

C

d

v

D

track of particle

metal cylinders

5

8 A bore hole contains both oil and water as shown. The depth of the water is 730 m. The pressure difference between the top and the bottom of the bore hole is 17.5 MPa. The density of the oil is 830 kg m-3 and the density of the water is 1000 kg m-3.

What is the depth x of the oil?

A 907 m B 1000 m C 1090 m D 1270 m

9 The figure below shows a massive column held stationary in position by a group of people

pulling at a rope.

The 4.0 m high column has a mass of 180 kg and its centre of gravity X is at a distance of

2.3 m from the base. The rope makes an angle of 35 to the column and the column itself

makes an angle of 40 to the horizontal. The tension T in the rope is

A 8.76 102 N B 9.50 102 N C 1.14 103 N D 1.36 103 N

10

Two blocks, X and Y, of masses m and 2 m respectively, are accelerated along a smooth horizontal surface by a force F as shown in the diagram below.

What is the magnitude of the force exerted by block Y on block X during the acceleration?

A 6

F B

3

F C

3

2F D

6

5F

40

X Y F

730 m

6

11 Students A and B engage in a tug of war. Student A wins the game, and student B falls forward. Which of the following statements is correct?

A The force exerted by student A on student B is larger than that exerted by student B on student A.

B The frictional forces exerted by the ground on both students are the same. C The force exerted by student A on student B is smaller than the frictional force

exerted by the ground on student B. D The force exerted by student A on student B is larger than the frictional force exerted

by the ground on student B.

12

An object of mass 1.5 kg is sliding with a velocity of 3.0 m s-1 on a frictionless surface towards another object which is stationary and has a mass of 2.0 kg. This head-on collision is completely inelastic.

If the duration of the collision is 0.050 s, the average force that is exerted between the objects during the collision is

A 39 N B 51 N C 90 N D 119 N

13 A trolley runs freely down a slope with a constant acceleration a. The mass of the trolley is

now doubled and the trolley is allowed to run down the same slope. In both cases the effects of friction and air resistance can be ignored. Which statement is correct for the second experiment?

A The accelerating force is the same. B The acceleration is½ a. C The acceleration is a. D The acceleration is 2a,

14

A small steel sphere is held just below the surface of a deep tank of water and released.

Which one of the following best illustrates the relationship between the acceleration a, and the displacement z, of the sphere? (Take g = 10 m s-2 and you may neglect upthrust.)

A B

C D

z

a / m s-2

10

z

a / m s-2

10

z

a / m s-2

10

z

a / m s-2

10

7

15 Peter and Susan both stand at the edge of a tall building.

Susan throws a stone vertically downwards and, at the same time, Peter throws a

stone upwards at an angle of 30 to the horizontal. The speed v with which both stones are thrown is the same. Neglecting air resistance, which one of the following statements is true?

A The stone thrown by Susan will hit the ground with a greater speed than the stone thrown by Peter.

B Both stones will hit the sea with the same speed no matter what the height of the building.

C In order to determine which stone will hit the ground with a greater speed, the height of the building must be known.

D In order to determine which stone hits the ground first, the height of the building must be known.

16 The graph shows the variation with time of the velocity of a body when it is acted on by a force. If mass of the body is 2.0 kg, the work done by the force on the body is

A 64 J B 16 J C 64 J D 80 J

v (Peter)

v (Susan) building

30

0

10

6

10

t/s

v / m s-1

8

17 Figure (a) shows the positions of equally spaced molecules in a solid lattice. A longitudinal sound wave travels from left to right through the solid. At a certain instant, the displaced positions of the molecules are shown in Figure (b).

What will be the directions of motion of particle 1 and particle 7 immediately afterwards?

Particle 1 Particle 7

A to the right to the right

B to the right to the left

C to the left to the right

D to the left to the left

9

18 Two particles X and Y are situated a distance

2

1apart on a stationary wave of wavelength .

The variation with time t of the displacement dx of X is shown below.

Which one of the following shows the variation with time t of the displacement dY of particle Y?

A B

C D

10

19

Two sound sources S1 and S2, which are separated by 10 m, are connected to a signal generator such that they produce coherent waves. A detector D is placed 24 m directly in front of source S2 as shown in the diagram below. The signal generator is set to a frequency of 680 Hz. Given that the speed of sound is 340 m s-1, how many sound minima will the detector detect as it moves to point P, which is directly in front of source S1?

A 4 B 5 C 8 D 9 20 The intensity of a wave depends on the amplitude. It is also proportional to the square of

the frequency. The variation with time t of the displacement x of the particles in a medium, when two progressive waves P and Q pass separately through the medium, are shown in the graphs below.

The intensity of wave P is Io. What is the intensity of wave Q?

A 2

1Io B Io C 4Io D 16Io

P

D

S1

S2

10 m

24 m

11

21 Monochromatic light of wavelength 4.0 x 10-7 m passes through two narrow slits and produces light and dark fringes on a screen. What is the separation of the slits such that the angular separation between the two first order bright fringes is 4.00 x10-4 rad?

A 0.5 x 10-3 m

B 1.0 x 10-3 m C 1.50 x 10-3 m D 2.0 x 10-3 m

22 Two cells of e.m.f E1 and E2 and negligible resistance are connected with two variable

resistors as shown in the diagram.

When the galvanometer deflection is zero, the resistances of the variable resistors are P

and Q. What is the value of the ratio 1

2

E

E?

A

Q

P

B

QP

P

C

QP

Q

D

P

QP

23

Three light bulbs, each rated at 120 V, 50 W, are connected in series to a 120 V power supply. The power dissipated by each bulb is

A 5.6 W B 17 W C 50 W D 150 W

24 The ammeter A1 of the circuit below reads 6.0 A.

Assuming that both ammeters have negligible resistance, what is the reading on ammeter A2?

A 4.5 A B 6.0 A C 13.5 A D 18.0 A

A1 A2

12

25 The diagram below shows an 8-pin package consisting of ten identical resistors, each of resistance 1.0 Ω, connected together. What is the effective resistance if one were to plug into pins 4 and 7, while leaving the rest of the pins unused?

A 0.33 B 1.3 C 2.0 D 5.0

26 A 20-turn square coil of side 8.0 mm is pivoted at the centre and placed in a magnetic field

of flux density 0.010 T such that two sides of the coil are parallel to the field and two sides are perpendicular to the field, as shown below. A current of 5.0 mA is passed through the coil. What is the torque created on the coil?

A 1.6 x 10-9 N m

B 3.2 x 10-8 N m C 6.4 x 10-8 N m D 3.2 x 10-5 N m

magnetic field

8.0 mm

axis of pivot

13

27 In the diagram below, four long wires are placed at each corner of a square and carry equal currents. The direction of the current in wires P and R is into the plane and that in wires Q and S is out of the plane of the paper. Which labelled arrow correctly shows the direction of the resultant force acting on wire Q?

A Arrow A

B Arrow B C Arrow C D Arrow D

28 The apparatus shown below is used to measure the stopping potential Vs for

photoelectrons emitted from a metal surface. Vs is measured for different frequencies of light incident on the surface.

The variation with the frequency f of the stopping potential Vs is shown above. From the graph, it may be deduced that

A all the photoelectrons have the same kinetic energy for a given value of f.

B the maximum energy of the photoelectrons is proportional to (f - fo).

C the greater the value of f, the greater is the photocurrent detected.

D the slope of the graph is equal to the Planck constant.

Vs

f fo

incident light

metal plate

axis of pivot

14

29 Energy levels for an electron in the hydrogen atom are shown in the diagram below.

When an electron falls to the -3.41 eV level, it emits visible light. What is the spectrum seen in the visible light?

A

B

C

D

30 An α-particle having a de Broglie wavelength i collides with a stationary carbon nucleus.

Both particles move off in the same direction as shown below.

After the collision, the de Broglie wavelengths of the α-particle and the carbon nucleus are

f and c respectively. Which of the following is a true statement related to the de Broglie wavelengths?

A i > f B i < f C f = c D i = c

final direction of α -particle,

de Broglie wavelength f

final direction of carbon nucleus, de Broglie

wavelength c

initial direction of α -particle,

de Broglie wavelength i

carbon nucleus

15

READ THESE INSTRUCTIONS FIRST Write your Civics group, index number and name on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Section A Answer all questions. Section B Answer any two questions. At the end of the examination, fasten all your work securely

together and circle the questions you have answered in Section B in the grid provided.

The number of marks is given in brackets [ ] at the end of each

question or part question.


1

2

3

4

5

6

7

8

Total

This booklet consists of 21 printed pages.

TEMASEK JUNIOR COLLEGE 2010 Preliminary Examination

Higher 1

CANDIDATE NAME

CIVICS GROUP

INDEX NUMBER

PHYSICS

Paper 2 Structured Questions

8866/02

13 September 2010

2 hours

Candidates answer on the Question Paper. No Additional Materials are required.

2

Data








Formulae


v2 = u2 + 2as





3

Section A

Answer all the questions in this section. 1 The velocity-time graph in Fig. 1.1 shows the first 1.6 s of the motion of a ball which is

thrown vertically downward at an initial speed of 6.0 m s1.

(a) How far does the ball travel before hitting the ground?

distance travelled =

m [2]

(b) What is the maximum height attained by the ball after it hits the ground?

maximum height =

m [1]

(c) Calculate the magnitude of the acceleration of the ball when it is in the air.

acceleration =

m s2 [1]

6

12

10

0.8 1.6 t / s

Fig. 1.1

0

v / m s1

4

(d) At what time does the ball next reach the ground?

time = s [1]

(e) If the ratio of the incident speed to the rebound speed has a constant value, determine the rebound speed of the ball when the ball hits the ground the second time.

rebound speed = m s1 [1]

(f) Taking upward direction to be positive, sketch on Fig. 1.2, a clearly labelled displacement-time graph for the motion of the ball from time t = 0 up to the second time it hits the ground.

[2]

t / s

s / m

Fig. 1.2

5

2 Fig. 2.1 shows a catapult for launching a body vertically. A and B are fixed mounting points

and the diagram shows the system in equilibrium, ready for launch. The masses m1 and m2 are each 1.0 kg. You may assume that when the elastic band is horizontal the band is still under tension.

(a) Calculate the tension in the elastic band.

tension =

N [2]

(b) Determine the initial acceleration of m1 and that of m2 at the instant the thin cord breaks.

initial acceleration of m1 =

m s2

initial acceleration of m2 =

m s2 [3]

45 45

A B

m1

m2

thin cord

Fig. 2.1

elastic band

6

(c) State, with a reason, the acceleration of m1 just after it crosses the horizontal line AB.

[1]

(d) Suggest one reason why the resultant force on m1 decreases as m1 rises from its original position upwards.

[1]

3 In an experiment to measure the speed of sound, two coherent sources S1 and S2 produce

sound waves of frequency 1700 Hz. A sound detector is moved along a line AB, parallel to S1S2, as shown in Fig. 3.1. As the detector is moved along AB, regions of minimum and maximum loudness are detected. When the detector is at P such that S1P = S2P, maximum loudness of sound is detected. Point X is the third position of minimum loudness from P, and distances S1X = 1.00 m and S2X = 1.50 m.

(a) (i)

Use the information to determine the wavelength of the sound wave.

wavelength of sound wave =

m

[2]

S2

S1

P

X

B

A

Fig. 3.1

7

(ii) Hence, calculate the speed of sound.

speed of sound =

m s-1

[2]

(b)

At X, no sound is detected. The intensity of the sound produced by S1 alone is then reduced. State and explain the effect of this change on the intensity of sound heard at X and at P.

At X :

[2]

At P:

[2]

8

4 A wire carrying a current I1 is bent to form a circular loop P, which is then fixed in a vertical

plane as shown in Fig. 4.1.

(a) On Fig. 4.1, indicate the direction of the magnetic field, due to the current I1 in

loop P, at its centre O. [1]

(b) The magnitude of the flux density B at O is proportional to the current I. The relation is

B = kI

where k is 1.0 x 10-5 TA-1. In Fig. 4.2, another loop Q, which has the same diameter as loop P, is fixed in a horizontal plane with its centre also at O. This loop carries a current I2.

(i) If I1 = 3.0 A and I2 = 4.0 A, find the angle at which the resultant magnetic field

makes with respect to the horizontal plane. Draw a vector diagram, in the spaces provided below, showing how you obtain the direction of this resultant magnetic field. You may ignore the Earth’s magnetic field.

angle =

o

[3]

horizontal axis

Fig. 4.1

Fig. 4.2

9

(ii) Electrical connections are made to a short wire of length 5.0 mm arranged in the plane of Q passing through O as shown in Fig. 4.3.

A current of 7.0 A passes through the short wire. Calculate the magnitude of the maximum possible force on this current-carrying wire.

force =

N [3]

Fig. 4.3

5 .0 mm short wire carrying 7.0 A current

10

5 The ex In an experiment to investigate the light emitted by a filament lamp, the light output for a lamp rated at 12 V, 20 W was investigated when a range of potential differences was applied across it.

(a) Draw a circuit diagram showing how you would connect the lamp to a 12 V battery and a 10 Ω rheostat such that the potential difference across the lamp can be varied between 0 and 12 V. Include in your diagram: - a switch, situated so that the battery supplies no current when the switch is open; - a voltmeter and an ammeter, which will enable the power supplied to the lamp to

be determined.

[3]

(b) The lamp drawn in (a) is now used to illuminate the LDR as shown in Fig. 5.1.

The LDR is then connected to a circuit as shown in Fig. 5.2 where it is used in investigating the intensity of the light output of the lamp. The battery in the circuit is assumed to have negligible internal resistance and the milliammeter has a full scale deflection of 10 mA.

LDR

in Fig. 5.2

Fig. 5.1 Fig. 5.2

11

The graph in Fig. 5.3 below shows how the resistance R of the LDR varies with the incident illumination L, which is measured in W m-2. Both resistance and illumination are plotted using log10 scales.

(i) Calculate the minimum resistance of the LDR when the milliammeter is at its full scale deflection.

minimum resistance =

[2]

Log10 (R/)

Log10 (L/Wm-2) 0 1 2 3 4

1

2

3

4

5

0

Fig. 5.3

12

(ii) Use Fig. 5.3 to show that the maximum illumination which can be measured, using the circuit shown in Fig. 5.2, is about 1000 W m-2.

[2]

(iii) If the uncertainty of the milliammeter is 0.5 mA, determine whether there is a

detectable current when the illumination is 10 W m-2.

[3]

13

Section B

Answer two questions in this section. 6 (a) (i) What is meant by the linear momentum of a body?

[1]

(ii) State how the change in momentum of a body is related to the force acting on it.

[2]

(b) A projectile of mass 3.2 x 10-2 kg is fired from a cylindrical barrel of cross-sectional area 2.8 x 10-4 m2 by means of a compressed gas. The variation with time t of the excess pressure p of the gas in the barrel above atmospheric pressure is shown in Fig. 6.1.

Fig. 6.1

14

(i) Calculate the maximum force which the gas exerts on the projectile.

maximum force = N [2]

(ii)

Calculate the acceleration of the projectile which would result from the force calculated in (b)(i).

acceleration of the projectile = m s-2 [2]

(c) (i) Using Fig. 6.1, estimate the change of momentum due to the compressed gas which is experienced by the projectile.

change of momentum = kg m s-1 [3]

(ii)

The speed of the projectile changes from zero to 270 m s-1 as it leaves the barrel. What is the change in the momentum of the projectile?

change of momentum = kg m s-1 [2]

15

(iii) Compare and comment on your answers to (c) (i) and (ii).

[2]

(d) (i) Name the conservation principles that apply to a system of interacting particles.

[2]

(ii) Explain in detail how you can apply the conservation principles to the inelastic collision of a bullet with a stationary bag of sand suspended by a cord from the ceiling. The bullet is of mass m travelling with speed v, while the bag of sand is of mass 1000 m. The bullet gets embedded in the sand after the impact.

