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Class Index No Candidate Name:

2014 Preliminary Examination II

Pre-university 3

H2 PHYSICS Paper 1 Multiple Choice Questions 9646/01 Friday 26 September 2014 1 hour 15 minutes 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, Centre number and index number on the Answer Sheet in the spaces provided unless this has been done for you. There are forty 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 19 printed pages and 1 blank page.

2 Data

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

–1

permeability of free space, 0 = 4 10–7

H m–1

permittivity of free space, 0 = 8.85 10–12

F m–1

= (1/(36)) 10–9

F m–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

molar gas constant, R = 8.31 J K–1

mol–1

the Avogadro constant, NA = 6.02 1023

mol–1

the Boltzmann constant, k = 1.38 10–23

J K–1

gravitational constant, G = 6.67 10–11

N m2 kg

–2

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

Formulae

uniformly accelerated motion, s = ut + 2

1at

2

v2 = u

2 + 2as

work done on/by a gas, W = pV

hydrostatic pressure, p = g h

gravitational potential, =

r

Gm

displacement of particle in s.h.m. x = xo sin t

velocity of particle in s.h.m., v = vo cost

= )( 22 xxo

mean kinetic energy of a molecule of an ideal gas E = 2

3 kT

resistors in series, R = R1 + R2 + …

resistors in parallel,

R

1 = ...

11

21

RR

electric potential, V =

r

Q

04

alternating current/voltage, x = xo sin t

transmission coefficient T = exp(2kd)

where k = 2

2 )(8

h

EUm

radioactive decay, x = x0 exp(–t)

decay constant, =

2

1

6930

t

.

3

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1 Which of the following could be the correct expression for the velocity v of ocean waves in

terms of the density of seawater, g the acceleration of free fall, h the depth of the ocean

and the wavelength?

A g

B hg /

C gh

D /g

2 An object falls freely from rest and travels a distance s in time t. A graph of t2 against s is plotted and used to determine the acceleration of free fall g.

The gradient of the graph is found to be 0.204 s2 m-1.

Which statement about the value obtained for g is correct?

A It is both accurate and precise.

B It is accurate but not precise.

C It is neither accurate nor precise.

D It is precise but not accurate.

4

3 The time variation of the acceleration of an object is as shown in the graph below.

At which point is the magnitude of the velocity greatest?

4

In order that a train can stop safely, it passes a signal showing a yellow light before it reaches another signal showing a red light. Drivers apply the brake at the yellow light and this results in a uniform deceleration to stop exactly at the red light. The distance between the red and yellow lights is x. What must be the minimum distance between the lights if the train speed is increased by 20%, without changing the deceleration of the trains?

A 1.20x B 1.25x C 1.44x D 1.56x

5 Which of the following is not one of Newton's laws of motion?

A The rate of change of momentum of a body is directly proportional to the external force acting on the body and takes place in the direction of the force.

B The total momentum of a system of interacting bodies remains constant, provided no external force acts.

C If body A exerts a force on body B, then body B exerts an equal and oppositely-directed force on body A.

D A body continues in a state of rest or of uniform motion in a straight line unless acted upon by some external force.

5

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6 A stationary uranium nucleus, U238

92 , undergoes radioactive decay with emission of a helium

nucleus, He4

2 , of kinetic energy E.

What is the kinetic energy of the daughter nucleus?

A E234

4 B E

238

4 C E D E

4

238

7 The base area of a barge is 80 m2 and the sides of the barge are vertical. The depth h to

which it rests in fresh water of density 1.0 103 kg m3 is as shown on the left figure.

When further loaded, as shown on the right figure, with 5.0 103 kg of cargo, what is the

extra depth h to which the barge will rest?

A 0.063 m B 0.0064 m C 5.0 m D 610 m

8 The diagram shows two blocks of mass m and 2m connected by a light cord passing over a light, free-running pulley.

At what angle θ must the smooth slope be inclined such that the two blocks remain stationary?

A 19° B 30° C 45° D 60°

6

9 A ball rolls down a smooth inclined plane. The ball is first released from rest from P and then later from Q. Which of the following statements is/are correct?

(1) The ball takes twice as much time to roll from Q to O as it does to roll from P and O.

(2) The acceleration of the ball at Q is twice as large as the acceleration at P.

(3) The ball has twice as much K.E. at O when rolling from Q as it does when rolling from P.

A (1) and (2) only

B (2) and (3) only

C (1) only

D (3) only

10 A small electric motor is used to raise a weight of 3.0 N through a vertical height of 90.0 cm

in 6.0 s. The efficiency of the motor is 25%.

What is the electrical power supplied to the motor?

A 0.45 W B 1.80 W C 10.8 W D 17.7 W

11 The combined mass of a race car and its driver is 600 kg. Travelling at constant speed, the car completes one lap around a circular track of radius 160 m in a total time of 36 s.

What is the magnitude of the centripetal acceleration of the car?

A 0.17 m s-2 B 4.9 m s-2 C 100 m s-2 D 2900 m s-2

7

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12 A pendulum bob is released from rest in a horizontal position with the string taut.

Which of the following statements is correct when the pendulum reaches its vertical position at point P?

A The tension attained its least value.

B The tension depends only on the length of the pendulum.

C The tension depends on the mass and length of the pendulum bob.

D The magnitude of tension equals the weight of the pendulum bob.

13 An astronaut goes out for a “space-walk” at a distance above the earth equal to the radius of the earth. If the gravitational field strength at the surface of the earth is g, what is the astronaut’s acceleration due to gravity?

A zero B g / 4 C g / 2 D g

14 The gravitational potential at point X due to the Earth is 7.2 kJ kg1. At point Y, the

gravitational potential is 3.4 kJ kg1.

What is the change in gravitational potential energy of a 4.0 kg mass when it is moved from point X to point Y?

A 42.4 kJ B 15.2 kJ C +3.8 kJ D +15.2 kJ

P

bob in horizontal position

Earth point X

7.2 kJ kg1

point Y

3.4 kJ kg1

8

15 A trolley of mass 2.0 kg with free-running wheels is attached to two fixed points P and Q by two springs under tension as shown.

The trolley is displaced a small distance of 5.0 cm towards Q by a resultant force of 10 N

and is then released. The equation of the subsequent motion is a = -

2 x, where x is the displacement from the equilibrium position.

What is the constant 2?

A - 10 rad2 s-2 B - 100 rad2 s-2 C 10 rad2 s-2 D 100 rad2 s-2

16 A particle of mass 4.0 kg moves with a simple harmonic motion and its potential energy U varies with position x as shown.

What is the period of oscillation of the mass?

A π 2

s5

B π8

s25

C π4

s5

D π2 2

s5

17 A solid Y is in thermal equilibrium with solid Z. Solid X is at the same temperature as solid Y. Solid X is in thermal contact with solid Z.

Which of the following statements is incorrect?

A There is no net transfer of energy between solid Y and solid Z.

B Solid Y is at the same temperature as solid Z.

C Internal energy of solid X and the internal energy of solid Z are the same.

D Solid X is in thermal equilibrium with solid Z.

9

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18 The specific heat capacity of a liquid is to be found using a continuous flow calorimeter. First an input power of 10 W is used. When the input power is 20 W, it is found that the liquid flow rate must be quadrupled (four times) to give the same temperature rise in the same amount of time.

What is the rate of heat loss to the surroundings?

A 3.3 W B 5.0 W C 6.7 W D 7.5 W

19 A sound wave travelling towards the right through air causes the air molecules to be displaced from their original positions. The graph below shows the variation with distance of the displacement of air molecules at a particular instant of time.

Taking the displacement towards the right as positive, at which point is the pressure maximum?

20 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

Distance

Displacement

A

B

C

D

10

21 S1 and S2 are two identical sources of waves that are in phase. The instantaneous positions of two wave crests from each source are shown below.

Which of the following is true?

A X is a point of constructive interference.

B W is a point of destructive interference.

C S1Y – S2Y = n where n is an integer.

D S1Z – S2Z = (2n - 1) /2 where n is an integer.

22 When light of wavelength 570 nm is incident normally on a plane diffraction grating, the second-order diffraction images are formed at an angle of 34.8° to the normal of the grating.

What is the number of lines per millimetre of the grating?

A 500 B 1000 C 2000 D 500 000

23 A metal sphere of radius 0.1 m was insulated from its surroundings and given a large positive charge. A small charge was brought from a distant point to a point 0.5 m from the sphere’s centre. The work done against the electric field was W and the force on the small charge in its final position was F.