[4]

16

7

(a) Make estimates of the following quantities:

(i) the wavelength of blue light in a vacuum

wavelength = m [1]

(ii) the density of air at room temperature and pressure

density = kg m-3 [1]

(iii) the mass of a protractor

mass = g [1]

(iv) the amount of energy in 1 kilowatt-hour

energy = J [1]

(v) the resistance of a domestic light bulb when it is on

resistance = [1]

(b) A student takes readings to measure the mean diameter of a wire using a micrometer

screw gauge.

Make suggestions, one in each case, that the student may adopt in order to

(i) reduce a systematic error in the readings,

(ii) allow for a wire of varying diameter along its length,

(iii) allow for a non-circular cross-section of the wire.

[4]

17

(c) A cell has an electromotive force (e.m.f.) E and an internal resistance r. It is connected in series with a variable resistor R, as shown in Fig. 7.1.

(i) Distinguish between electromotive force (e.m.f.) and potential difference (p.d.).

[2]

(ii) The variable resistor R has resistance X. Show that

cellinproducedpower

Rindissipatedpower =

rX

X

.

[3]

Fig. 7.1

18

(iii) The variation with resistance X of the power PR dissipated in R is shown in Fig. 7.2.

Use Fig. 7.2 to state, for maximum power dissipation in resistor R, the magnitude of this power and the resistance of R.

maximum power = W

resistance = [2]

(iv) The cell has e.m.f. 1.5 V. Use your answers in (iii) to calculate the internal

resistance of the cell.

internal resistance = [3]

(v) In Fig. 7.2, it can be seen that, for larger values of X, the power dissipation decreases. Use the relationship in (ii) to suggest one advantage, despite the lower power output, of using the cell in a circuit where the resistance X is larger than the internal resistance of the cell.

[1]

Fig. 7.2

19

8 (a) Summarise the experimental evidence that suggests the existence of energy levels in atoms.

[4]

(b) Fig. 8.2 shows some of the electron energy levels of a hydrogen atom.

(i) One of the emitted spectral lines of hydrogen has a wavelength of 6.5 x 10-7 m. Calculate the energy, in eV, of a photon of this wavelength.

energy of photon = eV [3]

Fig. 8.2

20

(ii) On the diagram in Fig. 8.2, draw an arrow to indicate the transition responsible for this spectral line.

[1] (iii) An electron in the ground state of a hydrogen atom is struck by a photon. State

and explain what happens to the electron and the photon when the energy of the photon is

1. 10 eV,

2. 20 eV.

[4]

(c) The photoelectric effect is represented by the equation

hf = + Ek. Explain the meaning of each term in the equation.

hf:

:

Ek:

[3]

21

(d) A metal plate is illuminated with electromagnetic radiation of wavelength 190 nm. The metal has a work function of 7. x10-19 J. A photoelectron is emitted from the metal.

(ii) Calculate the maximum speed of emission that this photoelectron can have.

maximum speed =

m s-1 [3]

(ii) Explain why most electrons are emitted with speeds less than the maximum.

[2]

TJC Answers to 2010 Preliminary Exam H1 MCQ 8866/01

1D 2C 3C 4B 5D 6B 7C 8D 9D 10C

11D 12B 13C 14A 15B 16A 17C 18A 19C 20B

21D 22B 23A 24A 25C 26C 27B 28B 29B 30B

3. 5. 6. 7. 8. 9.

10. 12. 13. 14. 15. 16. 17.

19. 20. 21. 22. 23. 24. 25.

26. 27. 28. 29. 30.

TJC Solutions to 2010 Prelim H1 8866 Physics Paper 2 Section A

1 (a) Distance = Area under the graph = 6012621 .)( + [1]

= 5.4 m [1]

(b) Max height =Area under the graph = m .. 05100121

=×× [1]

(c) a = Gradient= 2s m 106.0

612 −=− [1]

(d) From graph, time taken to reach max height on rebound = time taken to next reach

ground = 1.0 s. Thus, time taken to next reach ground = 1.0 + 1.6 = 2.6 s [1] (e) upward v = (10/12) × 10 = 8.3 m s−1 [1] (f) [2] 0.6 2.6

t / s

s / m

0 0.4

1 m for correct shape, 1 m for correct values

5.4 2(a) 2 T cos 45o = 2 mg = 2x1.0x9.81 [1] T = 13.9 N [1]

2(b) When string breaks, T =0 Net force on m1 = m2g m1a = m2g

a = g =9.81 ms-2 upwards, since equal masses [2] m2 falls freely, acceleration of m2 = 9.81 m s−2 downwards [1]

2(c) The acceleration of m1 is 9.81 m s−2 downwards as the elastic band is horizontal so there is no vertical component to the tension that cancels out the weight. [1] 2(d) As m1 rises the elastic band becomes less stretched so the tension in the band decreases. [1]

2

3 (a)(i) Path difference = S2X – S1X = 1.50 – 1.00 = 0.50 m [1] ⇒ 50.05.2 =λ m ⇒ 20.0=λ m [1]

(a)(ii) 34020.01700 =×== λfv m s-1 [2]

(b) At X : Loudness increases. The waves arriving at X will no longer have the same amplitude and so the two amplitudes do not cancel out one another completely at X and so no complete destructive interference occurs at X. [2]

At P : Loudness decreases. The sum of the two amplitudes is less than before and hence the resultant intensity will be lower. [2] [correct answer + explanation gets 2 marks each]

4 (a) [1]

horizontal axis

4 (b) 0.30.4tan

2

1

1

2 ===kIkI

BBθ [1]

[1] o53=θ Diagram [1]

B1

BR

θ

B2

4 (c) ILIIkILBF R2

22

1 +== [1]

( ) ( )3225 1050.70.40.3100.1 −− ×××+×= [1] [1] N 6108.1 −×=

3

5 (a)

5 (b) (i) minimum resistance of the LDR = Ω=×

=−

150101050.1

3currentemf [2]

(ii) from graph: lg R = lg (150) = 2.18

this correspond to: lg L = 3.05 [1] 2m W −≈=∴ 100010 05.3L [1]

(iii) when L = 10 W m-2, lg (10) = 1

this corresponds to lg R = 4 (from graph) Ω=∴ 10000R [1]

Current in the circuit = mA emf 15.010

50.14 ==

R [1]

No. Cannot detect as milliammeter has a precision of up to ± 0.5 mA. [1]

correct placement of voltmeter and ammeter [ switch connected in series [ rheostat in series with lamp [

1]

1]

1]

A

V

4

Section B 6 (a) (i) The linear momentum of a body is defined as the product of its mass and its velocity. [1] (ii) The rate of change in momentum of a freely moving body is directly proportional to the

force acting on it, and the change takes place in the direction of the force. [2]

[2] ( )( )

( ) N

ApF446 1054110821055 ×=××=

=− ..

ib maxmax

[2]

( )

sm.

..

ii

2max

max

maxmax

−

−

×=⇒

×=×

=

5

24

10814

102310541

a

a

maF

[3]

( )( )( ) ( )

.

..

ic

1

364

715

103310171082−

−−

=

×××=×=

−=Δ

smkg

tpA

graphtFunderareap

[2] ( )( ) ( )

.

.iic1

2

648

02701023−

−

=

−×=Δ=Δ

smkg

vmp

(c)(iii) The actual change in the momentum of the projectile is less than the expected change is momentum from the force applied by the compressed gas. Some KE is lost due to work done against the friction between the projectile and the cylindrical barrel, OR due to leakage of gas.

[2] (d)(i) Conservation of momentum and Conservation of energy. [2] ( )

( )

( ) 999

100111

21

10011001

21

21

loss KE

[4] shown. is it if mark one award wecan and optional is equation following The g.surroundin the to heat as dissipated ultimately is and

bodies, colliding of system the ofenergy internal as lost is KE Some not. is KE the but conserved isenergy inelastic,perfectly is collison As

1001111000

momentum, of onconservatiBy conserved. is Momentum

2

22

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

=−=⎟⎠⎞

⎜⎝⎛−

=

=⇒+=

%..mv

vmmv

.v'v'mvmv

ii

5

7 (a) (i) allow (4.0 – 4.5) x 10-7 [1] (a) (ii) allow 0.5 kg m-3 → 1.5 kg m-3 [1] (a) (iii) allow 5 g → 50 g [1] (a) (iv) allow only 3.6 x 106 J [1] (a) (v) allow 600 → 3000 Ω [1] 7 (b) (i) check for zero error (on micrometer) and subtract it from the reading. [1] (ii) take readings along the length of the wire at different points [1] (iii) take readings spirally/rotate the wire [1] for (ii) and (iii) mention taking average of the readings to minimize random error [1] 7 (c) (i) Emf is energy transferred from source / changed from some other form to electrical per

unit charge through the source, p.d. is electrical energy converted to other forms per unit charge across a device. [2]

7 (c) (ii) Power in R = I2X [1] E = I (X + r) [1] Power in cell = EI and algebra clear leading to ratio = X / (X + r) [1] 7 (c) (iii) max P =1.4 W at R= 0.40 Ω [2] 7 (c) (iv) current in circuit = 1.4/0.4 = 1.87 A 1.5 = 1.87 (r + 0.40) r = 0.40 Ω [3] 7 (c) (v) either less power lost / energy wasted / lost or greater efficiency (of energy transfer) [1]

6

8 (a) Evidence: the existence of emission/absorption line spectra of atoms. Electrons are allowed to orbit in fixed energy levels/orbits When e are excited to higher levels/orbits, they relax/fall down and emit photons/em radiation Photon energies/frequencies are discrete as it is obtained by difference in energies between higher and lower energy levels. [4] (b)(i) Energy = hf = hc/λ = 6.63 x 10-34 x 3.00 x108/6.5 x 10-7

= 3.06 x 10-19 J = 1.9 eV [3] (ii) Arrow from n=3 to n=2. [1] (iii) 1. 10 eV : energy of this photon is not absorbed as it does not correspond to any energy

difference between any excited and ground state of hydrogen atom. [2]

2. 20 eV: this energy is absorbed as it is more than ionization energy (13.6 eV). The electron will be completely removed from the atom. [2]

(c) hf : energy of a photon Φ : work function which is the min energy to liberate an electron from the metal surface. EK : maximum kinetic energy of the electron emitted. [3] (d)(i) ½ mv2 = hf - Φ v = √(2/9.1x10-31)[( 6.63 x 10-34 x 3.00 x108/190 x 10-9) – 7.9 x10-19 ] = √(2/9.1x10-31)( 1.05 x 10-18 – 7.9 x10-19 = 7.51 x 105 ms-1 [3] (ii) Electrons on surface of metal are loosely bound and thus need less energy to be liberated.

However electrons below the surface need more energy to be liberated. Thus they move off with less KE and therefore less speed. [2]

1

TAMPINES JUNIOR COLLEGE

Preliminary Examination 2010

PHYSICS 8866/01 Higher 1

PAPER 1 Multiple Choice

Monday 20 September 2010

1 hour

Time 0800 – 0900 hr



Write in soft pencil.

Do not use staples, paper clips, highlighters, glue or correction fluid.

Write your name and class on the Answer Sheet in the spaces provided.

There are thirty questions on this paper. Answer all questions.

For each question there are four possible answers A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet.

Read the instructions on the Answer Sheet very carefully.



2

Data

speed of light in free space, c = 3.00 × 108 m s–1







Formulae


21 atuts +=

asuv 222 +=





3

1 The viscous force experienced by an object in a fluid under turbulent conditions can be

given by the expression2k vF ρ= , where ρ is the density of the fluid and v is the

velocity of the object in the fluid. The unit of the constant k, expressed in SI base units, is

A m3 s-1 B m-3 s-1 C m2 D m-4

2 Four experiments were conducted separately to measure the speed of light c. The table showed the results obtained. Which set of results could be described as precise but not accurate?

Experiment Results, c / x 108 ms-1

A 3.00 2.97 3.02 3.01

B 3.16 2.88 2.91 3.05

C 2.79 2.65 2.98 3.01

D 2.81 2.79 2.81 2.80

3 A student makes measurements from which he calculates the acceleration of free fall

as 9.7823 m s–2. He estimates that his result is accurate to ± 3%.

How should he present his result?

A (10 ± 3) m s–2

B (9.8 ± 0.3) m s–2

C (9.78 ± 0.29) m s–2

D (9.78 ± 0.03) m s–2

4 The period T of a simple pendulum of length L is given by the expression:

gLT π2=

A student carries out an experiment with a particular simple pendulum and measured the time for 20 oscillations for various lengths of pendulum L. He plots a graph of T2 against L. The student measured the length of the pendulum by measuring the length of the string, and did not include the short distance between the end of the string and the centre of mass of the pendulum. What effect does this have on the graph he plotted?

A The gradient of the graph will be smaller than the correct value.

B The gradient of the graph will be larger than the correct value.

C The y-intercept of the graph will occur above the origin.

D The y-intercept of the graph will occur below the origin.

4

5 A car at rest at a traffic junction starts to accelerate at 2.0 m s-2 when the traffic light turned green. At this moment, a truck passes it, travelling at a constant velocity of

14 m s-1. If the car is accelerating uniformly, how long will it take for the car to just overtake the truck?

A 7.0 s B 14 s C 28 s D 56 s

6 Fig. 6 shows a trolley traveling at a constant speed of 10 m s-1 to the left. A steel ball is held by an electromagnet attached to trolley.

The ball is released and stroboscopic photographs (a series of exposures on the same film at equal intervals) are taken of the path of the ball.

Which of the following diagrams best represents what is seen on the photograph?

A B C D

7 Fig. 7 shows a ball being thrown horizontally from a tower and lands 20 m away. At what speed is the ball thrown? (Ignore air resistance)

A 10 m s-1 B 15 m s-1 C 20 m s-1 D 28 m s-1

Fig. 7

Fig. 6

5

8 A stone is thrown from P and follows a parabolic path. The highest point reached is T. The vertical component of the acceleration of the stone

A decreases at a constant rate.

B is greatest at T.

C is greatest at P.

D is the same at P as at T.

9 A wire is stretched by a force F which causes an extension x. The energy stored in the wire is ½ F x only if

A the extension of the wire is proportional to the force applied.

B the weight of the wire is negligible.

C the wire is not stretched beyond its elastic limit.

D the cross-sectional area of the wire remains a constant.

10 Newton's third law concerns the forces of interaction between two bodies. Which of the following statements relating to the third law is false?

A The two forces must act on different bodies.

B The two forces are always in opposite direction.

C The two forces are at all times equal in magnitude.

D The two forces are equal and opposite so that the bodies are in equilibrium.

11 A kite is held stationary under the influence of three forces: the tension T in the string, the force F of the wind and the weight W of the kite. Which one of the following force diagrams could be correct?

A B C D

T

F

T W

F

W

F

T W

F

T W

6

12 A trailer of weight 30 kN is hitched to a cab at the point X as shown in Fig. 12.

If the trailer carries a weight of 20 kN at the position shown in the diagram, what upward force is exerted by the cab on the trailer at the point X?

A 15 kN B 20 kN C 30 kN D 40 kN

13 A pendulum is suspended in a train that is accelerating at 2.5 m s-2 (see Fig. 13). What angle does the string make with the vertical?

A 14o B 17o C 25o D 32o

14 Particles X (of mass 4 units) and Y (of mass 9 units) move directly towards each other, collide and then separate. If ∆vx is the change of velocity of X and ∆vy is the change of velocity of Y, the magnitude of the ratio ∆vx / ∆vy is

A 9/4 B 3/2 C 2/3 D 4/9

15 A trolley moves along a track from P to Q, as shown in Fig. 15. The trolley has a kinetic energy of 60 kJ at P. Its potential energy at Q is 40 kJ less than that at P. The work it does against friction from P to Q is 10 kJ.

The kinetic energy of the trolley at Q is

A 10 kJ B 50 kJ C 90 kJ D 100 kJ

P

Q

trolley

Fig. 15

Fig. 12

Fig. 13

a

7

16 An electric motor is required to haul a cage of mass 200 kg up a mine shaft through a vertical height of 800 m in 4.0 minutes. What will be its electrical power required if its overall efficiency is 75%?

A 0.89 kW B 4.9 kW C 5.2 kW D 8.7 kW

17 N small conductors, on the edge of an insulating disc of radius r, are each given a charge of Q, as shown in Fig. 17. The frequency of rotation of the disc is f.

What is the equivalent electric current at the edge of the disc?

A NQf B NQ/f C NπrQf D Nqf/πr

18 Fig. 18 shows the dimensions of a metal block used as a resistor of resistance R, with the current along the 20.0 mm direction as shown. The resistivity of the metal is 3.0 x

10–4 Ω m. What is the value of R?

A 3.0 x 10–4 Ω B 3.0 x 10–3 Ω C 3.0 x 10–1 Ω D 7.5 x 10–2 Ω

Current Direction

10.0 mm

20.0 mm

2.0 mm

Fig. 18

r

Q

Q Q

Q

Fig. 17

8

19 Two electrical conductors of 200 kΩ and 50 kΩ respectively, form a potential divider.

Junction Y is maintained at +3 V and junction P is earth as shown in Fig 19.

What is the potential at junction X?

A 12 V B –12 V C 15 V D –15 V

20 A constant 60 V d.c. source is connected across two resistors of resistance 400 kΩ and

200 kΩ as shown in Fig. 20.

What is the reading of the voltmeter, also of resistance 200 kΩ when connected across the second resistor as shown in the diagram?

A 12 V B 15 V C 20 V D 30 V

X

P

Y 200 kΩ 50 kΩ

V

60 V

d.c.

supply

400 kΩ 200 kΩ

200 kΩ

Fig. 20

Fig. 19

9

21 Three parallel conductors, carrying equal currents in the directions shown, pass vertically through the corners of an equilateral triangle PQR.

What is the direction of the resultant force F on the conductor at Q?

A B C D

22 An electromagnetic pump is used in a nuclear power station to move molten materials about. One such pump consists of a rectangular section of pipe as shown in Fig. 22. A current of 1000 A is passed horizontally in a vertical magnetic field of 0.02 T. What is the direction of the applied current and the magnitude of the force on the molten metal for a section of the pipe illustrated?

A The current is directed from X to Y and the force is 2.0 N

B The current is directed from Y to X and the force is 2.0 N

C The current is directed from X to Y and the force is 1.2 N

D The current is directed from Y to X and the force is 1.2 N

Fig. 22

10

23 Suppose a particle P is projected in a uniform field, which can be magnetic, electric or gravitational as shown in Fig. 23.

For the particle to move in the plane of the paper in parabolic path indicated, the conditions would have to be:

Particle Field

A Negatively charged Electric

B Positively charged Magnetic

C Uncharged Gravitational

D There are no conditions which could produce such a motion.

24 Data transmitted along glass-fibre cables is in the form of pulses of monochromatic red light each of duration 2.5 ns. Which of the following is the best estimate of the number of wavelengths in each pulse?

A 103 B 106 C 109 D 1012

25 The diagram shows a transverse wave on a rope. The wave is travelling from left to right. At the instant shown in Fig 25, what is the phase difference between points P and Q?

A

zero

B π

4

C π

2

D π

26 A stationary wave is formed by superimposing two longitudinal waves of frequency 20

MHz. The adjacent nodes in the stationary waves are 25 µm apart. What is the speed of the progressive waves?

A 330 m s-1 B 500 m s-1 C 1000 m s-1 D 2000 m s-1

P

Field

Fig. 23

Fig. 25

11

27 Under which of the following conditions will the separation between the bright fringes of a double slit interference pattern be the greatest?

Distance between slits Distance from slits to screen

Wavelength

A large small long

B large large short

C small large long

D small small long

28

In a photoelectric experiment, the saturation current produced by shining light of frequency f on a particular piece of metal is 6.0 nA. What would be the value of this current if f is increased to 1.5 f while keeping the rate of incidence of photons on the metal constant?

A 6.0 nA B 8.0 nA C 10 nA D 12 nA

29 What is the wavelength of electrons that are accelerated from rest across a potential difference of V? h is the Planck constant, e the electronic charge and m is the mass of electron.

A

eV

hm B

m

eVh

C

m

eVh2

D

meV

h

2

30 Fig. 30 shows the three lowest energy levels of an atom.

What is the highest frequency of radiation possible from transition within these levels?

A 2.10 x 1015 Hz B 1.17 x 1016 Hz C 7.21 x 1016 Hz D 7.75 x 1016 Hz

End of Paper

Fig. 30

For Examiner's Use

1 8

2 8

3 6

4 6

5 12

Section B

6 20

7 20

8 20

Total 80

Candidate Name _________________ ______________ Civics Class ___________

TAMPINES JUNIOR COLLEGE Preliminary Examination 2010

PHYSICS 8866/02 Higher 1 PAPER 2

THURSDAY 2 SEPTEMBER 2010 2 hour

Time 0800 – 1000 hr Candidates answer on the Question Paper. No additional materials are required.

READ THESE INSTRUCTIONS FIRST Write your name and class on all the work you hand in. Write in dark blue or black pen in the spaces provided on the Question Paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use paper clips, highlighters, glue or correction fluid. Section A Answer all questions.

Section B

Answer any two questions.

You are advised to spend about one hour on each section.

At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.


2

Data

speed of light in free space, c = 3.00 × 108 m s–1







Formulae


21 atuts +=

asuv 222 +=





3

Section A

Answer all questions.

1 (a) Galileo’s famous demonstration at the Tower of Pisa showed that falling objects

accelerate equally, regardless of their masses. This is strictly true if air resistance is

negligible.

Using Newton’s Second Law, show that a 10 kg canon ball and a 1 kg stone, when

dropped together from the top of the tower, can strike the ground at the same time.

[2]

(b) A body is released in a fluid. With the aid of a free body diagram, explain how the

body falling through a fluid can reach terminal velocity.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

[3]

(c) A parachutist has a mass of 80 kg. When he falls with his parachute open, the air

resistance R he encounters is given by the equation R = k v2, where v is the

parachutist’s velocity and k has the value of 35 N s2 m-2.

Determine the magnitude and direction of the acceleration of the parachutist when

his velocity is 5.0 m s-1.

magnitude of acceleration = ……………………………….. m s-2

direction of acceleration = …………………………………

[3]

4

2 Sphere P of mass 2.0 kg and sphere Q of mass 1.0 kg are moving towards each other

with speeds 2.0 m s–1 and 1.0 m s–1 respectively, as shown in Fig. 2.1.

The spheres have a head-on, inelastic collision. The force that P exerts on Q during the

collision varies with time as shown in Fig. 2.2.

(a) State the principle of conservation of momentum.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

[1]

(b) Determine the momentum change of mass Q after collision.

change of momentum = ……………………………….. kg m s-1

[1]

P Q

1.0 m s–1 2.0 m s–1

2.0 kg 1.0 kg

t / ms

F / N

150

20 40 0

0

Fig. 2.1

Fig. 2.2

5

(c) Sketch, with clear labeling of values, a graph of the force that Q exerts on P using

the axes provided.

[2]

(d) Calculate the velocities of P and Q after collision.

velocity of P = ……………………………….. m s-1

velocity of Q = ……………………………….. m s-1

[2]

(e) Calculate percentage loss in total kinetic energy of P and Q after the collision.

percentage loss in total kinetic energy = ……………………………….. %

[2]

F / N

0 t / ms

6

3 A rectangular coil ABCD has its plane set parallel to a uniform magnetic field of 0.2 T as

shown in Fig. 3 (not drawn to scale). The coil of sides AB and BC are of length 30.0 cm

and 20.0 cm respectively. A current of 2.0 A is flowing through the coil from P to Q.

(a) Indicate in Fig. 3, the direction of the force acting on sides AB and CD

respectively. Label them F.

[2]

(b) Calculate the force F.

force F = ……………………………….. N

[2]

(c) Hence calculate the torque acting on the coil ABCD at the instant shown in Fig. 3.

torque = ……………………………….. N m

[2]

4 (a) What is meant by the photoelectric effect?

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

[1]

A

B C

N S D

P Q

Fig. 3

7

(b) The circuit as shown in Fig. 4 is used to study the photoelectric effect with sodium.

When a piece of sodium metal is irradiated by monochromatic light of wavelength

420 nm, the stopping potential is found to be 0.65 V. When light of wavelength 310

nm is used, the stopping potential is 1.69 V.

(i) What is meant by stopping potential?

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

[1]

(ii) Determine the work function of sodium metal and the value of Planck

constant.

work function of sodium metal = ……………………………….. J

value of Planck constant = ……………………………….. J s

[4]

light

A

Variable voltage source

Fig. 4

8

5 Capacitors are used in virtually every electronics circuit that is built today. A capacitor is

an electrical device that is able to store electrical energy. It is basically made up of two

conducting sheets or plates which are separated by an insulator, such as mica, ceramic

or paper. It is charged by using direct current, which will result in the capacitor having a

potential difference and the two conductors carrying charges of opposite sign. A

charged capacitor is able to deliver electrical energy to a resistor in a way similar to a

cell.

A particular capacitor C is connected in a circuit as shown in Fig. 5.1, to a cell with an

emf of 12.0 V and a resistor of 30.0 kΩ. A current sensor is used to measure the

variation of current in the circuit with time, and a part of the graph is shown in Fig. 5.2

below.

C

30.0 kΩ 12.0 V

A

Current sensor

Fig. 5.1

Fig. 5.2

9

At any instant, the emf of the cell E, the potential difference across the capacitor Vc and

the potential difference across the resistor VR are related by the following equation:

E = VC + VR

(a) As the capacitor is charged by the current flow, indicate on Fig. 5.1 which plate is

positively charged.

[1]

(b) Suggest why the current decreases with time.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

[2]

(c) If the circuit remains closed for a sufficiently long time, state the final value of

(i) the current in the circuit,

current = ……………………………….. A

[1]

(ii) the potential difference across the capacitor

potential difference across capacitor = ……………………………….. V

[1]

(d) At time t = 10 s, deduce the potential difference across the capacitor.

potential difference across capacitor = ……………………………….. V

[2]

(e) Use Fig. 5.2 to estimate the charge stored on the capacitor after 10 s.

charge stored on the capacitor = ……………………………….. C

[2]

10

The capacitance of a capacitor is defined as the ratio of the charge stored to the

potential difference across it.

(f) Use your answers above to determine the capacitance of C.

capacitance of C = ……………………………….. C V-1

[1]

It is suggested that the relation between the current and time is

where I0 is the current at time t = 0 s, and k is a constant for this circuit.

Some data from Fig. 5.1 are used to plot the graph of ln I with time as shown in Fig. 5.3.

(g) Use Fig. 5.3 to deduce the value of k.

Value of k = ……………………………….. s

[2]

Fig. 5.3

11

Section B Answer two of the questions in this section

6 The following data concern a tennis ball at a given instant just before it is struck by a

tennis racket:

horizontal momentum of tennis ball = 2.4 N s

kinetic energy of tennis ball = 45 J

(a) State Newton’s three laws of motion.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

[3]

(b) Why is it correct to give the direction of the momentum but not of the kinetic

energy?

...................................................................................................................................

...................................................................................................................................

[1]

(c) Use the data provided to calculate the mass and the velocity of the tennis ball

mass = ……………………………….. kg

velocity = …………………………….. m s-1

[4]

12

(d) When the racket hits the ball, it strikes the ball with a constant force of 60 N in a

direction opposite to that of its momentum, bringing it to rest momentarily.

Calculate

(i) the time the tennis ball takes to stop,

time = …………………………….. s

[2]

(ii) the distance the tennis ball travels while stopping

distance = …………………………….. m

[3]

(e) The force of 60 N then continues to act on the tennis ball for a further 0.060s.

Calculate

(i) the new momentum of the ball

new momentum = …………………………….. N s

[1]

(ii) the new velocity of the ball

new velocity = …………………………….. m s-1

[1]

13

(f) Calculate the increase in kinetic energy of the ball for the whole time that the force

is applied to it and hence deduce the mean power being delivered to the ball while

it is in contact with the racket.

increase in kinetic energy = ……………………………….. J

mean power delivered = …………………………….. W

[3]

(g) Suggest why in practice it is impossible for a constant force to be applied to the

ball.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

[2]

7 (a) (i) Define potential difference and the volt

………………………………………………………………………………………....

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

[2]

(ii) Using energy consideration, distinguish between electromotive force (e.m.f.)

and potential difference (p.d.).

………………………………………………………………………………………....

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

[3]

14

(b) The variation of resistance R of a thermistor with temperature T is shown in Fig.

7.1. Temperature, T, is given in Kelvin (K) and is related to degree Centigrade , θ ,

by the relationship: θ = T – 273

The above thermistor is connected in a potential divider circuit as shown in Fig. 7.2

with a battery of e.m.f. 12.0 V and negligible internal resistors. The thermistor is

placed in the freezer of a meat handling factory. It functioned as a temperature

probe to activate a switch to power the freezer and the switch will be on if the

potential at point P is at 4.5 V.

(i) What is meant by the expression an e.m.f. of 12 V ?

…………………………………………………………………………………………

…………………………………………………………………………………………

[1]

Fig. 7.1

R / kΩ

T / K

Fig. 7.2

12.0 V

0 V P

5.0 kΩ

15

(ii) Explain, in microscopic terms, the shape of the graph in Fig. 7.1.

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

[3]

(iii) State and explain the effect of a decrease in surrounding temperature in the

freezer on the potential at point P.

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

[3]

(iii) Use Fig. 7.1 to determine the temperature that would trigger the switch.

temperature = …………………………….. K

[3]

(v) Suggest why it is reasonable to choose a value of 4.5 V as a trigger potential

in this context.

…………………………………………………………………………………………

…………………………………………………………………………………………

[1]

16

(vi) Without changing the thermistor and keeping the trigger potential at 4.5 V,

suggest one way that the circuit could be modified if a different trigger

temperature is desired.

…………………………………………………………………………………………

…………………………………………………………………………………………

[1]

(vii) Noting the usefulness of such a temperature probe, it was suggested that a

similar circuit in Fig. 7.2 to be used in a device for controlling a boiler. It is

desired that when the temperature is 78oC, the switch will be activated to boil

the liquid. Discuss whether this proposal is feasible.

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

[3]

8 (a) (i) State the principle of superposition.

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

[2]

(ii) Explain what is meant by constructive interference and destructive

interference.

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

[2]

17

(b) Sound produced by the loudspeaker shown in Fig. 8.1 has a frequency of 4.0 x 103

Hz. The sound waves arrive at microphone M via two different paths, LXM and

LYM. The left-tube is fixed in position, while the right-tube is a sliding-section. At

position M, the sound waves from the two paths interfere.

Initially, the lengths of paths LXM and LYM are equal. The sliding-section is then

pulled out horizontally by 0.020m, and the loudness at microphone M changes from

a maximum to a minimum.

(i) Determine the path difference between the two waves after the sliding-

section is pulled out.

path difference = …………………………….. m

[2]

(ii) Calculate the speed at which sound travels through the tube.

speed = …………………………….. m s-1

[2]

loudspeaker

microphone

L

M

sliding-section which can be

moved horizontally

X Y

Fig. 8.1

18

(iii) When the opening at M is sealed, explain why a standing wave can be set up

in the tube.

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

[3]

(iv) The frequencies of the sound produced by the loudspeaker ranges from 40

Hz to 4.0 kHz. Calculate the range of wavelengths of sound produced by

loudspeaker.

range of wavelengths = …………………………….. m

to …………………………….. m

[2]

(v) A good loudspeaker should be able to diffract sound over a large area.

Estimate the optimal diameter of the loudspeaker in order to achieve the

maximum spreading of sound waves at the frequency of 4.0 x 103 Hz. Explain

your answer.

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

…………………………………………………………………………………………

[2]

19

(c) (i) Fig. 8.2 below shows a stationary wave formed between two fixed points.

State the point/s which is/are at rest at the moment as shown in the figure.