If the small charge had been moved to only 1 m from the centre of the sphere, what would have been the values for the work done and the force?

work done force

A W/4 F/2

B W/2 F/4

C W/2 F/2

D W/2 F/ 2

11

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24 A positive charge is placed at P and a negative charge is placed at Q. The electric potential at different points between these two charges is shown in the figure below.

Which of the following graphs correctly shows the variation of the electric field strength E with distance x along line PQ?

A

C

B

D

25 A high electric potential is applied between two electrodes of a hydrogen discharge tube so that the gas is ionised. Electrons then move towards the positive electrode and protons towards the negative electrode. In each second, 5.0 x 1018 electrons and 2.0 x 1018 protons pass a cross-section of the tube.

What is the current flowing in the discharge tube?

A 0.16 A B 0.48 A C 0.80 A D 1.1 A

12

26 The figure shows the current, I, through a filament lamp changes with the p.d. V, applied across it.

Which of the following explains why it is not a straight line graph?

A electricity is used to produce light.

B the resistance of the filament increases.

C the filament of the lamp is of uneven thickness.

D the potential difference from the battery is not stable.

27 Three identical light bulbs are connected to a constant-voltage d.c. supply as shown in the diagram. Each bulb operates at normal brightness and the ammeter 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 bulbs?

ammeter reading bulb brightness

A increases increases

B increases unchanged

C decreases unchanged

D decreases increases

13

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28 What is the potential difference between the points A and B in the following circuit?

A 0 V B 3.5 V C 4.5 V D 7.5 V

29 A doubly charged ion is moving in a uniform magnetic field of flux density B in a circle of radius r at a speed v.

What is the flux density which will maintain a singly-charged ion of the same mass in a circle of half the radius at the same speed?

A 4

B B

2

B C 2B D 4B

30 The magnetic flux density at the centre of a flat circular coil is given by the equation

2

oNB

r

I

.

Two such coils, X and Y, each with 50 turns, are arranged as shown in the diagram.

X has radius 0.060 m and carries a current of 1.5 A in the anti-clockwise direction, Y has radius 0.12 m and carries a current of 1.0 A in the clockwise direction.

What is the magnitude and direction of the total magnetic flux density at the centre of the coils?

A o417 out of the page

B o417 into the page

C o833 out of the page

D o833 into the page

14

31 A coil has area A and n turns.

A uniform magnetic field of flux density B acts at an angle to the plane of the coil, as shown.

What is the decrease in magnetic flux linkage when the coil rotates so that angle is reduced to zero?

A BAn cos B BAn sin C 2BAn cos D 2BAn sin

15

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32 The figure below shows a copper disc rotating at a constant rate about its centre O in a uniform magnetic field between two bar magnets. The magnetic field is acting perpendicularly to the disc.

Which of the following graphs correctly shows the variation of the induced e.m.f. between the centre O and a point R on the rim of the disc with time t?

A

B

C

D

33 An electric kettle has the following label:

Power : 2000 to 2400 W Voltage : 220 to 240V Frequency : 50 to 60 Hz

Which of the following is a probable expression of the current that passes through the kettle when used in Singapore?

A I = 8.33 sin (315t)

B I = 10.9 sin (315t)

C I = 14.1 sin (375t)

D I = 16.0 sin (375t)

16

34 A direct current of 10 A flowing through a heating coil produces a certain power P.

What is the new power produced in the same heating coil by a sinusoidal alternating current of 10 A peak value?

A P B 2 P C 4

1 P D

2

1P

35 A figure shows how the wave function of a particle varies with position.

At which position is the particle most likely to be found?

A x = a B x = b C x = c D x = d

17

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36 An electron of energy E is incident on the left-hand side of a potential barrier of energy U. The energy U is greater than E.

Which diagram represents the wave function of the electron to the right of the barrier?

A

B

C

D

37 The resistance of a piece of pure silicon falls as the temperature rises. Which statement is true?

A The ratio of the positive to negative charge carriers increases.

B The ratio of the positive to negative charge carriers decreases.

C The charge carriers can move more easily at a higher temperature.

D The total number of charge carriers increases with temperature.

18

38 A semiconductor X is made by doping germanium crystal with arsenic (donor). Another semiconductor Y is made by doping germanium with indium (acceptor). The two are joined end to end and connected to a battery as shown.

Which of the following statements is correct?

A X is P-type, Y is N-type and the junction is forward biased.

B X is N-type, Y is P-type and the junction is forward biased.

C X is P-type, Y is N-type and the junction is reverse biased.

D X is N-type, Y is P-type and the junction is reverse biased.

39 Radon 222

86Rn decays by and emission to bismuth 214

83Bi .

For the decay of each nucleus of radon, how many and particles are emitted?

particles particles

A 1 1

B 2 1

C 1 2

D 2 2

X Y

19

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40 The activity of a sample of Iodine-131 varies with time as shown. The activity scale is logarithmic.

What is the approximate half-life of Iodine-131?

A 8 days B 28 days C 55 days D 180 days

20

BLANK PAGE

Millennia Institute

PU3 H2 Physics 9646

PRELIMINARY EXAMINATION II 2014

Mark Scheme

Paper 1

1 2 3 4 5 6 7 8 9 10

A B B C B A A B D B

11 12 13 14 15 16 17 18 19 20

B C B D D D C C A A

21 22 23 24 25 26 27 28 29 30

C A B B D B C B D A

31 32 33 34 35 36 37 38 39 40

B D C D C A D D B A

1 Answer – A

Units on LHS = m/s Units on RHS = [(m/s

2)(m)]

0.5 = m/s

2 ANSWER – B

Presence of scatter => low precision

s = 0 + ½ g t2 => a correct graph should pass through the origin

=> no systematic error in the measurements here

=> accuracy

3 ANSWER – B (Area under a-t graph having the largest value)

4 Answer - C v

2 = u

2 – 2as, v = 0

(u1)2 = 2ax ……………….. (1)

(u2)2 = 2ax2, and u2 = 1.2 u1

hence, (1.2u1)2 = 2ax2 ……….(2)

2

from (1) & (2), ax

ax

u

u

2

2

)(

)(44.1 22

1

21

x2= 1.44x

5 ANSWER – B

The total momentum of a system of interacting bodies remains constant, provided no external force acts.

6 ANSWER – A

Conservation of momentum: 0= 234 v + 4 vHe

v = (4 / 234 ) vHe

KE: helium, E = ½ m vHe2 = ½ (4u) vHe

2

Daughter nucleus, E = ½ m v2 = ½ (234u) ((4 / 234 ) vHe)

2

= 4 / 234 E

7 ANSWER – A

Weight of displace fluid = weight of the object

Vg = mog

hA = mo

h = mo/A = (5.0 x 103) / (1.0 x 10

3 x 80) = 0.0625 0.063 m

8 Answer - B

At equilibrium,

T = mg

2mgsin = T

2mgsin = T = mg

sin = 0.5

angle = 30 degreee

9 Answer – D

(1) Ball released from Q will arrive at some speed when it reaches point P, as a result, it will take shorter time to complete the remaining distance from P to Q. Hence the ball will take less than twice as much time to roll from Q to O as it does to roll from P and O.

(2) Since the gradient remains the same throughout the slope, resultant force acting on the ball remains the same, hence no change in the acceleration of the ball at point P and Q.

(3) Using principle of conservation of energy, gain in KE equals loss in GPE, since the height of Q is twice as compared to P, the ball has twice as much K.E. at O when rolling from Q as it does when rolling from P.

10 Answer - B

Output power = 3.0 (0.90) / 6.0 = 0.45 W

Input power = 0.45 / 0.25 = 1.80 W

11 Answer - B

3

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ac =

=

(

)

=

(

)

= 4.9 m s

-2

12 Answer - C

At P, T-W = Fc

T = Fc + mg

= mr2 + mg

tension depends on r (length of pendulum) and m (mass of bob)

13 Answer – B

Since g = GM / r2, at a height of r above the earth surface, the new g1 = GM / (2r)

2 hence

new g1 =g / 4

14 ANSWER – D

Change U = Uf – Ui = (-3.4 x 1000 )(4) – (-7.2 x 1000 )(4)

= + 15.2 kJ

15 Answer – D

At the amplitude position,

ao = - 2 xo

maxF

m=

2 xo

210(0.05)

2.0

2 =100

16 Answer – D

From graph, PEmax at amplitude position = 1.0 J By conservation of energy, KEmax at equilibrium position is also 1.0 J. KEmax = ½ m vo

2 = ½ (4.0) vo

2 = 1.0

vo = 1

2 m s

-1

For SHM, vo = xo

1

2=(0.2)

2π

T

1

2=

2π

5T

T =2π 2

5s

17 Answer – C

Internal energy includes also total PE of atoms/molecules.

Total number of atoms/molecules for solid X, Y and Z may be different.

X, Y and Z may be different types of solids.

4

Hence internal energy of the 3 solids may be different.

18 Answer – C

Let the total heat input be Qi, the heat transfer to the liquid be QL and the heat loss to the surrounding be Qs.

Qi = QL + Qs

Pt = mc + Qs

With an input power of 10 W,

10t = mc + Qs Equation (1)

With an input power of 20 W,

20t = 4mc + Qs Equation (2)

Combining the 2 equations,

20t = 4(10t - Qs) + Qs

3Qs = 20t

= 6.7 kW

19 Answer – A

Displacement towards Right is positive

At point A, air molecules are displaced on either side to create a Compression.

20 Answer – A

Period, T = 60 ms = 0.060 s

Frequency, f = 1/T = 16.7 Hz

21 Answer – C

Z, Y, W are points of constructive interference => Path Difference = n

X is a point of destructive interference => Path Difference = (2n - 1) /2

5

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22 Answer – A

dsinθ = nλ

dsin(34.8) = (2)(570 x 10-9

)

d = 1.997 x 10-6

N = 1/d = 500 625 lines per metre = 500 lines per mm ( 3 SF)

23 ANSWER – B

Work done = change in Electrical PE = Uf - UI

= (0)0.5

kQqW

= > W 2kQq

New Work done = 2

(0) / 21

kQqW

Force = 20.5

kQqF

F = 4kQq

New Force = 2

/ 41

kQqF

24 Answer – B

Field strength E of the field at a point is numerically equal to the potential gradient at that point.

As the equipotential lines are closer at the two ends, the potential gradient is steeper at these regions, i.e. a stronger E field.

25 ANSWER - D

Direction of flow of electrons and protons both contributes to the conventional current

Net current = (7.0 x 1018

)( 1.6 x 10-19

)= 1.12 A

26 Answer – B

The resistance of the filament increases.

27 ANSWER – C

Suppose V is the voltage of the supply and R is the resistance of each bulb, then effective resistance = R/3 and the current in the ammeter = 3V/R provided all three bulbs are working properly. If one bulb has broken down, then effective resistance = R/2 and the current in the ammeter = 2V/R. Hence the current reading decreases and since current through each bulb and the voltages across each bulb is the same as before, the brightness of the bulbs is not affected.

28 ANSWER – B

Potential at A = (11/12)(6) = 5.5 V

Potential at B = (1.5/4.5)(6) = 2 V

Potential diff V_AB = 5.5 – 2 = 3.5 V

29 ANSWER = D

Equation (1)

6

Equation (2)

Combine both equations =

B2 = 4B1

30 ANSWER = A

From X, 2

oNB

r

I

= (50)(1.5)µo / (2)(0.060) = 625 µo pointing out of page (using RHGR)

From Y, 2

oNB

r

I

= (50)(1.0)µo / (2)(0.12) = 208 µo pointing into page (using RHGR)

Net B = 625 µo – 208 µo = 417 µo pointing out of page

31 ANSWER = B

Initially,

= nBA cos , where is the angle between the magnetic field and normal to the plane.

= nBA cos (90 - )

= nBA sin

As becomes zero, = 0. Hence the decrease is nBA sin .

32 ANSWER – D

Since the angular velocity is constant, the rate of cutting of magnetic flux by the disc is constant, hence constant induced e.m.f.

33 ANSWER – C Range of Irms = P/V = 8.333 A to 10.9 A Range of corresponding I0= 11.79 A to 15.4 A

Expression for I= I0 sint

34 ANSWER = D

For D.C, P = I2R = (10)

2R

For A.C, power produced <P> = ½ Po = ½ Io2R = ½ (10)

2R = ½ P

35 Answer = C

Highest probability density at c due to highest amplitude of wave function, Ψ where the square of the amplitude of wave function IΨI

2 gives the probability of finding the electron at a point. (No

mathematical treatment is required.)

36 ANSWER – A

On RHS , wavelength unchanged, but diminished amplitude

7

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37 Answer – D

For intrinsic semiconductor, the number of electron-hole pair increases with temperature.

38 Answer – D

X is N-type, Y is P-type and the junction is reverse biased.

39 Answer – B

222

86Rn 214

83Bi + 4

22 He + 0

1e

40 Answer – A

8 DAYS

END

Class Adm No Candidate Name:

This question paper consists of 18 printed pages. [Turn over


Pre-university 3

H2 Physics 9646/02 Paper 2 Structured Questions

Thursday 18 Sept 2014 1 hour 45 minutes

Candidates answer on the Question Paper.

No Additional Materials are required.

READ THESE INSTRUCTIONS FIRST Write your name, class and admission number in the spaces 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, and glue or correction fluid. Section A Answer all questions. It is recommended that you spend about 1 hour 15 minutes on this section. Section B Answer Question 8 It is recommended that you spend about 30 minutes on this 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

1

2

3

4

5

6

7

8

Total

2

Data

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

permeability of free space, 0 = 4 10–7 H m–1

permittivity of free space, 0 = 8.85 10–12 F m–1

= (1/(36)) 10–9 F m–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

molar gas constant, R = 8.31 J K–1 mol–1

the Avogadro constant, NA = 6.02 1023 mol–1

the Boltzmann constant, k = 1.38 10–23 J K–1

gravitational constant, G = 6.67 10–11 N m2 kg–2


Formulae


1at2

v2 = u2 + 2as




r

Gm



= )( 22 xxo


3 kT



R

1 = ...

11

21

RR


r

Q

04



where k = 2

2 )(8

h

EUm


decay constant, =

2

1

6930

t

.

[Turn over

3


Section A (40 Marks)

Answer all questions

It is recommended that you spend about 1 hour 15 minutes on this section.

1 50 copper rods are arranged side by side closely without any gaps between them as shown in Fig 1.1. A metre rule is used to measure L, the total length as shown, and recorded as

(60.5 0.1) cm.

Fig 1.1

(a) Calculate the diameter of a single rod, together with its uncertainty.

diameter = …………………………….. cm [2]

(b) Given that the resistivity of copper is 1.7 x 10-8 m and the average length of each rod is measured by the same metre rule to be 14.2 cm, calculate the percentage uncertainty of the resistance of a single copper rod.

percentage uncertainty = …………………………….. % [3]

(c) Explain what is meant by random errors, and identify a source of random error which can occur in the measurement of the diameter of a single copper rod.

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

4


2 A small cube of mass m slides down along a spiral path round a cone as shown in Fig. 2.1. There

is a smooth wall along the outer edge of the spiral path to prevent the cube from falling out of the path. This wall is inclined such that it always exerts a horizontal contact force on the cube as it

spirals down. The path is always inclined at an angle to the horizontal at any point as shown in Fig. 2.2. All frictional forces are negligible.

(a) There are three distinct forces acting on the cube, including the horizontal contact force.

Fig. 2.3 is a zoomed-in view of the cube when it is at the position in Fig. 2.2. In Fig. 2.3, draw the forces that act on the cube, paying particular attention to the point of application of each force. Your forces should be clearly labelled in words, describing the nature of each force. [3]

Fig. 2.3

(b) Based on your answer in (a), explain how the forces affect the motion of the cube as it slides down the spiral path.

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

spiral path taken by cube

Fig. 2.2

cube

wall

cube

cone

spiral path

Fig. 2.1

5

[Turn Over


(c) Derive an expression for the rate of change of kinetic energy of this cube in terms of , m,

acceleration of free fall g, and its instantaneous speed v. [2]

3 At the National Day parade, a parade baton is twirled by a member of the marching contingent. The baton can be modelled to be a small ball of mass m fixed to one end of a light rigid rod. During the twirl, the ball can be assumed to move at constant speed around the circumference of a vertical circle with centre at C, as shown in Fig. 3.1.

Fig. 3.1

(a) Explain what is meant by centripetal force.

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

(b) When the rod is vertical with the ball above point C, the tension T in the rod is

T = 2mg

where g is the acceleration of free fall.

(i) State in terms of mg, the magnitude of the centripetal force. centripetal force = …………………………….. [1]

6


(ii) Determine the magnitude of the tension, in terms of mg, in the rod when it is vertical,

with the ball below point C. tension = …………………………….. [1]

(iii) Determine the angular speed of the ball. angular speed = …………………………….. rad s-1 [2]

(iv) Given that the ball moves with a constant angular speed, explain why work has to be done for it to move from the position where it is vertically above point C to the position where it is vertically below C.

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

4 (a)

An electric field may be produced in the region between two charged parallel plates. Fig. 4.1 shows two such plates, which are nearer in separation at the bottom ends.