…………………………………………………………………………………………

[1]

(ii) If the distance between the two fixed points is 1.00 m and the frequency of

the waveform in Fig. 8.2 is 50 Hz, find the frequencies of three other modes

of oscillations which are lower than 50 Hz.

frequency 1 = …………………………….. Hz

frequency 2 = …………………………….. Hz

frequency 3 = …………………………….. Hz

[4]

End of Paper

A B

C

D E

F

Fig. 8.2

This document contains 14 printed pages.

VJC Preliminary Exams 2010 Physics H1/P1/8866/1

VICTORIA JUNIOR COLLEGE 2010 JC2 PRELIMINARY EXAMINATIONS

PHYSICS 8866/01 Higher 1 Paper 1 Multiple Choice 23/9/2010 1400 h – 1500 h THURSDAY (1 h )

READ THESE INSTRUCTIONS FIRST Write in soft pencil. Do not use staples, paper clips, highlighters, glue or correction fluid. Write your name and NRIC number on the Answer Sheet in the spaces provided. There are thirty questions on this paper. Answer all questions. For each question there are four possible answers A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the separate Answer Sheet. Read the instructions on the Answer Sheet very carefully. Please shade the ovals on the Answer Sheet correctly. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet.

2


Data

speed of light in free space, c = 3.00 × 108 m s-1

elementary charge, e = 1.60 × 10-19 C

the Planck constant, h = 6.63 × 10-34 J s

unified atomic mass constant, u = 1.66 × 10-27 kg

rest mass of electron, me = 9.11 × 10-31 kg

rest mass of proton, mp = 1.67 × 10-27 kg


Formulae

uniformly accelerated motion, s = ut +

21

at2

v2 = u2 + 2as




resistors in parallel, 1/R = 1/R1 + 1/R2+ …

3


1 Which of the following gives the estimated number of atoms in your body? [Avogadro’s constant = 6.02 x 1023] A 1024 B 1027 C 1030 D 1033 2 The ideal gas equation can be given as pVm = RT, where p is the pressure of a gas,

Vm is the volume per mole of gas, T is the thermodynamic temperature of the gas, and R is a constant. The behaviour of many real gases deviates from the ideal gas equation but can be represented quite closely by an equation of the form

p +a

Vm2

⎛

⎝ ⎜

⎞

⎠ ⎟ Vm − b( )= RT

in which the values of a and b are characteristic of the particular gas. What are the units of a and b?

a b

A Pa m6 mol-2 m3 mol-1

B Pa m6 mol-2 m-3 mol

C Pa m-6 mol2 m3 mol-1

D Pa m-6 mol2 m-3 mol-1

3 An experiment was conducted to determine the mass per unit length m of a vibrating

wire by measuring its resonant length I and the tension T in it. The table shows the results obtained, together with their uncertainties.

I =(14.5 ± 0.2) cm T =(10.5 ± 0.2) N

The formula which relates T and I is T = 4mf2 l2 where f is the frequency of vibration. It is given that f had a percentage uncertainty of 1%. What was the percentage uncertainty of m? A 4% B 5% C 6% D 7%

4


4 A rocket is launched from Earth with a constant vertical acceleration. After some time, the engines are switched off, and the rocket is allowed to fall freely back to Earth. Which one of the velocity-time graphs best represents the journey?

5 Experimental data taken of a child sliding down a playground slide provided the

following data.

Time/s 0 1.0 2.0 3.0 4.0 5.0 6.0 Speed/m s-1 0 1.0 2.0 3.0 3.5 4.0 4.5

Which diagram represents the slope of the playground?

v

t

v

t

v

t

v

t

A B

C D

A

C

B

D

5


6 An artillery gun sited at the top of a cliff fires a shell horizontally so as to hit a target

2.0 km away from the bottom of the cliff. If the cliff is 180 m high, the initial velocity of the shell is

A 54 m s-1 B 99 m s-1 C 110 m s-1 D 330 m s-1

7 A sphere of mass 3.00 kg rests on a frictionless slope as shown.

The spring obeys Hooke’s Law. The spring constant is 500 N m-1. What is the compression in mm of the spring?

A 58.9 B 51.0 C 29.4 D 34.3 8 The figure below shows two masses connected by a light cord passing over a light,

free-running pulley.

Given that m1 rests on a frictionless plane inclined at an angle of 37.0o to the

horizontal, what is the ratio of the masses m1/m2 in order for the system to remain in equilibrium?

A 0.602 B 0.799 C 1.33 D 1.66

30˚Wall

m2 m1

37.0o

6


9 The figure below represents the various forces acting on a car moving towards the right. The driving force, D acts on the front wheels and the total resistive force is represented by the force, R. The weight W of the car is 12000 N and it acts on the centre of mass, G which is 90 cm above the ground.

Given that the values of D and R are both 7000 N, what are the values of the normal reaction forces at A and at B acting on the wheels?

Normal reaction force at A Normal reaction force at B A 8100 N 3900 N

B 6000 N 6000 N

C 6150 N 5850 N

D 5850 N 6150 N

10 A helicopter rises vertically with a constant speed. According to Newton’s third law,

there is a force which makes an action-reaction pair with the weight of the helicopter. Which of the following is this force? A The lift force created by the engine of the helicopter. B The gravitational force on the Earth due to the helicopter.

C The air resistance on the helicopter as it rises up.

D The upthrust acting on the helicopter due to air around it.

11 The graph below shows how the force acting on a 2.0 kg body varies with time.

Assuming that the body is initially moving in a straight line at 3.0 m s-1, what is its final velocity? A 8.0 m s-1 B 10.0 m s-1 C 13.0 m s-1 D 16.0 m s-1

2.0

F/N

t/s

3.0 0

6.0

1.0

A B

1.5 m 0.50 m

R G

W

DB A

7


12 The figure below shows a 7.00 kg and a 2.00 kg blocks hung by an inextensible string over a smooth pulley.

What is the magnitude of the acceleration of the 7.00 kg block when released? A 1.96 m s-2 B 2.80 m s-2 C 5.45 m s-2 D 7.01 m s-2

13 A small metal sphere of mass m is falling vertically from rest in liquid glycerine. When

it reaches a constant velocity v, which of the following statements is false?

A The resistive force acting on the metal sphere is constant B The gravitational potential energy decreases at a rate of mgv.

C The kinetic energy is constant and equal to ½ mv2.

D The total mechanical energy of the sphere is constant.

14 Two identical blocks are released from rest from the tops of two ramps as shown below.

Assuming no friction, what is the ratio of their speeds if the ratio of the length X/Y is 2.0? A 1.1 B 1.9 C 2.0 D 3.5

7.00 kg

2.00 kg

Y

30°

X

60°

8


15 The speed of a vehicle of total mass 1.60 x 103 kg was brought down to 14.0 m s-1 on a level road by applying brakes. On braking, 550 kJ of heat was produced. What is the speed of the vehicle just before the brakes were applied? A 40.2 m s-1 B 29.7 m s-1 C 26.2 m s-1 D 22.2 m s-1

16 Which expression may be used to calculate power?

A Work done x Time taken

B Force x Distance moved in the direction of the force

C Charge x Electrical Potential Difference

D Velocity x Force in the direction of the velocity

17 In a progressive transverse wave set-up in a string, Fig 17.1 below shows the shape

of the string at time t = 0. X and Y are two points on the string.

Which of the following statements is true if Fig 17.2 represents the displacement-time graph for point X? A Point Y will have a similar displacement-time graph as it is of the same phase

as X in oscillation.

B Point X has maximum kinetic energy while Y has maximum potential energy.

C The progressive wave is travelling towards the left.

D The point Y is moving upward with maximum speed at time t = 0.

Fig 17.2

Displacement

time 0

Displacement

position X Y

Fig 17.1

9


18 The planet Neptune is 30 times further from the Sun than the Earth so the quantity of solar energy falling per unit time on an area of Earth of 1.0 m2 covers an area of 900 m2 on Neptune.

How does the intensity and amplitude of light waves from the Sun compare on Earth and Neptune?

Amplitude at Earth

Intensity at Earth

Amplitude at Neptune

Intensity at Neptune

A a I a / 30 I / 900

B a I a / 900 I / 900

C a I a / 30 I / 30

D a I a / 900 I / 30

19 Which one of the following statements must be true about two wave-trains of

monochromatic light arriving at a point on a screen if the wave-trains are coherent? A They are in phase.

B They interfere constructively.

C They have a constant phase difference.

D They have approximately equal amplitudes.

20 A vertical pipe open at both ends is partially submerged in water as shown in the

diagram below. A tuning fork vibrating at frequency f is placed over the top of the pipe. The sound waves generated by the fork are reinforced when the length of air column L corresponds to one of the resonant frequencies of the pipe. What is the value of f if the smallest value of L for which resonance occurs is 10.0 cm? You may assume the speed of sound is 340 m s-1.

A 850 Hz

B 1700 Hz

C 2750 Hz

D 3400 Hz

L

10


21 Two wave generators S1 and S2 produce water waves of wavelength 2.0 m. They are

placed 6.0 m apart as shown and are operated in phase. A sensor D which measures the amplitude of water waves is 7.0 m away from S1 as shown in the diagram below.

The shortest distance D could be moved along the straight line S1D in order to detect large amplitude of the resultant wave motion is

A 1.0 m towards S1

B 3.0 m towards S1

C 1.0 m away from S1

D 3.0 m away from S1

22 Two wires X and Y, each of the same length and the same material, are connected in parallel to a battery. The diameter of X is half that of Y. What fraction of the total current passes through X? A 0.20 B 0.25 C 0.33 D 0.50

23 An electrical source with internal resistance r is used to operate a lamp of resistance R. What fraction of the total power is delivered to the lamp?

A R

rR + B

RrR −

C rR

R+

D rR

S1 S2

D

6.0 m

7.0 m

11


24 The current I flowing through a component varies with the potential difference V across it as shown. Which graph best represents how the resistance R varies with V?

25 In the figure shown, a potential difference of 6.0 V is applied across XY.

The current I through the resistor A in the circuit is A 0.6 A B 1.2 A C 1.8 A D 3.6 A

DCA

BA

A

12


26 A p-n junction diode with the forward characteristic shown in Fig 25.1 is connected in series with a variable, low voltage d.c. power supply, a meter of negligible internal resistance and a 50 Ω resistor as shown in Fig 25.2.

When the meter reads 5 mA, the potential difference across the supply is about

A 0.25 V B 0.75 V C 1.05 V D 1.25 V

27 A small horse shoe magnet is placed on a smooth horizontal table. A wire carrying a current is inserted into the space between the poles of a magnet as shown in the figure. The wire is held fixed by two insulating stands on the ground.

What happens to the magnet? A It remains stationary

B It accelerates towards the North

C It accelerates towards the East

D It accelerates towards the West

Fig 25.2

current / mA

Fig 25.1 5

0

15

20

10

0.20 0.40 0.60 0.80 1.00 p.d. / V

13


28 Two long straight wires, X and Y, are placed perpendicular to each other at a distance d apart. A current flows out of page in wire X. The same current flows from left to right in wire Y. What are the directions of the forces acting on wire Y at points P and Q due to the magnetic field produced by wire X?

Force at P Force at Q A out of page into page B into page out of page C towards X away from X D away from X towards X

29 A blue laser beam is incident on a metallic surface, causing electrons to be ejected

from the metal. If the frequency of the laser beam is increased while the intensity of the beam is held fixed,

A the rate of ejected electrons will decrease and the maximum kinetic energy will increase.

B the rate of ejected electrons will remain the same but the maximum kinetic energy will increase.

C the rate of ejected electrons will increase and the maximum kinetic energy will increase.

D the rate of ejected electrons will remain the same but the maximum kinetic energy will decrease.

P Q

X

Y

d

14


30 Part of the energy level diagram of a certain atom is shown in Fig 30 below. The energy spacing between levels 1 and 2 is twice that between 2 and 3. If an electron makes a transition from level 3 to level 2, the radiation of wavelength λ is emitted.

What possible radiation wavelengths might be produced by other transitions between the three energy levels?

A Only 2λ

B Both 2λ

and 3λ

C Only 2λ D Both 2λ and 3λ

Fig 30

Name: ________________________ Class: 09S ___________

VICTORIA JUNIOR COLLEGE

2010 JC2 PRELIMINARY EXAMINATION PHYSICS 8866/2 Higher 1 Paper 2 21/9/2010 0800h – 1000h TUESDAY (2 Hours)

This paper consists of two sections: Section A (40 marks) consists of 5 short structured questions. Write your answers in the spaces provided for each question. Section B (40 marks) consists of 3 long structured questions. Answer any two questions. Write your answers in the spaces provided for each of the chosen questions. The intended marks for each question or part question in sections A and B are given in brackets [ ]. N.B. You will hand in the whole question set issued to you at the end of the examination. Do not separate the question set into parts.

For marker’s use

Section A

Q1 Q2 Q3 Q4 Q5

Section B

Q6 Q7 Q8 s.f. unit Total (80)

This question set consists of a total of 19 printed pages.

2

Data speed of light in free space, c = 3.00 × 108 m s-1 elementary charge, e = 1.60 × 10-19 C the Planck constant, h = 6.63 × 10-34 J s unified atomic mass constant, u = 1.66 × 10-27 kg rest mass of electron, me = 9.11 × 10-31 kg rest mass of proton, mp = 1.67 × 10-27 kg acceleration of free fall, g = 9.81 m s-2 Formulae uniformly accelerated motion,

s = ut + 21

at2

v2 = u2 + 2as work done on/by a gas, W = pΔV hydrostatic pressure, p = ρgh resistors in series, R = R1 + R2 + … resistors in parallel, 1/R = 1/R1 + 1/R2+ …

3

Section A (40 marks) Answer all questions in the spaces provided.

1 (a) A student set up the apparatus shown in Fig 1 in order to determine the

spring constant k of a spring by finding the extension of the spring when additional mass is loaded. The following readings with their errors were recorded in a particular experiment:

mass added initial scale reading final scale reading

(20 ± 1) g (32.00 ± 0.05) cm (36.30 ± 0.05) cm

Using the readings above, calculate the spring constant k with its associated uncertainty and present your answer in SI units of N m-1.

[4]

metre rule

scale reading

mass

Fig 1

4

(b) A second student repeated the experiment in (a) with the same spring. In this new experiment, the additional masses were loaded and the corresponding extension readings were tabulated. A graph showing the variation of the extension and loaded masses was then plotted. Discuss three advantages of this procedure for the determination of the spring constant as compared to that used in (a).

[3]

2 (a) The figure below shows a thin taut wire held horizontally by two supports

placed 0.40 m apart. When the wire is plucked at its centre, a standing wave is formed and the wire vibrates in its fundamental mode of frequency 50 Hz. Explain why a standing wave is formed between the supports.

[2]

weights

0.40 m

Fixed Movable

5

(b) The wire is then connected to an a.c. source in a closed circuit and a magnet is brought near to the wire as shown in the next figure below. This causes the wire to vibrate in its fundamental mode with a large amplitude. When the movable support is shifted from its position, the amplitude of vibration decreases abruptly.

(i) Explain the change in amplitude of the wire’s vibration when the movable support is shifted. Hence, deduce the frequency of the a.c. source.

[3]

(ii) Suggest how the same wire can be made to resonate with a

fundamental frequency of 100 Hz.

[1]

a.c. supply

0.40 m

Fixed Movable

weights

B-field due to magnet

6

3 (a) State the Law of Conservation of Momentum.

[1]

(b) A 200g rubber ball is tied to a 1.0 m long string and released from rest at angle θ. It swings down and at the very bottom has a elastic collision with a 1.0 kg block. The block is resting on a frictionless surface and is connected to a 20 cm long spring of spring constant 2.0 kN m-1. After collision, the spring compressed a maximum distance of 2.0 cm.

(i) Determine the strain energy stored in the spring.

[1]

(ii) Determine the speed of the block after collision with the ball.

[2]

spring1.0 kg

200 g

1.0 m θ

20 cm

7

(iii) Given that the collision is elastic, determine the speed of the ball before collision with the block.