On Fig 4.1, sketch the pattern of field lines between the plates. [2]

Fig. 4.1

(b) An isolated point charge Q is situated in a vacuum. At a distance of 1.0 x 10-10 m from this charge, the electric potential is +14.4 J C-1.

(i) Explain what is meant by electrical potential at a point in an electric field. ……………………………………………………………………….………...………………… ……………………………………………………………………………..……..……………. [1]

+ -

7

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(ii) Determine the charge Q.

charge = …………………………….. C [1]

(iii) An electron is moved from a distance of 3.0 x 10-10 m to a distance of 1.0 x 10-10 m from charge Q.

Determine the work done in moving the electron. work done = …………………………….. J [3]

(iv) State and explain whether the work done in b(iii) is positive or negative.

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

5 (a) Explain the difference between the conductivity of a conductor and an insulator. ……………………………………………………………………….………...……………….………… ……………………………………………………………………………..……..……………..……. [1]

(b) (i) Define resistance. ……………………………………………………………………………..……..……………. [1]

(ii) A resistor made from a metal oxide has a resistance of 1.5 . The resistor is in the form of a cylinder of length 2.2 x 10-2 m and radius of 1.2 x 10-3 m.

Calculate the resistivity of the metal oxide.

resistivity = …………………………….. m [2]

8


(iii) The manufacturer of the resistor in b(ii) guarantees its resistance to be within 10% of

1.5 provided the power dissipation in the resistor does not exceed 1.0 W.

Calculate the maximum current in the resistor for the power dissipation to be equal to 1.0 W.

maximum current = …………………………….. A [1]

(iv) Three of the resistors in (iii) are connected in the circuit as shown in Fig. 5.1.

Fig. 5.1

The cell has an e.m.f. of 2.0 V and negligible internal resistance.

Determine the maximum power that could be dissipated in this circuit.

maximum power = …………………………….. W [2]

9

[Turn Over


6 (a) The following experiment is set up to observe two-source interference fringes.

Fig. 6.1

(i) Suggest an appropriate separation for the two slits in the double slit.

separation = …………………………….. m [1]

(ii) State and explain what changes, if any, occurs in the separation of the fringes and in the contrast between the bright and dark fringes observed on the screen, when the following changes is made separately:

1. increasing the separation between the double slits,

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

2. reducing the intensity of light incident on one slit of the double slit.

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

(iii) Standing waves are formed in microwave ovens. Suggest why it is desirable that food is rotated whilst being cooked in the microwave oven.

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

screen double-slit

green light

10


(b) Fig. 6.2 shows an organ pipe that is open at one end. The length of the pipe is L. The

frequency of the fundamental note emitted by the pipe is 16 Hz.

Fig. 6.2

(i) The speed of sound in the air in the pipe is 330 m s-1.

Determine the length L.

length L = …………………………….. m [2]

(ii) With reference to your answer in b(ii), suggest why it is better to use organ pipes that are closed at one end for producing low frequency notes rather than pipes that are open at both ends.

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

11

[Turn Over


7 In 2011, Japan was struck by a 9.0 magnitude earthquake near the island of Honshu. Tsunami

waves created by the quake resulted in vast damage to the Fukushima I Nuclear Power Plant. The incident has been widely referred as the Fukushima Daiichi nuclear disaster and it is the largest nuclear disaster since the Chernobyl incident in 1986.

The Japanese government estimates the total amount of radioactivity released into the atmosphere to be approximately one tenth of that released during the Chernobyl disaster. Significant amounts of radioactive material have also been released into the ground and the ocean. In December 2011, Japanese authorities declared the plant to be stable, although it would take decades to decontaminate the surrounding areas and to decommission the plant altogether.

15

The Fukushima I Nuclear Power Plant generates power from fission of uranium 235 bombarded by slow moving neutrons. One particular fission process reaction is of this type:

EnXeSrUn 1

0

143

54

90

38

235

92

1

0 3

where E represents energy released. When conditions are suitable, a chain reaction can occur and if it is controlled, a source of continuous power may be created. Fig. 7.1 shows the variation with mass number of the binding energy per nucleon for various nuclides.

Fig. 7.1

12


The fission products, strontium (Sr) and xenon (Xe) are mostly contained within fuel cans. The

neutrons, on the other hand, have high speed and are uncharged. They are able to escape from the fuel cans into a graphite compartment where they are slowed down. One of the three neutrons is needed to sustain the chain reaction and the other two are absorbed by the graphite compartment and the structural materials (concrete and steel) of the reactor. The plans for decommissioning (shutting down) nuclear reactors have to take into account the following information.

1. The radioactive elements in the fuel cans can simply be removed from the site. This removes about 99.99% of the radioactivity which was on site when the reactor was working.

2. The remaining radioactivity is mostly neutron-induced in the steel, concrete and graphite.

3. A substance can be said to be radioactive when it has an activity greater than 400 Bq kg-1.

4. There are about 2500 known nuclides. Of these, 79 which have a half-life longer than 1 year may be present in a reactor. However, most of them do not reach the activity of 400 Bq kg-1 to necessitate them being called radioactive.

5. Fig. 7.2 shows the current mass and activity of 13 problem nuclides, 10 years after the shutdown of a reactor. A dash indicates an insignificant amount of nuclide. All values are given to 2 significant figures.

Nuclide Half-life

/ yr

Activity in 8.0 x 10

6 kg Concrete

/ 1012

Bq


6 kg Graphite

/ 1012

Bq


6 kg Steel /

1012

Bq

Total Activity

/ 1012

Bq

H3

1 12 - 110 - 110

C14

6 5700 - 42 1.7 44

Cl36

17 310 000

- 1.3 - 1.3

Ca41

20 130 000

0.10 0.90 - 1.0

Fe55

26 2.7 0.82 4.0 2400 2400

Co60

27 5.2 0.28 11 680 690

Ni59

28 80 000 - 0.096 2.1 2.2

Ni63

28 92 - 17 230 250

Nb63

41 20 000 - - 0.013 0.013

Ag108

47 130 - 0.0017 0.017 0.019

Sm151

62 90 0.15 0.051 - 0.20

Eu152

63 12 0.82 0.11 - 0.93

Eu154

63 16 0.10 0.61 - 0.71

Totals 2.3 190 3300 3500

Fig. 7.2

13

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(a) Explain what is meant by radioactive.

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

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

(b) The energy released in the fission reaction occurs partly as kinetic energy of the fission products and the neutrons.

Suggest one other mechanism by which energy is released in the fission reaction.

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

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

(c) (i) Use Fig. 7.1 to calculate the energy released during the fission process of a uranium-235 nucleus to a strontium-90 nucleus and a xenon-143 nucleus. energy released = …………………………… J [3]

(ii) Why does a release of energy occur when there is an increase in binding energy?

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

(d) (i) Determine the total activity in the graphite section of the reactor.

total activity in graphite section = …………………………… Bq kg-1 [1]

(ii) Over a period of 100 years from now, the radioactive iron 55 in the reactor is less of a problem than the radioactive nickel 59.

Suggest why this is so, using calculations to support your reasoning. [3]

14


(iii) Determine the length of time required from now before the activity of the tritium

(hydrogen 3) in the reactor is below 0.43 x 1012 Bq. length of time = …………………………… years [2]

(e) The waste products from a nuclear reactor are often stored in sealed metal cans which are placed under water for a few months. Give a reason why metal cans are used and a reason why they are placed under water. ……………………………………………………………………….………...……………….………… ……………………………………………………………………….………...……………….………… ……………………………………………………………………………..……..……………..……. [2]

15

[Turn Over


Section B (12 Marks)

It is recommended that you spend about 30 minutes on this section

8 Fig. 8.1 illustrates a bow used in archery competitions.

Fig. 8.1

A designer of bows is attempting to maximise the efficiency of his bow. This means that as much of the potential energy stored in the bow as possible is converted to the kinetic energy of an arrow.

Some preliminary experiments are carried out with the bow when the centre of the string is moved through a distance x by a force F as shown in Fig. 8.2.

Fig. 8.2

16


These experiments indicate that x is not proportional to F.

The efficiency of the bow may be defined as

The efficiency of a bow is thought to depend on the distance x. The relation between the efficiency and the distance x may be written in the form

= axb

where a and b are constants.

Design an experiment to determine the value of b.