[2]

(iv) Hence, determine from what angle was the rubber ball released.

[2]

4 (a) Define resistance.

[1]

(b) A wire with a resistance of 6.0 Ω is stretched so that its new length is three times its original length. Assuming that the resistivity and density of the material are not changed during the stretching process, calculate the resistance of the longer wire.

[3]

8

(c) The circuit shown in Fig. 4 is constructed of resistors, each of which has a maximum safe power rating of 0.40 W.

(i) Find the maximum potential difference that can be applied between X and Y without damage to any of the resistors.

[3]

(ii) If this potential difference were exceeded, explain which resistor would be most likely to fail.

[2]

Fig.4

X

Y

160Ω

1000Ω 1000Ω

9

5 Read the following passage and then answer the questions which follow it.

Lithium solid-state batteries

Lithium solid-state batteries represent a new concept in battery technology. Solid-state means that the liquids and pastes present in ordinary battery systems are replaced by a solid plastic film which cannot leak. This plastic film separates a lithium metal anode (positive electrode) from a composite cathode (negative electrode) which is in contact with aluminum foil. (See Fig 5.1) The resultant cell can be constructed so that it has a large electrode area but is less than 0.2 mm thick. It is in many ways similar to a sheet of paper and can be cut and formed into almost any shape. Lithium solid-state cells such as this are rechargeable and can be incorporated into the cases of equipment or into such items as credit cards.

Fig. 5.1

The initial e.m.f. of the cell at full charge is 3.4 V but it rapidly falls to about 2.8 V when being used and thereafter falls as shown in Fig. 5.2. The cell needs to be recharged when the e.m.f. reaches 2.0 V. In practice, its average e.m.f. is 2.5 V. The current density, energy density and charge capacity all have to be considered for a particular application. The recommended maximum value of discharge current density is 0.15 mA cm-2 of electrode area, the charge capacity is 3.6 C cm-2 of electrode area, and the energy density is 4.32 x 105 J kg-1 of cell mass. Charging one of these cells should be carried out with a constant applied voltage of 3.4 V and with a current density limited to 2.5 mA cm-2. A typical charging current against time graph is shown in Fig. 5.3 for a cell of electrode area 50 cm2.

10

Fig. 5.2 Fig. 5.3

(a) By reference to the paragraphs between Fig. 5.1 and Fig. 5.2, answer the following questions for a cell of electrode area 50 cm2.

(i) Calculate the charge-storage capacity of this cell.

(ii) Calculate the recommended maximum value of the discharge current.

(iii) Calculate the length of time for which the cell can supply this maximum current.

11

(iv) Calculate the energy it supplies in this time, assuming that the e.m.f. has a constant value of 2.5 V.

[6]

(b) Fig. 5.3 shows the charging graph for a cell of the same electrode area as in (a).

(i) From the graph, estimate the average charging current over the 5-hour charging time.

(ii) Calculate the energy used in charging the cell.

[3]

(c) Using your answers to (a)(iv) and (b)(ii), deduce the electrical efficiency of the charge/discharge cycle.

[1]

12

Section B [40 marks] Answer any two questions for this section. Each question carries 20 marks. Write your answers to each part of the questions in the spaces provided. 6 (a) (i) The figure below shows a uniform shelf of width 60.0 cm and weight

50.0 N, which is hinged at H. A box of tiles is placed at a distance 10.0 cm from the edge of the shelf. The chain is attached to the table near its edge to keep it in equilibrium and the force in the chain is 90.0 N. Determine

1. the weight of box.

[3]

2. the reaction force acting on the shelf at the hinge.

[4]

60° wall

box

60.0 cm

5.0 cm

10.0 cm

H

13

(ii) State and explain how the tension in the chain would change if the box is placed closer to the hinge.

[2]

(b) A painter of mass m1 stands on a platform of mass m2 and pulls himself up by two ropes which hang over massless pulleys. He pulls each rope with a force F and accelerates upwards with a uniform acceleration a.

(i)

Draw on separate diagrams, the forces acting on the platform and those acting on the man.

[4]

14

(ii) Hence or otherwise, show that the acceleration of the man, a, can be

expressed as 1 2

1 2

4 ( )( )

F m m gam m− +

=+

, where g = acceleration due to gravity.

[3]

(iii) The mass of the man is 55.0 kg and the mass of the platform is 5.0 kg. If the breaking tension in the rope is 160 N, determine the maximum acceleration at which the man can pull himself up safely.

[2]

(iv) Hence, determine the maximum force that the man can exert on the platform.

[2]

15

7 (a) (i) Define magnetic flux density and state its SI unit.

[2]

(ii) Express the unit of magnetic flux density in terms of its base units.

[1]

(b) In the space below, draw a diagram to illustrate the magnetic field near a long, straight wire carrying a current.

[2]

A rail gun is basically a large electric circuit, made up of three parts: a power source, a pair of parallel conducting rails and a movable conducting projectile as shown in Fig 7.1. Fig 7.2 shows the top view of the same construction.

Fig 7.1

16

Fig 7.2

(c) Both rails have an identical cross-section of 2.25 x 10−4 m2 and are made of metal of resistivity 2.00 x 10−5 Ωm.

(i) Calculate the resistance of one metre length of the rail.

[1]

(ii) Assuming that the projectile has negligible resistance, show that when a 1.0 kV potential difference is applied, the current that passes through the rails is 56 kA. (The position of the projectile is fixed at 0.100 m away from the power supply.)

[2]

(d) When the power is on, the current I will run from the power supply to the positive rail, across the projectile and back to the power supply through the negative rail as shown in Fig 7.2. With reference to Fig 7.2, state clearly the following:

(i) the direction of the resultant magnetic field acting on the projectile

[1]

17

(ii) the direction of the force experienced by the projectile.

[1]

(iii) Calculate the resultant magnetic field B at the centre of the projectile. (The magnetic flux density B at a distance r from a straight long

conducting wire is given by r2I

B o

πμ

= , where μ0 = 4π x 10-7 H m-1).

[3]

(iv) Assuming that the magnetic field calculated in (d)(iii) is the same throughout the projectile, find the magnitude of the force experienced by the projectile.

[2]

(v) State with a reason whether this force would be higher or lower in practice.

[2]

(e) Explain one way in which the force exerted on the projectile can be increased.

[1]

(f) Discuss two design problems of a rail gun in practice.

[2]

18

8 (a) The photoelectric equation may be written in the form

. Explain the physical meaning of the three terms in this equation.

[3]

(b) Light of wavelength 540 nm is incident normally on a metal surface having a work function of 3.38 eV. The light energy is totally absorbed by the surface. Calculate the threshold wavelength for this metallic material and discuss whether the photoelectric emission of electrons occurs.

[3]

(c) The light has intensity 1.2 mW m-2 and the area of the metal surface is 1.4 cm2. Calculate

(i) the momentum of a photon of the incident light,

[1]

(ii) the rate at which photons are incident on the metal surface,

[3]

19

(iii) the force exerted by the light on the surface, assuming that all the

light is absorbed.

[2]

(iv) Suppose that the light is now incident on a piece of thin metal foil. Suggest whether the force calculated in (c)(iii) is a practicable means of moving the piece of foil.

[2]

(d) Although electrons, protons and neutrons are usually treated as particles, they also possess “wave” characteristics, which can be exploited by Transmission Microscopes to obtain high-resolution images of extremely small objects. For instance, electrons with a de Broglie wavelength of 5.0 nm can be used by such microscopes to image the structure of viruses.

(i) Determine the kinetic energy of an electron which has a de Broglie wavelength of 5.0 nm.

(ii) The resolution of an image can be improved by using particles with shorter de Broglie wavelengths. Suggest two ways to decrease the de Broglie wavelength further, and explain your answer.

[6]

- 1 -

Suggested Solution to 2010 JC2 Physics Prelims H1 P1

Section A (MCQs) 1. Ans: B

The mass of an average person is about 60 kg and it consists of mainly water. Molar mass of water is 18 g = 0.018 kg. 60 kg consist of 60/0.018 = 3.3 x 103 moles. Hence no. of molecules = 3.3 x 103 x 6.02 x 1023 = 2 x 1027 molecules.

2. Ans: A

p +a

Vm2

⎛

⎝ ⎜

⎞

⎠ ⎟ Vm − b( )= RT

Units of (a/Vm

2) is equivalent to units of pressure. Hence units of a = Pa x (m3. mol-1)2 = Pa m6 mol-2 Units of b = units of Vm = m3 mol-1

3. Ans: D T = 4mf2 l2 m = T/f2 l2 Δmm

=ΔTT

+ 2 Δff

+ 2 Δll

=0.2

10.5+ 2(0.01) + 2 0.2

14.5⎛ ⎝ ⎜

⎞ ⎠ ⎟

= 0.066 = 0.07

4. Ans: B Gradient of the v-t graph gives the acceleration. When rocket engine is on, the vertical acceleration is a positive constant (upwards). When engine is switched off, the acceleration is acceleration of freefall downwards (negative g). This is true provided the rocket is not to high up (constant value of g).

- 2 -

5. Ans: A

For the first 3 s, the acceleration is constant and equal to 1.0 m s-2. For t = 3 to 6 s, the acceleration is constant and equal to 0.5 m s-2. The slope in option A gives the best possible way to attain this acceleration.

Time/s 0 1.0 2.0 3.0 4.0 5.0 6.0 Speed/m s-1 0 1.0 2.0 3.0 3.5 4.0 4.5 Acc/m s-2 1.0 1.0 1.0 0.5 0.5 0.5

6. Ans: D sy

= uyt + ½ gt2 180 = 0 + ½ (9.81)t2 t = 6.06 s sx = uxt 2000 = ux(6.06) ∴ ux = 330 m s-1

7. Ans: C F = kx mg sin θ = kx

x = (3.00)(9.81)sin 30 0.0294 m 29.4 mm500

°= =

8. Ans: D m1g sin 37° = T = m2g

1

2

1sin 37

mm

=°

=1.66

9. Ans: D Taking moments about B: W (1.5) = R(0.90) + FA(2.0)

FA = (12000)(1.5) (7000)(0.90) 5850 N2.0−

=

m2 m1

37.0o

T

m1g 37.0o

T

m2g

- 3 -

Since net force in the vertical plane = 0 12000 = 5850 + FB FB = 6150 N

10. Ans: B Action and reaction pair must act on different bodies.

11. Ans: A Change in momentum,

( ) ( ) 1smkg10324221 −=×+=−=Δ xgraphtFunderAreap

Final velocity, 1sm0.82

100.3 −=+=Δ

+=mpuv

12. Ans: C Applying Newton’s 2nd Law on both masses,

2

2121

sm45.5)27(

)81.9)(27()(

−=+

−=

+=−

a

ammgmgm

13. Ans: D Total mechanical energy is not constant since energy is lost to the surrounding as heat produced by drag force.

14. Ans: B Using asuv 222 +=

86.1)30sin60sin

12(

)sin(

)sin(20

21

21

2

=°°

==

∝∴

+=

Y

X

vvRatio

lv

lgv

θ

θ

- 4 -

15. Ans: B By conservation of energy,

1

3223

322

sm7.29

10550)14)(106.1(21

10550)(21

heat aslost Energy

−=⇒

×=−×

×=−

=Δ

u

u

vum

KE

16. An: D At constant velocity, Power = Force x Velocity

17. Ans: C If the wave is travelling to the left, its next position can be represented by the dotted line shown above. X can be seen to be moving from equilibrium to a displacement in the positive direction. This matches the displacement-time graph of X shown in Fig 17.2.

18. Ans: A

22

1 1I a ar r

∝ ∝ ⇒ ∝

30

NE

N E

EN E

N

raa r

r aa ar

⇒ =

⇒ = × =

Displacement

position X Y

Figure 1

- 5 -

2

2130

N E

E N

I rI r

⎛ ⎞= ⎜ ⎟

⎝ ⎠

⎛ ⎞= ⎜ ⎟⎝ ⎠

900N

II⇒ =

19. Ans: C Coherent means having a constant phase difference.

20. Ans: A 10 cm = ¼ λ => λ = 40 cm v = f λ f = (340)/(40 x 10-2) = 850 Hz

21. Ans: C By quick calculation of the 4 options given, it can be shown that only option C will meet the condition for constructive interference to occur (i.e. path difference = nλ, where n is an integer): When D is moved 1.0 m further away from S1,

Path difference = ( )2 28.0 6.0 8.0+ − = 2.0 = nλ, where n is 1.

22. Ans: C

II

IIcurrenttotal

IIAlAl

RR

II

VV

x

x

xy

x

y

y

x

yx

31

3,

2

212

=

=

=

=⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

==

=

ρ

ρ

10 cm

- 6 -

23. Ans: C

Total power , P = I2(R + r) Power dissipated by lamp, PR = I2R

( )rRR

PPfraction R

+=,

24. Ans: B

↑↓⇒↓↑

⇒↑↑

=

RR

IVas

IVasVI

R

1,

constantisgraph ofgradient linearly,

1

25. Ans: B

VXY = 6.0 = IARBC

= IA ⎟⎠⎞

⎜⎝⎛

+×

+42422

IA = 1.8 A VCD = 6.0 - VBC (2.0) I = (6.0 – 1.8 x 2.0) = 2.4 I = 1.2 A

Ans: C I = 5 mA, V across diode= 0.80 V (from graph) VR = (5x10-3)x 50 = 0.25 V Vsupply = V across diode + VR = 0.80 + 0.25 = 1.05 V

27. Ans: D Using Fleming’s Left Hand rule, the wire experiences a force to the East. By Newton’s 3rd Law, the magnet will experience a force to the West.

Y

2.0Ω

2.0Ω

2.0Ω 2.0Ω

2.0Ω

X

IIA B C D

- 7 -

28. Ans: B

The magnetic field Bx due to current in wire X is as shown. It acts in the directions as given by the arrows Bx at points P and Q as shown. By Fleming’s Left hand rule, the point P will experience a force into the page, and the point Q experiences a force out of the page.

29. Ans: A

maxKhf +Φ= Φ is a constant, depending on the type of metal. When the frequency of the incident photons is increased, Kmax will increase.

Constant intensity, ( )area

hftn

areapowerI ==

The area illuminated remains unchanged, so the increase in f will be accompanied by a decrease in (n/t), i.e. the no. of incident photons per unit time will decrease. As a result, the rate of ejected electrons will decrease.

30. Ans: B

Let E32 = E = λhc

The other possible transitions are:

E21 = 2E = 2 ⎟⎠⎞

⎜⎝⎛

λhc =

)2/(λhc and E31 = 3E = 3 ⎟

⎠⎞

⎜⎝⎛

λhc =

)3/(λhc

These transitions will produce the wavelengths 2λ and

3λ .

P Q

X

Y

d Bx

Bx

1

Suggested Answer to VJC Prelim 2010 H1 P2

Section A

1(a)

Hence k = (4.6 ± 0.3) N m‐1 (b) Advantages of many sets of readings and drawing graph: (state any 3) 1. By drawing best fit line, random errors are reduced. 2. Systematic error can be spotted eg. if the F‐e graph does not pass

through origin. 3. Can spot erroneous points that are out of the trend. 4. Can check if the proportionality limit is exceeded eg. if the F‐e

graph turns into a curve instead of a straight line. 2 (a) (i) Incident waves travel along the wire to the ends are reflected.

The incident and reflected waves travelling in opposite directions have same frequency and amplitude. They superimpose to form standing waves.

(b) (i) When the support is shifted, the natural frequency of the wire is changed and no longer matches that of the driving frequency of the periodic force produced by the alternating current in the wire and magnetic field.

The system no longer resonates and hence its amplitude decreases.

The frequency of the a.c. source must therefore be the natural frequency of the wire which is 50 Hz.

(ii) The length l can be reduced to 0.20 m to double the fundamental frequency.

k = Fe=

mg(x2 − x1)

=0.020 x 9.81

(36.30− 32.00)= 4.563 N m−1

Δkk=Δmm

+Δee

=1

20+

0.14.3

= 0.073

Δk = 0.073 x 4.563 = 0.3 N m-1 (to 1 sf)

2

The weights attached to the wire can be increased to increase the speed of the waves to 80 m s‐1.

3 (a) In a system of interacting bodies, the total momentum of the system remains constant provided no external force acts on the system.

(b) (i) Strain energy stored = ( )( ) J40.0100.2100.221

21 2232 =××= −kx

(ii) By Conservation of Energy,

KE of block after collision = Strain energy stored in spring

1

22

894.0

40.0)0.1(2140.0

21

−=

=⇒=∴

smv

vmv

(iii) By conservation of momentum, 22112211 vmvmumum +=+

211 )0.1()2.0(0)2.0( vvu +=+

For elastic collision, 1221 vvuu −=−

121

121 0uvvvvu

−=⇒−=−

1121

2121

68.2)894.0(4.02.12.14.0

)(2.02.0

−==⇒=

+−=∴

smuvu

vuvu

Speed of ball = 2.68 m s‐1

(iv) By Conservation of Energy,

Gain in KE of ball = Loss in GPE of ball

°=

==−⇒

−=−∴

7.50)0.1)(81.9(2

68.22

)cos1(

)cos(021

22

2

θ

θ

θ

glv

llmgmv

3

4 (a) The resistance of a conductor is the potential difference across the

conductor per unit current flowing through it. (IVR = )

(b)

( )

540.69

9 (1)(2)

(2)------------- 3

)3(R

(1)------------- 6A

R Using

'

'

'

Ω==

=

=

==

xRRR

Al

l

ρ

ρ

(c)

(i) If the safe power rating is 0.40 W,

Using R

VP2

= , the maximum safe voltage for

V8 160

0.40 160

V20 1000

0.40 1000

2

2

=

=Ω

=

=Ω

V

V

V

V

for same density of material,

3)3( ,

,

' Al

mAareanew

lmAareaoriginal

==

=

ρ

ρ

X

Y

160Ω

1000Ω 1000Ω

A

C

B

4

26.4V be would voltagesafeMax

33

, 160160500

8 ,8V if

4.26

, 500160500

20 ,20V if

160500 I , )160

21000(

BC

AB

∴

=

×⎟⎠⎞

⎜⎝⎛

+==

=

×⎟⎠⎞

⎜⎝⎛

+==

=

+=+=

VV

VV

VV

VV

IRV

VIV

XY

XY

XY

XY

ABAB

XYXY

(ii) (iii)

(iv) If this potential difference were exceeded, one of the 1000 Ω resistor would most likely fail. This is because when VXY exceeds 26.4 V , the max safe power for the 1000 Ω would be exceeded first.

Or By Potential divider principle (good to know this method!)

V

VV

V

VV

VV

XY

XY

XYAB

33V 160500

1608 ,8V if

4.26V 160500

50020 ,20V if

1605002

1000

XY

AB

XY

AB

=

×+

==

=

×+

==

×+

=

5

5 ai. Charge‐storage capacity = (charge capacity) x (electrode area)

= 3.6 x 50

= 180 C

ii. Maximum discharge current = (maximum discharge current density) x (electrode area)

= 0.15 x 50

= 7.5 mA

iii. Time t = IQ

= 3105.7180

−×

= 24 000 s

iv. Energy supplied = IVt

= 7.5 x 10‐3 x 2.5 x 24 000

= 450 J

bi. The area under the graph (Fig. 5.3) is the total charge. Divide it by the time period of 5 hours to get the average charging current.

Average current = 42.5 / 5

= 8.5 mA

ii. Energy used = IVt

= 8.5 x 10‐3 x 3.4 x 5 x 3600

6

= 520 J

c. Efficiency = %100520450

×

= 87 %

Section B

6 (a) (i) 1. sum of clockwise moment = sum of anticlockwise moment

(50.0)(30.0) + (Wbox )(50.0) = (90.0 cos 60)(55.0)

Wbox = 19.5 N

2. Since the shelf is in equilibrium, ∑F = 0

Vertical component of reaction force at hinge:

Fy = 50.0 + 19.5 – 90.0 cos 60

= 24.5 N

Horizontal component of reaction force at hinge:

Fx = 90.0 sin 60

= 77.94 N

Reaction force = 2 224.5 77.94+ = 81.7 N

1 77.94tan24.5

θ −= = 72.5° to the vertical

(ii) The tension will be smaller.

When box is placed closer to the hinge, the clockwise moment due to its weight is thus smaller. The anti‐clockwise moment due to the tension will thus be smaller too and hence the tension in the chain will be smaller.

7

(b )(i)

(ii) From free body diagram of platform:

2F – m2g – N = m2a ‐‐‐‐‐‐‐‐‐‐‐ (1)

From free body diagram of man:

2F + N – m1g = m1a ‐‐‐‐‐‐‐‐‐‐‐ (2)

(1)+(2):

4F – m1g – m2g = (m1 + m2 )a

Hence 1 2

1 2

4 ( )( )

F m m gam m− +

=+

(shown)

(iii) max4(160) (55.0 5.0)(9.81)

(55.0 5.0)a − +

=+

= 0.86 m s‐2

(iv) From eqn (1):

2(160) – (5.0)(9.81) – N = (5.0)(0.86)

N = 266.7 = 270 N

Wplatform

N

F F

F : force of string on platform (tension)

Wplatform : weight of platform

N : Force of man on platform

F F

N

Wman

F : force of string on man (tension)

Wman : weight of man

N : Force of platform on man

8

7 5(a)(i) Magnetic flux density is defined as the force per unit current per unit length acting on a straight conductor that is placed perpendicularly to the field.

SI units: tesla (T) (ii) (b)

(c)(i)

0889.010 x 25.2

0.1 x 10 x 00.24

5

Ω==

=

−

−

ALR ρ

(ii) Resistance in 0.200 m of rail = 0.0889 x 0.200 = 0.0178 Ω Hence current I = V/R = 1000/0.0178 = 56 kA (d)(i) Direction of B‐field is into the plane of paper. (ii) The force is towards the right. (iii)

Hence, the resultant B- field due to 2 rails is 0.56 x 2 = 1.12 T (iv) F = BIL = 1.12 x 56000 x 0.040 = 2.5 kN

A s kg = mA

s m kg =

mA

N = of Units

1-2-2-

B

ILFB =

T 0.56 0.020 x 2

56000 x 10 x 42

is rail one todue field-B The

7

==

=

−

πππμ

rI

B o

9

(v) Possible answers: The force may be lower in reality because at high current, the wires would be

very hot and hence increased resistance. Or: The force may be higher because the B‐field calculated in d(iii) is the B‐field at the centre. The B‐field nearer the rails will be of higher value, thus the force may be larger.

(e) Increasing the p.d. of the power supply, thus increasing the current in the rails and projectile. In

this way, both B‐field due to wire and the current increases through projectile. (f) Any two design problems: 1. Current may be too high. May produce so much heat that it would melt the rails.

2. The current in each rail of a rail gun runs in opposite directions. This creates a repulsive force, proportional to the current, that attempts to push the rails apart. Because the currents in a rail gun are so large, the repulsion between the two rails is significant. 3. Wear and tear on rail guns is a serious problem. Many break after a few uses, and sometimes they can only be used once.

8 (a) hf is the energy of the incident photon

Φ is the work function, which is the minimum energy required to cause photoelectric emission

2

21 mv is the maximum kinetic energy of the emitted electrons

(b) Work function, th

hcλ

=Φ , where λth is the threshold wavelength.

So, =×

××=

Φ= −

−

)1060.1(38.3)1000.3)(1063.6(

19

834hcthλ 3.68 × 10−7 m = 368 nm

Since 540 nm is above λth, the incident photons do not possess sufficient energy to cause photoelectric emission.

(c) (i) Momentum of an incident photon,

==λhp =

××

−

−

9

34

105401063.6

1.23 × 10−27 kg m s−1

(ii) Incident power on the metal surface, P = Intensity × Area

= (1.2 mW m−2)(1.4 × 10−4 m2)

= 1.68 × 10−7 W

10

Energy of a single incident photon, 9

834

10540)1000.3)(1063.6(

−

−

×××

==λhcE

= 3.683 × 10−19 J

No. of photons incident per unit time, n = =EP

=××

−

−

19

7

10683.31068.1

4.56 × 1011 s−1

(iii) Magnitude of the change in momentum of each photon as it is absorbed,

Δp = | pf − pi | = | 0 − 1.23 × 10−27 | = 1.23 × 10−27 kg m s−1

Force exerted on the surface, F = ( ) ⎟⎠⎞

⎜⎝⎛ΔΔ

Δtptn = pn Δ×

= (4.56 × 1011)(1.23 × 10−27)

= 5.61 × 10−16 N

(iv) Suppose the piece of foil has a mass of 1 g, the acceleration resulting from F would be

=××

== −

−

3

16

1011061.5

mFa 5.61 × 10−13 m s−2

This is extremely small, so the effect on the foil would be negligible. Hence, the force would not be a practicable means to move the piece of foil.

(d )(i) Momentum of the electron, ==λhp =

××

−

−

9

34

100.51063.6

1.326 × 10−25 kg m s−1

Kinetic energy of the electron, ( )

=××

== −

−

)1011.9(210326.1

2 31

2252

mpK 9.65 × 10−21 J

(ii) The de Broglie wavelength of a particle may be expressed as: mKh

ph

2==λ

If we increase the kinetic energy K of the particle, the above relation tells us that λ would be reduced.

So, the electrons can be accelerated through a larger potential difference to achieve a

greater K, so that λ is smaller.

11

If we use a more massive particle (larger m), then λ would also be reduced.

So, instead of electrons, we can accelerate more massive particles like protons to

achieve a shorter λ.

8866/02/JC2 Prelims/YJC2010

YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE YISHUN JUNIOR COLLEGE

Candidate’s Name ………………………………. CTG ……….…

YISHUN JUNIOR COLLEGE JC 2 Preliminary Examinations 2010

PHYSICS 8866/2 HIGHER 1

19 August 2010 Paper 2 Thursday

2 hours

INSTRUCTIONS TO CANDIDATES Do not open this booklet until you are told to do so. Write your name and CTG in the spaces at the top of this page. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Section A Answer all questions. Section B Answer any two questions. You are advised to spend about one hour on each section. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.


For Examiner’s Use Section A

1 /4

2 /6

3 /8

4 /6

5 /8

6 /8

Section B

7 /20

8 /20

9 /20

Total /80

Candidates to answer on the Question Paper

2

8866/02/JC2 PRELIM/YJC2010

Data speed of light in free space, c = 3.00 × 108 m s-1






acceleration of free fall,

g = 9.81 m s-2

Formulae

uniformly accelerated motion, s = ut + 21 at2

v2 = u2 + 2as



resistors in series, R = R1 + R2+……….

resistors in parallel, R1 ........11

21++

RR

=

3


Section A Answer all questions in this section.

1 Estimate the following quantities and give appropriate units.

(a) The momentum of an Olympic sprinter during a 100 m race.

momentum = …………... Unit ……...[2] (b) The energy of a photon of red light.

energy = …………... Unit ……….[2] 2 A satellite orbiting the Earth receives electromagnetic signals and then re-transmits back to

Earth at a frequency of 2.3 GHz.

(a) Calculate the wavelength of the re-transmitted signal.

Wavelength ...........................m [2] (b) State the region of the electromagnetic spectrum to which these waves might belong.

...........................................................................................................................................[1] (c) The satellite is positioned 35 000 km from the Earth. The power received by the dish

antenna on the Earth is 16 nW. Calculate the power that would be received at the dish if the satellite were to be re-positioned at a distance of 17 500 km from Earth. Give your reasoning.

Power received = .........................W [2]

.............................................................................................................................................[1]

4


3 Fig. 3.1 shows a stretched string driven by a vibrator on one end and is fixed to a wall on the other end. A stationary wave is produced on the string as shown.

(a) State the physical conditions that are necessary for a stationary wave to form on the string. ................................................................................................................................................

............................................................................................................................................[2]

(b) Explain how you know that the wave on the string is transverse.

................................................................................................................................................

............................................................................................................................................[1]

(c) Compare the amplitude and phase of the oscillations of points A and B on the string.

Amplitude............................................................................................................................[1] Phase..................................................................................................................................[1]

(d) The length of the string is 1.2 m and the speed of the transverse wave on the string is 6.2

m s-1. Calculate the vibration frequency of the vibrator.

Vibration frequency.......................Hz [2]

Fig 3.1

vibrator

Position of string ½ cycle later than solid curve

wall

5


(e) The frequency of the vibrator is tripled. Sketch the new shape of the stationary wave on Fig. 3.2.

[1] 4 (a) State the conditions for the equilibrium of a body which is acted upon by a number of

forces.

................................................................................................................................................

............................................................................................................................................[2]

(b) A student holds a uniform metre rule at one end in two different ways, as shown in Fig. 4.1

and 4.2 below.

(i) On Fig. 4.1 draw and label an arrow to represent the weight W of the metre rule and an arrow to represent the force F exerted by the student’s hand on ruler. State the relationship between the magnitudes of F and W. [2]

Fig 3.2

Fig. 4.2 Fig. 4.1

6


(ii) In Fig. 4.2, the rule is held horizontally using the thumb and first finger. On Fig. 4.2 draw and label the three forces acting on the metre rule. List these forces in order of increasing magnitude.

1 …………………………………………………….. 2 ……………………………………………………… 3 ……………………………………………………… [2]

5 Fig. 5 is a top view of a metal wire of length 0.53 m and cross sectional area 1.0 x 10-6 m2 is

situated at an angle of 60o to a uniform magnetic field of flux density 1.8 x 10-3 T.

The metal wire has a density of 7.9 x 103 kg m-3 and resistivity of 8.8 x 10-8 Ω m.

A potential difference is applied between the ends of the wire so that there is an electromagnetic force acting on the wire in the direction out of paper.

(a) On Fig. 5, mark the direction of the current in the wire. [1] (b) For the wire, calculate

i) its weight

Weight = …………………N [2] ii) its resistance

Resistance = …………………..Ω [2]

600

Magnetic field direction

Metal wire

Fig. 5

0.53 m

7


(c) Calculate the potential difference required between the ends of the wire so that the electromagnetic force on the wire can balance its weight.

Potential difference = ………………….. V [2] (d) the horizontal component of the Earth’s magnetic field is 1.8 x 10-5 T. State and explain

why in practice current-carrying wires are not seen to lift off the ground.

………………………………………………………………………………………………………… ………………………………………………………………………………………………..…….[1]

6 A model rocket of initial mass 1.3 kg is fired vertically into the air. Its mass decreases at a

constant rate of 0.23 kg s-1 as the fuel burns. When the fuel is completely burnt, the final mass of the rocket is 0.38 kg. During the flight, the gravitational field strength acting on the rocket may be considered to have a constant value of 9.8 N kg-1.

(a) Calculate (i) the initial weight of the rocket,

Initial weight = ………………….N [1] (ii) the final weight of the rocket,

Final weight = ………………….N [1] (iii) the time taken for the fuel to be completely burnt.

Time = ……………….s [1]

8


(b) The variation with time t of the upward force on the rocket during the first 3 seconds

after firing is shown in Fig. 6.

Fig. 6

(i) On Fig. 6, use the same scales to draw a line to represent the variation with time t of the total weight of the rocket during the first 5 seconds after firing.

[1] (ii) Read off from Fig. 6 the time delay between firing the rocket and lift-off.

Time delay = ……………………s [1] (c) Write down an equation to represent the relation between the resultant force F on a body,

the time t for which the force acts and the change in momentum ∆p of the body. [1]

(d) The energy stored in the fuel is converted partly into kinetic energy and thermal energy of

the rocket. State two other forms of energy into which the energy of the fuel is converted.

…………………………………………………………………………………………………..…..… ……………………………………………………………………………………………...………[2]

Force / N

9


Section B

Answer any TWO questions 7 The aeroplane shown in Fig. 7.1 is travelling horizontally at 95 m s-1. It has to drop a crate of

mass 10 kg of emergency supplies. The air resistance acting on the crate may be neglected.