You should draw a labelled diagram to show the arrangement of your apparatus. In your account you should pay particular attention to

(a) the identification and control of variables,

(b) the equipment you would use,

(c) the procedure to be followed,

(d) how to determine

(i) the potential energy stored in the bow just before the arrow is released, and

(ii) the kinetic energy of the arrow after the string is released,

(e) any precautions that would be taken to improve the accuracy and safety of the

experiment. [12]

DIAGRAM

17

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18


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END OF PAPER

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1



Pre-university 3

H2 Physics 9646/02

Paper 2 Structured Questions

XX PAPER 2 MARKSCHEME 1 hour 45 minutes



READ THESE INSTRUCTIONS FIRST

Write your name, class and admission number in the spaces 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, and glue or correction fluid.

Section A

Answer all questions.

It is recommended that you spend about 1 hour 15 minutes on this section.

Section B

Answer Question 8


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.


1

2

3

4

5

6

7

8

Total

2


1 50 copper rods are arranged side by side closely without any gaps between them as shown in

Fig 1.1. A metre rule is used to measure L, the total length as shown, and recorded as

(60.5 0.1) cm.

Fig 1.1

(a) Calculate the diameter of a single rod, together with its uncertainty.

Diameter of one rod = L/50 = 1.210 cm

Uncertainty in diameter, ∆d = ∆L / 60 = 0.0017 cm = 0.002 cm (1 SF)

Hence, d = 1.210 0.002 cm

diameter = …………………………….. cm [2]

C1

A1

(b) Given that the resistivity of copper is 1.7 x 10-8 m and the average length of each rod is measured by the same metre rule to be 14.2 cm, calculate the percentage uncertainty of the resistance of a single copper rod.

=

100 = 1.03%

percentage uncertainty = …………………………….. % [3]

C1

C1

A1

(c) Explain what is meant by random errors, and identify a source of random error which can occur in the measurement of the diameter of a single copper rod.

Random errors are errors with different magnitudes and signs in repeated measurements, occurring without any fixed pattern.

Non-uniformity in diameter of the rod along its length [2]

B1

B1

2 (a) A small cube of mass m slides down along a spiral path round a cone as shown in Fig. 2.1. There is a smooth wall along the outer edge of the spiral path to prevent the cube from falling out of the path. This wall is inclined such that it always exerts a horizontal

contact force on the cube as it spirals down. The path is always inclined at an angle to the horizontal at any point as shown in Fig. 2.2. All frictional forces are negligible.

3

[Turn Over


(a) (i) There are three distinct forces acting on the cube, including the horizontal contact

force.

In Fig. 2.2, draw a free-body diagram for the cube, paying particular attention to the point of application of each force. Your forces should be clearly labelled in words, describing the nature of each force. [3]

B1 x 3

– for each correct force

(ii) Based on your answer in (a)(i), explain how the forces affect the motion of the cube as it slides down the spiral path.

Normal horizontal contact force of wall on cube provides the centripetal force for cube to move in a circular path as it spirals downward. Component of the weight parallel to the slope causes the acceleration of cube down slope. [2]

B1

B1

X

Weight of cube

Normal Reaction / Contact force from path

Normal Reaction / Contact force from wall

Direction of the Normal Contact force from wall should be drawn into the page using the right symbol. Otherwise, a clear statement should be given to describe

its direction.

4


iii) Derive an expression for the rate of change of kinetic energy of this cube in terms of

, m, acceleration of free fall g, and its instantaneous speed v. [2]

Rate of increase of kinetic energy

= rate of decrease of gravitational potential energy

= sinmgv

OR

2 21 1 12 2 sin

d 2 2 2d

m v u m as m g sKE

t t t t

where a = g sin and s

vt

OR

2

2

1

2

d 1 d 1 d 12 2

d 2 d 2 d 2

KE mv

KE v vm m v m va

t t t

where a = g sin

M1

A1

5

[Turn Over


3 A the National Day parade, a parade baton of is twirled by a member of the marching contingent.

The baton can be modelled to be a small ball of mass m fixed to one end of a light rigid rod. During the twirl, the ball can be assumed to move at constant speed around the circumference of a vertical circle with centre at C, as shown in Fig. 3.1.

Fig. 3.1

(a) Explain what is meant by centripetal force.

Centripetal force is the force needed to maintain a body in circular motion, and is provided by the resultant force acting on the body. Its direction is always perpendicular to the velocity of the body, directed toward the center of curvature of the path. [2]

B1

B1

(b) When the rod is vertical with the ball above C, the tension T in the rod is given by

T = 2mg

where g is the acceleration of free fall.

(i) State in terms of mg, the magnitude of the centripetal force.

3 mg

centripetal force = …………………………….. N [1]

A1

(ii) Determine the magnitude of the tension, in terms of mg, in the rod when it is vertical, with ball below point C.

4 mg

tension = …………………………….. N [1]

A1

(iii) Determine the angular speed of the ball.

At top, T + W = Fc

3 mg = m r 2

= √

= 6.4 rad s-1

angular speed = …………………………….. rad s-1 [2]

M1

A1

(iv) Given that the ball moves with a constant angular speed, explain why work has to be done for it to move from the position where it is vertically above point C to the position where it is vertically below C.

By conservation of energy, the ball loses GPE as it moves downwards, which may be converted to KE. Hence, in order to move the ball at constant angular speed, work has to be done to convert the GPE (which it would otherwise gain as KE when it moves from position above C to below C) to other forms. [1]

B1

6


4 (a)

An electric field may be produced in the region between two charged parallel plates. Fig. 3.1 shows two such plates.

On Fig 4.1, sketch the pattern of field lines between the plates. [2]

Fig. 4.1

9

(b) An isolated point charge Q is situated in a vacuum. At a distance of 1.0 x 10-10 m from this charge, the electric potential is +14.4 J C-1.

(i) Explain what is meant by electrical potential at a point in an electric field.

Electrical potential at a point in a field is the work done per unit positive charge in moving it from infinity to that point in the field. [1]

B1

(ii) Determine the charge Q.

Q = +1.6 x 10-19 C (with +ve sign)

charge = …………………………….. C [1]

A1

(iii) An electron is moved from distance of 3.0 x 10-10 m to a distance of 1.0 x 10-10 m from charge Q.

Determine the work done in moving the electron.

V3m =

JC-1

WD = q (V1m – V3m )= (-1.6 x 10-19 ) [ + 14.4 – (+4.79)]

= -1.54 x 10-18 J = -1.5 x 10-18 J

work done = …………………………….. J [3]

C1

M1

A1

(iv) State and explain whether the work done in (iii) is positive or negative.

Negative work done as force between the 2 charges is attractive, and as the electron comes nearer to charge Q, it loses potential energy. Work done is really by the e-field of charge Q.

[2]

A1

B1

+ -

field lines starting from + to -, starting perpendicularly at surface of plates = B1

field lines closer at bottom, and more spaced out near top = B1

7

[Turn Over


5 (a) Explain the difference between the conductivity of a conductor and an insulator.

Conductor has good conductivity due to presence of mobile charge carriers (electrons) / free electrons, while insulators are devoid of mobile charge carriers. [1]

B1

(b) (i) Define resistance.

Resistance is the ratio of potential difference across a device/resistor to the current that flows in it. [1]

B1

(ii) A resistor made from a metal oxide has a resistance of 1.5 . The resistor is in the form of a cylinder of length 2.2 x 10-2 m and radius of 1.2 x 10-3 m.

Calculate the resistivity of the metal oxide.

resistivity = …………………………….. m [2]

C1

A1

(iii) The manufacturer of the resistor in (ii) guarantees its resistance to be within 10% of

1.5 provided the power dissipation in the resistor does not exceed 1.0 W.

Calculate the maximum current in the resistor the power dissipation to be equal to 1.0 W.

Rmin = 0.9 x 1.5 1.35

maximum current = …………………………….. A [1]

A1

(iv) Three of the resistors in (iii) are connected in the circuit as shown in Fig. 5.1.

Fig. 5.1

The cell has an e.m.f. of 2.0 V and negligible internal resistance.

Determine the maximum power that could be dissipated in this circuit.

maximum power = …………………………….. W [2]

C1

A1

8


6 (a) The following experiment is set up to observe two-source interference fringes.

Fig. 6.1

(i) Suggest an appropriate separation for the two slits in the double slit.

1 to 9 x 10-4 m ( 0.1mm to 0.9 mm)

separation = …………………………….. m [1]

B1

(ii) State and explain what changes, if any, occurs in the separation of the fringes and in the contrast between the bright and dark fringes observed on the screen, when the following changes is made separately:

1. increasing the separation between the double slits,

The fringes will become closer (smaller fringe separation) according to

,

while contrast remains unchanged.

[2]

2. reducing the intensity of light incident on one slit of the double slit.