Fig. 7.1

(a) (i) The crate is released from the aircraft at point P and lands at point Q. Sketch the path followed by the crate between P and Q as seen from the ground. [1]

(ii) Explain why the horizontal component of the crate’s velocity remains constant while

it is moving through the air.

............................................................................................................................................ …….....................................................................................................................................

…….................................................................................................................................[2]

95 m s-1

P

Q R

10


(b) (i) To avoid damage to the crate, the vertical component of the crate’s velocity on

landing should not exceed 32 m s-1. Determine the maximum height from which the crate can be dropped.

Maximum height = .......................m [2] (ii) Calculate the time taken for the crate to reach the ground if the crate is dropped

from a height of 52 m.

Time taken = .......................s [2]

(iii) If R is a point on the ground directly below P, calculate the horizontal distance QR.

QR = .......................m [2] (c) In practice, air resistance is not negligible. State and explain the effect of air resistance on

the maximum height from which the crate can be dropped.

………………………………………………………………………………………………………… ………………………………………………………………………………………………………[2]

(d) (i) After the crate landed on Q, it continued to move with initial horizontal velocity

reduced to ¼. It came to rest after travelling a distance of 4.0 m. Determine the frictional force experienced by the crate.

Frictional force = .......................N [3]

11


(ii) Assuming the frictional force is constant, sketch in Fig. 7.2 the variation of speed of the crate with distance covered, after it landed on Q. [2]

Fig. 7.2

(iii) After covering a distance of 1.5 m, determine the speed of the crate.

Speed of crate = .......................m s1 [2] (iv) To ensure the emergency supplies reach a longer distance, describe and explain

the changes that need to be made.

………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………[2]

8 (a) Define the terms potential difference and resistance.

.…..…………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………[2]

(b) Two sets of coloured lamps A and B are designed for use with a 240 V supply. There is a

total of 12 lamps in each set. In set A, the lamps are arranged in series, while in set B, they are arranged in parallel. The lamps in each set are identical, but the lamps in set A are different from the lamps in set B.

v / ms-1

d /m

12


The total power dissipated by the lamps in each set is 60 W. For each lamp in the set connected in series and in parallel, calculate the following

quantities. [8]

Set A (Series) Set B (Parallel) (i) current flowing

(ii) potential difference

(iii) resistance

(c) The circuit for set A (connected in series) is shown in Fig. 8.

Fig. 8

The lamps do not light up when the circuit is closed. Hence a voltmeter is used to test the

circuit. For each of the following observations, identify the fault.

(i) the potential difference between A and M is zero

………………………………………………………………………………………………………… …………………………………………………...………………………………………………….[1]

(ii) the potential difference is zero across every lamp except EF, across which the potential difference is 240 V.

………………………………………………………………………………………………………… …………………………………………………...………………………………………………….[1]

13


(iii) potential difference between A and M is 240 V but the potential difference is zero across every single lamp.

…………………………………………………………………..………………………..…………… …………………………………………………...………………………………………………….[1]

(d) A battery of e.m.f 8.00 V and internal resistance 0.60Ω is connected to a resistor of

resistance 8.36 Ω. Determine


Current = ……………….. A [2]

(ii) the potential difference across the 8.36 Ω resistor

Potential difference = ……………………… V [2]

(iii) the power dissipated by the internal resistor.

Power dissipated = ……………… W [2]

(iv) Explain why the potential difference across the terminals of a battery is normally lower then the battery’s e.m.f.

………………………………………………………………………………………………………[1]

14


9 (a) (i) Describe the meaning of a photon.

………………………………………………………………………………………………………… ………………………………………………………………………………………………………[1]

(ii)

Show that E, the energy of a photon is related to λ its wavelength by E λ = 1.99 x 10-16, where E is measured in J and λ is measured in nm.

[2]

(b) Wave theory predicts that, if electromagnetic radiation strikes a metal surface and ejects an electron, the kinetic energy of the electron should depend on the intensity of the wave. However observation shows that, in its interaction with matter to release an electron, it is the frequency of the electromagnetic wave, and not the intensity, which controls the maximum kinetic energy of the electron. A lamp is placed above a metal surface which contains atoms of radius 2.0 x 10-10 m. Each electron in the metal requires a minimum energy of 3.2 x 10-19 J before it can be emitted from the metal surface, and it may be assumed that the electron can collect energy from a circular area which has a radius equal to that of the atom. The lamp provides energy at an intensity of 0.40 W m-2 at the metal surface.

(i) Estimate on the basis of wave theory the time required for an electron to collect sufficient energy for it to be emitted from the metal.

Time = …………………….s [4]

15


(ii) Using the particulate nature of matter, comment on the validity of your answer to (b)(i).

………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………[2]

(b) Two metal electrodes A and B are sealed in an evacuated glass envelope and a potential difference V, measured using the voltmeter, is applied between them as shown in Fig. 9.1.

Fig. 9.1

B is then illuminated with monochromatic light of wavelength 365 nm and I, the current in

the circuit is measured using the ammeter for various values of V. The results are shown in Fig. 9.2.

(i) From this graph, deduce the p.d. required to stop photoelectric emission from B.

P.d = …………………. V [1]

-

+

A

V Variable d.c. supply

A

B

4

I/mA

-1 1 2V/V

Fig. 9.2

16


(ii) Calculate the maximum kinetic energy of the photoelectrons.

Maximum kinetic energy = ………………………….J [2] (iii) Calculate the work function of B.

Work Function energy = ……………….. J [2] (iv) Deduce the threshold frequency of the metal surface B

Threshold frequency = …………………. Hz [2]

(v) State with a reason, what modifications would be required, separately, to increase

1. the kinetic energy of a photoelectron [2] ………………………………………………………………………………………. ……………………………………………………………………………………………. ……………………………………………………………………………………………. 2. the rate of production of photoelectrons [2] …………………………………………………………….……………………………… …………………………………………………………………………………………… ……………………………………………………………………………………………

End of paper


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YISHUN JUNIOR COLLEGE JC 2 Preliminary Examination 2010

PHYSICS 8866/1 HIGHER 1 19 August 2010 Paper 1 Multiple Choice Thursday Additional Material: Optical Mark Sheet 1 hour

INSTRUCTIONS TO CANDIDATES

Do not open this booklet until you are told to do so. Write your name and CTG on the Optical Mark Sheet in the spaces provided. Shade your last two digits of your CTG and the last 3 digits of your IC number in the space provided. E.g. if you are from CTG 219 and the last 3 digits of your IC number were

S92XX808 Z, you will shade 19808. There are thirty questions in this paper. Answer all questions. For each question there are four possible answers, A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the separate optical mark sheet. Read the instructions on the answer sheet very carefully. INFORMATION FOR CANDIDATES

Each correct answer will score a credit. Marks will not be deducted for a wrong answer. Any rough working should be done in this booklet.



2








g = 9.81 m s-2

Formulae


v2 = u2 + 2as





21++

RR

=


3

1. The energy of a photon of wavelength λ is given byλhcE = , where c is the speed of light and

h is the Planck constant. What are the base units of h?

A kg m s1 B kg m2 s1 C kg m2 s2 D kg m2 s3

2. A body of mass 10 kg is dropped from rest from a tower of measured height (20 ± 2) m. If the

acceleration of free fall is taken as 10 m s2, the time it takes to fall to the ground should be recorded as

A (2.00 ± 0.02) s B (2.0 ± 0.1) s C (4.00 ± 0.02) s D (4.0 ± 0.1) s

3. Which of the following pairs includes a vector and a scalar?

A Displacement; acceleration B Momentum; force C Power; velocity D Frequency; speed

4. A small rubber ball is thrown upwards from a horizontal table and allowed to bounce on a

horizontal table. Which graph best represents the variation with time, t of the acceleration experienced by the ball, a?

a

t

a

t

a

t

a

t

A B

C D


4

5. An object is projected to reach T, as shown below at an angle to the horizontal in a gravitational field and it follows a parabolic path, PQRST. These points are the positions of the object after successive equal time intervals.

The displacements PQ, QR, RS, and ST

A have equal horizontal component B have equal vertical component C decrease at constant rate in the horizontal direction D increase at constant rate in the vertical direction

P

Q R

S

T


5

6. A mass of m hits a massive wall normally at a speed of u. If the collision is inelastic, which of the following is correct?

Motion of mass Principle of

conservation of momentum

Total kinetic energy

A Mass returns along its original path with speed u.

Conserved Not conserved

B Mass returns along its original path with speed less than u.

Conserved Conserved

C Mass does not rebound

Conserved Not conserved

D Mass does not rebound Not conserved Not conserved 7 A body of mass 5 kg, starts from rest and is acted on by a net force, F which varies with time,

t as shown below. What is the value of the momentum at t = 4 s?

A 0 N s B 10 N s C 30 N s D 40 N s

8. A parachutist descends vertically with uniform acceleration towards the ground, the net

resultant force acting on him

A Is zero B Is constant and non-zero C Increases uniformly with respect to time D Is proportional to the displacement moved

F /N

t /s

10

2 4 6 0

0


6

9. A spring obeying Hooke’s law has an unstretched length of 50 mm. When the spring is extended to 70 mm, the tension in the spring measures 8.0 N. What is the value of the stored elastic potential energy in the spring?

A 0.08 J B 0.98 J C 8 J D 0.098 J

10. A ladder resting on a rough floor and leaning against a smooth wall is in equilibrium. It is of

weight W and the contact forces exerted on the ladder by the wall and floor are X and Y respectively. Which of the following shows the correct free body diagram of the ladder?

11. An electric motor is required to haul a cage of mass 400 kg up a mine shaft through a vertical

height of 1000 m in 3.00 minutes. How much electrical power is required if the overall efficiency is 87%?

A 2.55 kW

B 19.0 kW C 21.8 kW D 25.1 kW

W W

W W

A B

C D

X X

X X

Y

Y

Y Y


7

12. The diagram shows a skateboarder descending a ramp.

The skateboarder starts from rest at the top of the ramp at P and leaves the ramp at Q

horizontally with a velocity v. In going from P to Q, the skateboarder’s centre of gravity descends a vertical height of 1.5 m.

What is the horizontal velocity, v? A 3.8 m s1

B 5.4 m s1 C 14.7 m s1 D 29.4 m s1

13. A raindrop falls at a constant vertical velocity of 1.8 m s1 in still air. The mass of the raindrop is 7.2 × 109 kg. What is the work done on the raindrop as it falls through a vertical distance of 4.5 m?

A 3.2 x 107 J B 1.2 x 107 J C 2.0 x 107 J D 4.2 x 107 J 14. Transverse progressive sinusoidal waves of wavelength λ are passing vertically along a

horizontal rope. P and Q are points on the rope 5λ/4 apart and the waves are traveling from P to Q. Which one of the following correctly describes Q at an instant when P is displaced upwards but is moving downwards?

Displacement of Q Movement of Q A upwards downwards B upwards upwards C downwards upwards D downwards downwards

P

Q

skateboarder


8

15. A sound wave of amplitude 0.20 mm has an intensity of 3.0 W m2.

What will be the intensity of a sound wave of the same frequency which has an amplitude of 0.40 mm?

A 4.2 W m2 B 6.0 W m2 C 9.0W m2 D 12 W m2

16. In a Young’s double slit interference experiment, monochromatic light placed behind a single slit illuminates two narrow slits and the interference pattern is observed on a screen placed some distance away from the slits. Which one of the following decreases the separation of the fringes?

A increasing the width of the single slit B decreasing the separation of the double slits C increasing the distance between the double slits and the screen D using monochromatic light of higher frequency 17. Which of the following correctly states the difference between a progressive wave and a

stationary wave? Progressive wave Stationary wave A all the particles on the wave some of the particles on the wave do not vibrate vibrate B all the particles on the wave vibrate all the particles on the wave vibrate with different amplitudes with the same amplitude C all the particles on the wave none of the particles on the wave vibrate in vibrate in phase with each other phase with each other D some of the particles on the wave all the particles on the wave vibrate in phase do not vibrate in phase


9

18. The diagram shows a microwave transmitter T which directs microwaves of wavelength λ at two slits S1 and S2 formed by metal plates. The microwaves that pass through the two slits are detected by a receiver.

When the receiver is moved to P from O, which is equidistant from S1 and S2, the signal

received decreases from a maximum to a minimum. Which one of the following statements is a correct deduction from this observation?

A The path difference S1O - S2O = 0.5 λ B The path difference S1O - S2O = λ C The path difference S1P -S2P = 0.5 λ D The path difference S1P - S2P = λ 19. A battery of e.m.f 24 V and negligible internal resistance is connected to a resistor network as

shown in the circuit diagram below.

What is the resistance of the single equivalent resistor that could replace the four resistors

between the points A and B A 50.0 Ω B 20.0 Ω C 250 Ω D 70.0 Ω

T

S2

S1

P

O Receiver

30 Ω 40 Ω

60 Ω 120 Ω

A B

R1 24 V


10

20. Referring to question 19, if R1 is 50 Ω, what is the current in the 60 Ω resistor? A 0.08 A B 0.12 A C 0.16 A D 0.24 A 21. A metal wire has resistance, R. The wire is now stretched to twice its original length by a

process that keeps its volume constant. If the resistivity of the metal of the wire remains constant, determine the new resistance in terms of R.

A 0.5R B R C 2 R D 4 R

22. In the circuit shown the battery has emf and internal resistance r.

When the switch S is open, the voltmeter, which has infinite resistance, reads 8.0 V. When the switch is closed, the voltmeter reads 6.0 V.

Determine the value of r. A 0.5 Ω B 0.8 Ω C 1.0 Ω D 1.2 Ω

2.4 Ω


11

23. Four resistors are connected as shown.

Between which two points does the maximum resistance of the combination occur? A P and Q B Q and S C R and S D S and P

24. Three similar light bulbs are connected to a constant-voltage d.c. supply as shown below.

Each bulb operates at normal brightness and the ammeter (of negligible resistance) registers a steady current.

The filament of one of the bulbs breaks. What happens to the ammeter reading and to the brightness of the remaining bulb? Ammeter reading Bulb brightness A increases increases B increases unchanged C unchanged unchanged D decreases unchanged

R S

Q P

1 Ω

4 Ω

3Ω

2Ω

A


12

25. An electron is moving along the axis of a current carrying solenoid. Which of the following is a

correct statement about the electromagnetic force acting on the electron?

A the force acts in the direction of motion B the force acts in the opposite direction to the motion C the force acts perpendicular to the direction of motion D no force acts on the electron

26. The diagram shows three long straight wires P, Q and R normal to the plane of the paper.

Wires P and R carry currents directed into the plane of the paper, and wire Q carries a current directed out of the paper. All three currents have the same magnitude.

Which arrow best represents the direction of the resultant force on wire P?

Q

R

C

B

A

D

P


13

27. A long straight wire XY lies in the same plane as a square loop of wire PQRS which is free to move. The sides PS and QR are initially parallel to XY.

When steady current passes through the wire and the loop, as shown in the diagram, what will be the effect on the loop? A It will move towards the long wire. B It will move away from the long wire. C It will rotate about an axis parallel to XY. D It will be unaffected.

28. The energy levels of an electron in a hydrogen atom are given by eVn

E 2

6.13−= , where n =

1, 2, 3, ….

The energy required to excite an electron from the ground state to the first excited state is

A 3.4 eV B 4.5 eV C 10.2 eV D 13.6 eV

Q

X

Y

P

R S


14

29. When a parallel beam of white light passes through a cool vapour, dark lines appear in the spectrum of the emergent light. This is principally because energy is absorbed and

A is not re-radiated at all. B is re-radiated as infra-red. C is re-radiated as ultra-violet. D is re-radiated uniformly in all directions.

30. An ultra-violet radiation causes the emission of electrons from a zinc plate. How would a

more intense source having radiation of the same wavelength affect the maximum energy per electron, AND on the number of electrons emitted per second?