Fringe separation is not changed (as it is independent of intensity of light source), While contrast of the fringes is reduced as there is incomplete cancellation at the dark fringes due to the unequal amplitudes of light from the slits, and also reduced intensity at the bright fringes. [2]

B1

B1

B1

B1

(iii) Standing waves are formed in microwave ovens. Suggest why it is desirable that food is rotated whilst being cooked in the microwave oven.

[1]

B1

(b) Fig. 5.3 shows an organ pipe that is open at one end. The length of the pipe is L. The frequency of the fundamental note emitted by the pipe is 16 Hz.

Fig. 6.2

screen double-slit

green light

9

[Turn Over


(i) The speed of sound in the air in the pipe is 330 m s-1.

Determine the length L.

= v/f

length L = …………………………….. m [2]

C1

A1

(ii) With reference to your answer in b(ii), suggest why it is better to use organ pipes that are closed at one end for producing low frequency notes rather than pipes that are open at both ends.

Wavelength of open pipe for fundamental is 2L, ~ 10 m, thus using closed pipes is better as use up less space/material/cheaper

(Or to the same effect)

[1]

B1

10


7 In 2011, Japan was struck by a 9.0 magnitude earthquake near the island of Honshu. Tsunami

waves created by the quake resulted in vast damage to the Fukushima I Nuclear Power Plant. The incident has been widely referred as the Fukushima Daiichi nuclear disaster and it is the largest nuclear disaster since the Chernobyl incident in 1986.

The Japanese government estimates the total amount of radioactivity released into the atmosphere to be approximately one tenth of that released during the Chernobyl disaster. Significant amounts of radioactive material have also been released into the ground and the ocean. In December 2011, Japanese authorities declared the plant to be stable, although it would take decades to decontaminate the surrounding areas and to decommission the plant altogether.

15

The Fukushima I Nuclear Power Plant generates power from fission of uranium 235 bombarded by slow moving neutrons. One particular fission process reaction is of this type:

EnXeSrUn 1

0

143

54

90

38

235

92

1

0 3

where E represents energy released. When conditions are suitable, a chain reaction can occur and if it is controlled, a source of continuous power may be created.

Fig. 7.1 shows the variation with mass number of the binding energy per nucleon for various nuclides.

Fig. 7.1

11

[Turn Over


The fission products, strontium (Sr) and xenon (Xe) are mostly contained within fuel cans. The

neutrons, on the other hand, have high speed and are uncharged. They are able to escape from the fuel cans into a graphite compartment where they are slowed down. One of the three neutrons is needed to sustain the chain reaction and the other two are absorbed by the graphite compartment and the structural materials (concrete and steel) of the reactor.

The plans for decommissioning (shutting down) nuclear reactors have to take into account the following information.

1. The radioactive elements in the fuel cans can simply be removed from the site. This removes about 99.99% of the radioactivity which was on site when the reactor was working.

2. The remaining radioactivity is mostly neutron-induced in the steel, concrete and graphite.

3. A substance can be said to be radioactive when it has an activity greater than 400 Bq kg-1.

4. There are about 2500 known nuclides. Of these, 79 which have a half-life longer than 1 year may be present in a reactor. However, most of them do not reach the activity of 400 Bq kg-1 to necessitate them being called radioactive.

5. Table 7.1 shows the current mass and activity of 13 problem nuclides, 10 years after the shutdown of a reactor. A dash indicates an insignificant amount of nuclide. All values are given to 2 significant figures.

Nuclide Half-life

/ yr


6 kg Concrete

/ 1012

Bq


6 kg Graphite

/ 1012

Bq


6 kg Steel /

1012

Bq

Total Activity

/ 1012

Bq

H3

1 12 - 110 - 110

C14

6 5700 - 42 1.7 44

Cl36

17 310

000 - 1.3 - 1.3

Ca41

20 130

000 0.10 0.90 - 1.0

Fe55

26 2.7 0.82 4.0 2400 2400

Co60

27 5.2 0.28 11 680 690

Ni59

28 80 000 - 0.096 2.1 2.2

Ni63

28 92 - 17 230 250

Nb63

41 20 000 - - 0.013 0.013

Ag108

47 130 - 0.0017 0.017 0.019

Sm151

62 90 0.15 0.051 - 0.20

Eu152

63 12 0.82 0.11 - 0.93

Eu154

63 16 0.10 0.61 - 0.71

Totals 2.3 190 3300 3500

Table 7.1

12


(a) Explain what is meant by radioactive.

A nucleus is radioactive if it is unstable (due to presence of too many nucleons) and

undergoes transformation in its proton-neutron ratio/ gains stability by the emission of

radiation or particles.

[1]

B1

(b) The energy released in the fission reaction occurs partly as kinetic energy of the fission products and the neutrons.

Suggest one other mechanism by which energy is released in the fission reaction.

Gamma radiation/photons

[1]

B1

(c) (i) Use Fig. 7.1 to calculate the energy released during the fission process of a Uranium-235 nucleus to a Strontium-90 nucleus and a Xenon-143 nucleus.

Energy released

= BE of product nuclei – BE of reacting nuclei

= BE of Sr + BE of Xe – BE of U

= (8.20 x 90 ) + (7.90 x 143 ) - ( 7.1 x 235 )

= 199.2 MeV = 3.19 x 10-11 J

energy released = …………………………… J [3]

M1

C1

A1

(ii) Why does a release of energy occur when there is an increase in binding energy?

An increase in binding energy of the products means that they are more stable, hence there is a release of energy (that leads to the better stability).

[1]

B1

(d) (i) Determine the total activity in the graphite section of the reactor.

8.6 x 107 Bq kg-1

total activity in graphite section = …………………………… Bq kg-1 [1]

A1

13

[Turn Over


(ii) Over a period of 100 years from now, the radioactive iron 55 in the reactor is

less of a problem than the radioactive nickel 59.

Suggest why this is so, using calculations to support your reasoning. [3]

t

OeAA

For iron 55, 17000102400)100(

7.2

2ln

12

eA Bq

For nickel 59, 12

)100(80000

2ln

12 102.2102.2

eA Bq

Nickel 59 is a bigger problem than iron 55 because of its much longer half life, causing it to decay much more slowly.

A1

A1

B1

(iii) Determine the time required from now before the activity of the tritium (hydrogen 3) in the reactor is below 0.43 x 1012 Bq.

t

OeAA

t

e 12

2ln

1212 101101043.0

t = 96 years

length of time = …………………………… years [2]

M1

A1

(e) The waste products from a nuclear reactor are often stored in sealed metal cans which are placed under water for a few months.

Give a reason why metal cans are used and a reason why they are placed under water.

The emissions from radioactive waste products produce a lot of heat energy. Metal cans are used as they can better conduct heat away, and placed in water as water can act as a good coolant due to its high specific heat capacity.

[2]

B1

B1

14


Section B (12 Marks)


Defining the problem (1 mark)

P1 x is the independent variable and efficiency, , is the

dependent variable or vary x and calculate .

Alternative dependent variable : velocity v of arrow / kinetic energy of arrow / maximum potential energy of bow.

Stage correctly dependent and independent variables [B1]

Controlled Variables (2 marks)

P2

1. Distance between bow to target remains unchanged 2. Same arrow and bow to be used throughout the

experiment 3. Fixed point at the string for positioning the tail of the arrow 4. Arrow to be horizontal when it is been released from the

bowl

Any TWO points

[B2]

Methods of data collection (5 marks)

M1 Diagram: 1. Bow properly clamped at the centre to a fixed object/mass 2. Labelled distance travelled by arrow to target 3. Position of centre of bow should be higher than target

board (since arrow will fall vertically as it travels)

Any ONE point

[B1]

M2 Force F is measured using a force meter / newton-meter / force gauge hooked to the centre of the string and pulled horizontally.

Method of use is described or implied in diagram [B1]

M3 Distance x is measured with a metre rule Position & method of use is described or implied in diagram [B1]

M4 Determination of kinetic energy, K, of arrow:

1. Measure distance L from front of bow to target using a measuring tape + time taken for arrow to travel, t, is measured using a stopwatch / video recorder to capture the motion and replay to check for duration of travel.

Any ONE point

Details on marking the 2 points to aid in measurement are needed]. [B1]

2. Mass of arrow, m, is measured using a mass balance / electronic balance.

3. Average velocity v of arrow is calculated using v =

L

t

Average Kinetic energy of arrow, K =

21

2

L(m)

t

15

[Turn Over


M5 Determination of stored potential energy, P, of bow:

Plot a graph of F against x. For any given x, P = area under the F-x graph.

Do not accept answers based on Hooke’s law.

[B1]

Method of analysis (1 mark)

A Plot a graph of lg against lg x. The equation is valid if a straight line is obtained.

Value of b = gradient of graph.

Correct linearization, with method to find constant b

[B1]

Safety considerations (1 mark)

1. Target should be made from soft material such as cork or styrofoam to reduce chances of arrows being deflected in other directions

2. Arrows should be aimed only at target 3. Ensure firing area cleared of people during experiment

Any ONE point

[B1]

Additional detail (2 marks)

D Relevant points might include [maximum : 2 marks]

1. Distance from bow to target, L > 25 m, to ensure the time of flight is adequately long to be measured on a stopwatch.

2. Carry out trial runs to determine the workable range of values of variables.

3. Perform experiment in an enclosed area with no wind / neglect measurements if wind is detected during experiment.

12 marks can be scored in total

End of Paper

Any TWO points.

Do not award for vague computer methods.

[B2]



2014 Preliminary Examination II Pre-university 3

H2 Physics 9646/03

Paper 3 Longer Structured Questions Monday 15 Sept 2014 2 hours



READ THESE INSTRUCTIONS FIRST Write your name, class and admission number in the spaces 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, and 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.


Section A

1

2

3

4

Section B

5

6

7

Total

2


Data

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

permeability of free space, 0 = 4 10–7 H m–1

permittivity of free space, 0 = 8.85 10–12 F m–1

= (1/(36)) 10–9 F m–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

molar gas constant, R = 8.31 J K–1 mol–1

the Avogadro constant, NA = 6.02 1023 mol–1

the Boltzmann constant, k = 1.38 10–23 J K–1

gravitational constant, G = 6.67 10–11 N m2 kg–2


Formulae


1at2

v2 = u2 + 2as




r

Gm



= )( 22 xxo


3 kT



R

1 = ...

11

21

RR


r

Q

04



where k = 2

2 )(8

h

EUm


decay constant, = 2

1

6930

t

.

3

[Turn over


Section A

Answer all the questions in this section.

1 A toy car with a rocket engine moves along a horizontal track, as shown in Fig. 1.1.

Fig. 1.1

The rocket engine produces a constant forward force of 4.6 N. The car loses mass continuously as exhaust gases are produced by the rocket.

(a) Use momentum considerations to explain why the rocket produces a forward force on the car.

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

(b) The variation with time t of the speed v of the car is shown in Fig. 1.2.

Fig. 1.2

At time t = 2.0 s, the mass of the car is 440 g.

4


(i) For the time t = 2.0 s,

1. use Fig. 1.2 to determine the acceleration of the car,

acceleration = ………………………. m s-2 [2]

2. use your answer in (b)(i)1. to determine the magnitude of the resistive force acting on the car.

force = ………………………. N [2]

(ii) Explain how it can be deduced that the resistive forces acting on the car increases with increase of speed. .……………………………………………….……………………………………………….……… .……………………………………………….……………………………………………….……… .……………………………………………….……………………………………………….……… ……………………………………………………………..……….…………………………….. [2]

(c) The toy car is now re-fuelled and then rotated so that it is pointing upwards. It is suggested that the rocket engine produces sufficient force to propel the car vertically.

By considering the acceleration of the car at time t = 0 in Fig. 1.2, comment on this suggestion.

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

5

[Turn over


2 A 8.50 kg mass is connected to a 5.00 kg mass by a light inextensible string that passes over a

frictionless pulley. The 5.00 kg mass is connected to a light spring of spring constant k that is equal to 200 N m-1.

At the equilibrium position, the spring is stretched by an amount e and the 5.00 kg mass is

20.0 cm above the floor as shown in Fig. 2.1. The smooth incline plane makes an angle of 40 to the horizontal. It can be assumed that the tension in the string remains constant throughout.

Fig. 2.1

(a) Draw a free body diagram of the 5.00 kg mass when it is in its equilibrium position. Label all the forces clearly in your diagram. [3]

(b) The 8.50 kg mass is now given a slight displacement, x, down the slope.

By considering the forces now acting on the 5.00 kg mass and using Fnet = ma, show that the acceleration of the 5.00 kg mass is given by the expression

a = - 40 x. [3]

6


(c) (i) Using your answer in part (b), prove that the motion of the 5.00 kg mass is

simple harmonic. .……………………………………………….……………………………………………….……… .……………………………………………….……………………………………………….……… ……………………………………………………………..……….…………………………….. [2]

(ii) Hence show that the period of the oscillating mass is given by the expression

√

[2]

(d) The 8.50 kg mass is pulled 2.0 cm down the incline from its equilibrium position and is released from rest.

Find the speed of each mass when the 5.00 kg object is 21.0 cm above the floor.

speed = ………………………. m s-1 [2]

(e) In the axes below, sketch the speed-time graphs of the 8.50 kg mass for the cases of when the slope is smooth and when it is rough. Label your graphs S and R respectively. [2]

speed

time

7

[Turn over


3 A potentiometer is used to measure the small e.m.f. produced by a thermocouple, as shown in

Fig. 3.1. The metre wire has a resistance of 5 . The thermocouple has an e.m.f. of 6.00 mV

and an internal resistance 1 . The balance length is found to be 0.500 m.

Fig.3.1

(a) Moveable jockey J can be connected to any point along XY.

When contact J is connected to end Y, a current flow through the thermocouple. In Fig. 3.1, indicate using an arrow the direction of this current in the thermocouple. [1]

(b) Given that the balance length is found to be 0.500 m, calculate the potential difference across the metre wire.

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

(c) Calculate the value of resistance R.

resistance R = ………………………. [2]

(d) A resistor of 2 is now connected across the terminals of the thermocouple of e.m.f. 6.00 mV, calculate the new balance length. new balance length = ………………………. m [3]

8


4 An X-ray spectrum is shown in Fig. 4.1.

Fig. 4.1

(a) Explain why there is a minimum wavelength for the emitted X-rays.

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

(b) Explain why the series of peaks in Fig. 4.1 are called the characteristic X-ray spectrum.

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

(c) A characteristic X-ray wavelength using a copper target is 1.54 x 10-10 m.

Calculate the energy change giving rise to this wavelength.

energy change = ………………………. J [2]

9

[Turn over


Section B

Answer two questions in this section

5 (a) The word ‘field’ is used in connection with electrostatics and gravitation.

(i) With reference to the above, explain what is meant by a field of force.

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

(ii) An electrostatic field may be produced by a small charge and a gravitational field by a small mass.

Explain clearly

1. one way in which these fields behave similarly, and, 2. one way in which these fields behave differently.

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

(b) Fig. 5.1 shows some equipotential lines around Mars. The mass of Mars is 6.4 x 1023 kg and the radius of Mars is 3.4 x106 m.

Fig. 5.1

10


(i) Define gravitational field strength at a point.

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

(ii) Explain how Fig 5.1 shows that the gravitational field strength decreases as the distance from the surface of the Mars increases. .……………………………………………….……………………………………………….……… .……………………………………………….……………………………………………….……… ……………………………………………………………..……….…………………………….. [2]

(iii) A spacecraft at point X drops a satellite, of mass 90 kg, from rest onto the surface of Mars. 1. State and explain whether the mass gains or losses gravitational potential energy as it falls freely from point X to point Y. .……………………………………………….……………………………………………….……… .……………………………………………….……………………………………………….……… ……………………………………………………………..……….…………………………….. [2]

2. Calculate the change in gravitational potential energy as the satellite falls freely from point X to point Y.

change in gravitational potential energy = ………………………. J [2]

3. Hence, or otherwise, calculate the velocity of the satellite when it reaches point Y. velocity = ………………………. m s-1 [2]

11

[Turn over


(c) Fig. 5.2 below shows the variation of the gravitational potential with distance r from its

centre, of the planet Pluto, which has a radius of 1150 km.

Fig 5.2

(i) On Fig. 5.2, draw a tangent to the graph at r = 2500 km, and hence determine the magnitude of the gravitational field strength at this location.

gravitational field strength = ………………………. N kg-1 [3]

12


(ii) The term escape velocity refers to the lowest velocity which a body must have in

order to escape the gravitational attraction of a particular planet or other object. Use the graph of Fig. 5.2 to determine the escape velocity for an object at the surface of planet Pluto.

escape velocity = ………………………. m s-1 [2]

(iii) 1. Helium-4 may be assumed to be an ideal gas.

Calculate the temperature of Helium-4 gas at which the r.m.s. speed of its atoms is equal to the escape velocity of Pluto.

temperature = ………………………. K [2]

2. Hence suggest, with a reason, whether helium-4 is found on the surface of Pluto.

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

13

[Turn over


6 (a) This part of the question is about the feasibility of using pressurised air to propel a vehicle.