Maximum energy Number of electrons emitted per second

per electron A less more B the same the same C the same more D more the same

END OF PAPER

1 B 2 B 3 C 4 D 5 A 6 C 7 C 8 B 9 A 10 C 11 D 12 B 13 A 14 B 15 D 16 D 17 A 18 C 19 A 20 A 21 D 22 B 23 B 24 D 25 D 26 C 27 A 28 C 29 D 30 C

8866/02/JC2 Prelims/YJC2010

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YISHUN JUNIOR COLLEGE JC 2 Preliminary Examinations 2010

PHYSICS 8866/2 HIGHER 1

19 August 2010 Paper 2 Thursday

2 hours

INSTRUCTIONS TO CANDIDATES Do not open this booklet until you are told to do so. Write your name and CTG in the spaces at the top of this page. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Section A Answer all questions. Section B Answer any two questions. You are advised to spend about one hour on each section. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.


For Examiner’s Use Section A

1 /4

2 /6

3 /8

4 /6

5 /8

6 /8

Section B

7 /20

8 /20

9 /20

Total /80

Candidates to answer on the Question Paper. .

2









g = 9.81 m s-2

Formulae


v2 = u2 + 2as





21++

RR

=

3


Section A Answer all questions in this section. 1 Estimate the following quantities and give appropriate units.

(a) The momentum of an Olympic sprinter during a 100 m race.

Mass = 50 – 70 kg Speed = 10 ms-1 Momentum = 500 to 700 kg ms-1 or Ns

momentum = …………... Unit ……...[2] (b) The energy of a photon of red light.

λred approx = 700 nm

E = =λhc 2.84x10-19 J or 1.78 eV

energy = …………... Unit ……….[2] 2 A satellite orbiting the Earth receives electromagnetic signals and then re-transmits them back

to Earth at a frequency of 2.3 GHz.

(a) Calculate the wavelength of the re-transmitted signal.

recognises GHz as 109 λ = 3 × 108/2.3 × 109 = 0.13 m

Wavelength ...........................m [2] (b) State the region of the electromagnetic spectrum to which these waves might belong.

.........................radiowaves(microwave is acceptable)...................................................[1] (c) The satellite is positioned 35 000 km from the Earth. The power received by the dish

antenna on the Earth is 16 nW. Calculate the power that would be received at the dish if the satellite were to be re-positioned at a distance of 17 500 km from Earth. Give your reasoning.

4


mention of/evidence of use of inverse-square law 64 nW

Power received = .........................W [2]

.............................................................................................................................................[1] 3 Fig. 3.1 shows a stretched string driven by a vibrator on one end and is fixed to a wall on the

other end. A stationary wave is produced on the string as shown.

(a) State the physical conditions that are necessary for a stationary wave to form on the string. Reflection implied /2 waves in opposite directions/fixed end (not ends)

Similar amplitude/little energy loss at wall frequency constant or same frequency/wavelength (any 2)

...........................................................................................................................................[2]

(b) Explain how you know that the wave on the string is transverse. String displacement perpendicular to rest/average/mean position of string or string

displacement perpendicular to energy propagation

(c) Compare the amplitude and phase of the oscillations of points A and B on the string.

Amplitude.......... A larger than B Phase....... A 1800 (or π) out of phase with B

Fig 3.1

vibrator

Position of string ½ cycle later than solid curve

wall

5


(d) The length of the string is 1.2 m and the speed of the transverse wave on the string is 6.2 m s-1. Calculate the vibration frequency of the vibrator.

λ = 1.2 c = fλ; f = 6.2/1.2 = 5.2 Hz

Vibration frequency.......................Hz [2] (e) The frequency of the vibrator is tripled. Sketch the new shape of the stationary wave on

Fig. 3.2.

Correct diagram :6 loops must be drawn

[1] 4 (a) State the conditions for the equilibrium of a body which is acted upon by a number of

forces.

The sum of forces acting on the body must be zero and the sum of moments about any

point must also be zero

(b) A student holds a uniform metre rule at one end in two different ways, as shown in Fig. 4.1

and 4.2 below.

(i) On Fig. 4.1 draw and label an arrow to represent the weight W of the metre rule and an arrow to represent the force F exerted by the student’s hand on ruler. State the relationship between the magnitudes of F and W. [2]

Fig 3.2

6


For Fig 4.1, F = W Length of F and W should be reasonably equal and location of W should be at centre of gravity of rule For Fig 4.2, Direction and location of the arrows are important

(ii) In Fig. 4.2, the rule is held horizontally using the thumb and first finger. On Fig. 4.2 draw and label the three forces acting on the metre rule. List these forces in order of increasing magnitude.

1 ……Index finger force upwards……………….. 2 ……Thumb force downwards………………… 3 ……Weight of ruler downwards……………………

Fig. 4.2 Fig. 4.1

W

F

7


5

Fig. 5 is a top view of a metal wire of length 0.53 m and cross sectional area 1.0 x 10-6 m2 is situated at an angle of 60o to a uniform magnetic field of flux density 1.8 x 10-3 T.

The metal wire has a density of 7.9 x 103 kg m-3 and resistivity of 8.8 x 10-8 Ω m.

A potential difference is applied between the ends of the wire so that there is an electromagnetic force acting on the wire in the direction out of paper.

(a) On Fig. 5, mark the direction of the current in the wire. [1] (b) For the wire, calculate

i) its weight weight, mg = (1.0 x 10-6)(0.53)(7.9 x 103)( 9.81) = 0.0411 N

Weight = …………………N [2] ii) its resistance

resistance of wire = (ρl)/A = (8.8 x 10-8 x 0.53)/(1.0 x 10-6) = 4.7 x 10-2 Ω

Resistance = …………………..Ω [2] (c) Calculate the potential difference required between the ends of the wire so that the

electromagnetic force on the wire can balance its weight.

I = F/(BLsin600) Potential difference = R (I) =2.32 V

600

Magnetic field direction

Metal wire

Fig. 5

0.53 m

8


Potential difference = ………………….. V [2] (d) the horizontal component of the Earth’s magnetic field is 1.8 x 10-5 T. State and explain

why in practice current-carrying wires are not seen to lift off the ground.

The component of Earth’s magnetic field is even smaller than the magnetic field in this question. This would mean that an extremely large current would be required for the wire to be lifted off the ground

6 A model rocket of initial mass 1.3 kg is fired vertically into the air. Its mass decreases at a

constant rate of 0.23 kg s-1 as the fuel burns. When the fuel is completely burnt, the final mass of the rocket is 0.38 kg. During the flight, the gravitational field strength acting on the rocket may be considered to have a constant value of 9.8 N kg-1.

(a) Calculate (i) the initial weight of the rocket,

Wi = 1.3 (9.8) = 12.7 N

Initial weight = ………………….N [1] (ii) the final weight of the rocket,

Wf = 0.38 (9.8) = 3.72 N

Final weight = ………………….N [1] (iii) the time taken for the fuel to be completely burnt.

Time taken = (1.3 – 0.38)/ 0.23 = 4 s

Time = ……………….s [1] (b) The variation with time t of the upward force on the rocket during the first 3 seconds

9


after firing is shown in Fig. 6.

Fig. 6

(i) On Fig. 6, use the same scales to draw a line to represent the variation with time t of the total weight of the rocket during the first 5 seconds after firing.

[1] A straight line with coordinates (0, 12.7) and (4, 3.72)

Or a line that has negative gradient = 0.23 (9.8) (ii) Read off from Fig. 6 the time delay between firing the rocket and lift-off. The time is the intersection of line and curve where upward force = weight of rocket.

Time delay = 0.52 s [1] (read to ½ the smallest square)

Time delay = ……………………s [1] (c) Write down an equation to represent the relation between the resultant force F on a body,

the time t for which the force acts and the change in momentum ∆p of the body. [1]

F =

tpΔ

(d) The energy stored in the fuel is converted partly into kinetic energy and thermal energy of

the rocket. State two other forms of energy into which the energy of the fuel is converted.

Gravitational potential energy and sound energy

Force / N

10


………………………………………………………………………………………...………[2]

Section B Answer any Two questions

7 The aeroplane shown in Fig. 7 is travelling horizontally at 95 m s-1. It has to drop a crate of mass

10 kg of emergency supplies. The air resistance acting on the crate may be neglected.

Fig. 7.1

(a) (i) The crate is released from the aircraft at point P and lands at point Q. Sketch the path followed by the crate between P and Q as seen from the ground. [1]

(ii) Explain why the horizontal component of the crate’s velocity remains constant while

it is moving through the air.

.......... no horizontal force acting (hence) no (horizontal) acceleration

…….................................................................................................................................[2]

(b) (i) To avoid damage to the crate, the vertical component of the crate’s velocity on

landing should not exceed 32 m s-1. Determine the maximum height from which the crate can be dropped.

[1]

11


(use of v2 = u2 + 2as gives) 322 = (0) + 2 × 9.81 × s s = 1024 /19.62 =52.2 m

Maximum height = .......................m [2] (ii) Calculate the time taken for the crate to reach the ground if the crate is dropped

from a height of 52 m.

(use of s = ½ at2 gives) 52 = ½ 9.81 × t2 t = 3.26 s

Time taken = .......................s [2]

(iii) If R is a point on the ground directly below P, calculate the horizontal distance QR.

x (= QR) = 95 × 3.26 = 310 m

QR = .......................m [2] (c) In practice, air resistance is not negligible. State and explain the effect of air resistance on

the maximum height from which the crate can be dropped.

maximum height is greater because vertical acceleration is reduced

(d) (i) After the crate landed on Q, it continued to move with initial horizontal velocity

reduced to ¼. It came to rest after travelling a distance of 4.0 m. Determine the frictional force experienced by the crate.

Fx d = ½ m v2 – ½ m u2

Fx 4 = -½ (10)(23.75)2 F = - 705 N

Frictional force = .......................N [3]

12


(ii)

Assuming the frictional force is constant, sketch in Fig. 7.2 the variation of speed of the crate with distance covered, after it landed on Q. [2]

Fig. 7.2

(iii) After covering a distance of 1.5 m, determine the speed of the crate.

Fx 1.5 = ½ m v2 – ½ m (23.75)2 -705x 1.5 = ½ m v2 – ½ (10)(23.75)2 v = 18.8 m s-1

Speed of crate = .......................m s1 [2] (iv) To ensure the emergency supplies reach a longer distance, describe and explain

the changes that need to be made.

Release the supplies at a higher height so that when the supplies reach the ground, they have a greater speed to cover a longer distance. No credit for reducing air resistance, friction or reducing mass ( because assuming friction is directly proportional to normal reaction, the deceleration remains unaffected, hence no change in the stopping distance)

8 (a) Define the terms potential difference and resistance.

Potential difference between 2 points is the amount of electrical energy that can be converted into other forms of energy per unit charge. Resistance is the ratio of the potential difference to the current flowing through it.

(b) Two sets of coloured lamps A and B are designed for use with a 240 V supply. There are a

total of 12 lamps in each set. In set A, the lamps are arranged in series, while in set B, they are arranged in parallel. The lamps in each set are identical, but the lamps in set A are

v / ms-1 23.8

4 d /m

13


different from the lamps in set B. The total power dissipated by the lamps in each set is 60 W.

For each lamp in the set connected in series and in parallel, calculate the following

quantities. [8]

Series Parallel (i) current P = 60/12 = 5 W

P = IV = I (20) I = 0.25 A

P = 60/12 = 5 W P = IV = I (240) I = 0.021 A

(ii) potential difference P.d = 20

12240

= V

p.d = 240 V

(iii) resistance V = I R 20 = (0.25) R R = 80 Ω

V = I R 240 = (0.021) R R = 11520 Ω

(c) The circuit for set A (connected in series) is shown in Fig. 8.

Fig. 8

The lamps do not light up when the circuit is closed. Hence a voltmeter is used to test the

circuit. For each of the following observations, identify the fault.

(i) the potential difference between A and M is zero

Open circuit in the connecting wires from bulb A to supply (or open circuit in connecting wire from bulb M to supply)

(ii) the potential difference is zero across every lamp except EF, across which the potential difference is 240 V.

Open circuit at lamp EF

(iii) potential difference between A and M is 240 V but the potential difference is zero across every single lamp.

14


More than one bulb is spoilt.

(d) A battery of e.m.f 8.00 V and internal resistance 0.60Ω is connected to a resistor of

resistance 8.36 Ω. Determine


E = IR + Ir 8 = I (8.36 + 0.6) I = 0.89 A

Current = ……………….. A [2]

(ii) the potential difference across the 8.36 Ω resistor

V = I R V = (0.89)(8.36) V = 7.46 V

Potential difference = ……………………… V [2]

(iii) the power dissipated by the internal resistor.

P = I2 R ] P = (0.89)2 (0.6) = 0.475 W

Power dissipated = ……………… W [2]

(iv) Explain why the potential difference across the terminals of a battery is normally lower then the battery’s e.m.f.

There is the presence of an internal resistance

9 (a) (i) Describe the meaning of a photon.

A photon is a quantum (or packet) of energy of electromagnetic radiation.

(ii)

Show that E, the energy of a photon is related to λ its wavelength by E λ = 1.99 x 10-16, where E is measured in J and λ is measured in nm. [2]

15


E = hc/λ = 6.63 x 10-34 x 3 x 108 / 10-9 = 1.99 x 10-16

(b) Wave theory predicts that, if electromagnetic radiation strikes a metal surface and ejects an electron, the kinetic energy of the electron should depend on the intensity of the wave. However observation shows that, in its interaction with matter to release an electron, it is the frequency of the electromagnetic wave, and not the intensity, which controls the maximum kinetic energy of the electron. A lamp is placed above a metal surface which contains atoms of radius 2.0 x 10-10 m. Each electron in the metal requires a minimum energy of 3.2 x 10-19 J before it can be emitted from the metal surface, and it may be assumed that the electron can collect energy from a circular area which has a radius equal to that of the atom. The lamp provides energy at an intensity of 0.40 W m-2 at the metal surface.

(i) Estimate on the basis of wave theory the time required for an electron to collect sufficient energy for it to be emitted from the metal.

A, Area of atom = π(2.0 x 10-10)2 = 4.0 x 10-20 π m2 P, Power of light on an area of atom = I x A

= 0.40 x 4.0 x 10-20 π W Time taken to collect energy, t = (3.2 x 10-19)/P = 6.4 s

Time = …………………….s [4] (ii) Using the particulate nature of matter, comment on the validity of your answer to

(b)(i).

The answer is not valid because using particulate nature of matter, there is no appreciable time delay between illumination and electron emission .

(b) Two metal electrodes A and B are sealed in an evacuated glass envelope and a potential difference V, measured using the voltmeter, is applied between them as shown in Fig. 9.1.

16


Fig. 9.1

B is then illuminated with monochromatic light of wavelength 365 nm and I, the current in

the circuit is measured using the ammeter for various values of V. The results are shown in Fig. 9.2.

(i) From this graph, deduce the p.d. required to stop photoelectric emission from B.

1 V

P.d = …………………. V [1]

(ii) Calculate the maximum kinetic energy of the photoelectrons.

KEmax = eVs = 1.6 x 10-19 J

Maximum kinetic energy = ………………………….J [2] (iii) Calculate the work function of B.

hf = Ф + KEmax Ф = KEmax – hf = 3.8 x 10-19

-

+

A

V Variable d.c. supply

A

B

4

I/mA

-1 1 2V/V

Fig. 9.2

17


Work Function energy = ……………….. J [2] (iv) Deduce the threshold frequency of the metal surface B

fo = Ф/h =5.8 x 1014 Hz

Threshold frequency = …………………. Hz [2]

(v) State with a reason, what modifications would be required, separately, to increase

1. the kinetic energy of a photoelectron [2] Increase the frequency of the wavelength of electromagnetic radiation because this would increase the energy of each photon 2. the rate of production of photoelectrons [2] Increase the intensity of the electromagnetic radiation because this would increase the number of photons hitting the metal surface

End of paper

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