(i) A cylinder contains 0.10 m3 of air at a pressure of 50 x 105 N m-2 at temperature 290 K. Molar mass of air is 0.030 kg mol-1.

1. Show that there are about 210 moles of air in the cylinder. [2] 2. Calculate the mass of air in the cylinder.

mass = ………………………. kg [2]

(ii) To obtain an estimate of the energy stored in the pressurised gas, consider the gas escaping into the atmosphere through a nozzle until the pressure in the cylinder has fallen to atmospheric pressure (1.0 x 105 N m-2). It can be assumed that the temperature of the gas remains constant in the process, while the pressure and volume varies as shown in Fig. 6.1.

Fig. 6.1

Volume / m3

Pressure /

105 Nm-2

14


1. Using Fig. 6.1, estimate the energy released as the air expands into the

atmosphere.

energy released = ………………………. J [3] 2. In reality, the air cools as it expands. Explain whether this means that the useful energy released is more or less than that calculated in a(ii)1, as the air expands into the atmosphere.

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

(iii) It is proposed to utilise this energy to propel a vehicle

1. The aerodynamic drag force on the vehicle is 44 N, when travelling at 10 ms-1.

Calculate the power required to propel the vehicle at this steady speed. power = ………………………. W [2] 2. Calculate the maximum time the vehicle could travel at this steady speed on just one cylinder of pressurised air.

maximum travel time = ………………………. hrs [2]

15

[Turn over


(iv) To increase the energy available from the pressurised air, it is proposed to

increase the initial pressure in the cylinder from 50 atmospheres to 300 atmospheres.

Suggest a possible disadvantage of this idea.

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

(b) Pressure of an ideal gas, derived from the kinetic theory, is given by the equation

.

(i) State meanings of the symbols N, m and <c2>. .……………………………………………….……………………………………………….……… .……………………………………………….……………………………………………….……… ……………………………………………………………..……….…………………………….. [1]

(ii) Using the expression given in (b)(i) and the ideal gas equation, derive an expression which shows that the mean-square speed of a gas molecule is directly proportional to the thermodynamic temperature of the gas. Hence, calculate the

root mean squared speed of oxygen molecules at a temperature of 27 C. (Assuming oxygen behaves ideally, and mass of one mole of oxygen molecules is 32 g.)

root mean squared speed = ………………………. m s-1 [3]

(iii) Calculate the internal energy of a mole of oxygen at this temperature.

internal energy = ………………………. J [2]

16


7 (a) A system consisting of two metal rods of same material and of length L = 1.500 m but of

different masses m = 0.90 kg and M = 1.00 kg, are connected by a smooth non-conducting cord of negligible mass. The system is hung over a smooth wooden support as shown in Fig. 7.1(a) and Fig. 7.1(b). A uniform magnetic field B is directed perpendicular to the rods and into the plane of the paper.

The ends of the smaller rod, A and B are connected to an accumulator. When a current flows through the rod, the system is in equilibrium as shown in Fig. 7.1(b).

(i) Define magnetic field strength. .……………………………………………….……………………………………………….……… .……………………………………………….……………………………………………….……… ……………………………………………………………..……….…………………………….. [2]

(ii) In Fig 7.1(a), draw an arrow to indicate the direction of the current in the smaller rod in order for the system to be in equilibrium. [1]

(iii) In the space below, draw a free body diagram for the smaller rod m. Label all the forces clearly. [2]

(iv) Calculate the magnetic force that keeps the system in equilibrium.

magnetic force = ………………………. N [2]

Fig. 7.1(a) Front view Fig. 7.1(b) Side view

17

[Turn over


(v) If a current of magnitude 1.3 A flows in the small rod m, calculate the magnetic flux

density B when the rod is in equilibrium.

magnetic flux density B = ………………………. T [2]

(b) Two coils A and B are placed in a vertical line as shown in Fig. 7.2. Coil A is connected in series with a cell and a switch. A milli-voltmeter is connected across terminals of coil B.

Fig. 7.2

(i) On Fig. 7.2, draw an arrow inside coil A to indicate the direction of the magnetic field in coil A when the switch is turned on. [1]

(ii) 1. State Faraday’s law of electromagnetic induction. .……………………………………………….……………………………………………….……… ……………………………………………………………..……….…………………………….. [1]

2. Explain why, when current in coil A is switched on, the milli-voltmeter indicates an induced e.m.f. for a short period of time.

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

(iii) 1. In Fig. 7.2, indicate using an arrow inside coil B, the direction of the magnetic field due to the induced current in coil B. [1]

18


2. State Lenz’s law, and hence explain direction as chosen in (b)(iii)1.

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

(c) Another coil of 500 turns of fine wire, each of area 4.0 x 10-4 m2 is placed with its plane normal to a magnetic field. The ends of the coil are connected together. The magnitude of the magnetic flux density varies with time as shown in Fig. 7.3.

Fig. 7.3

(i) Determine the magnitude of the e.m.f. induced in the coil during the first 3 ms. magnitude of induced e.m.f. = ………………………. V [2]

(ii) In Fig. 7.4, sketch a graph to show how the induced e.m.f. varies with time over the 6 ms interval shown in Fig. 7.3. Indicate numerical values where applicable in your graph. [2]

Fig. 7.4

END OF PAPER



2014 Preliminary Examination II Pre-university 3

H2 Physics 9646/03

Paper 3 Longer Structured Questions

MARKSCHEME



READ THESE INSTRUCTIONS FIRST Write your name, class and admission number in the spaces 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, and 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.


Section A

1

2

3

4

Section B

5

6

7

Total

2


Section A Answer all the questions in this section.

12

1 A toy car with a rocket engine moves along a horizontal track, as shown in Fig. 1.1.

Fig. 1.1

The rocket engine produces a constant forward force of 4.6 N. The car loses mass continuously as exhaust gases are produced by the rocket.

(a) Use momentum considerations to explain why the rocket produces a forward force on the car.

By principle of conservation of momentum, total momentum of the car-gas system is conserved i.e. sum of momentum of car-gas system before ejecting gas is equal to sum of momentum of the car-gas system after ejecting the gases

On exhaust gases, repel force = force by car on gas = rate of change of momentum = v(∆mass) / ∆time)

On car, forward Force = force by gas on car = rate of change of momentum = m(∆velocity) / ∆time)

[3]

B1 B1 B1

(b) The variation with time t of the speed v of the car is shown in Fig. 1.2.

Fig. 1.2

At time t = 2.0 s, the mass of the car is 440 g.

3

[Turn over

(i) For the time t = 2.0 s,

1. use Fig. 1.2 to determine the acceleration of the car,

tangent at t = 2.0 s is drawn

calculation of gradient done correctly

acceleration a = 2.7 m s-2 (acceptable range 2.4 to 3.1)

acceleration = ………………………. m s-2 [2]

C1 A1

2. use your answer in (i) 1. to determine the magnitude of the resistive force acting on the car.

Fforward – Fresistive = ma

Fresistive = Fforward – ma = 4.6 – (0.440 x 2.7)

= 3.4 N

force = ………………………. N [2]

C1 A1 ecf on 1.

(ii) Explain how it can be deduced that the resistive forces acting on the car increases with increase of speed.

From Fig 1.2, as speed of car increases, acceleration of car (given by gradient of graph) decreases

Since a constant forward force acts on the car which experiences smaller acceleration as it moves at higher speeds, the resistive forces acting on the car must be increasing.

[2]

B1 B1

(c) The toy car is now re-fuelled and then rotated so that it is pointing upwards. It is suggested that the rocket engine produces sufficient force to propel the car vertically.

By considering the acceleration of the car at time t = 0 in Fig. 1.2, comment on this suggestion.

To move car vertically, rocket engine must produce force that is bigger than weight of car to move it against gravitational pull of Earth

At t = 0, acceleration of car is ~ 8.0 ms-2, which is less than g = 9.81 ms-2 (or shown by a similar comparison of forces on car)

Hence the rocket engine will not be able to propel the car vertically [3]

B1 B1 B1

4


2 A 8.50 kg mass is connected to a 5.00 kg mass by a light inextensible string that passes

over a frictionless pulley. The 5.00 kg mass is connected to a light spring of spring constant k that is equal to 200 N m-1.

At the equilibrium position, the spring is stretched by an amount e and the 5.00 kg mass is 20.0 cm above the floor as shown in Fig. 2.1. The smooth incline plane makes an angle of

40 to the horizontal. It can be assumed that the tension in the string remains constant throughout.

Fig. 2.1

(a) Draw a free body diagram of the 5.00 kg mass when it is in its equilibrium position. Label all the forces clearly in your diagram. [3]

Max score = 3 -1 mark for each mistake

(b) The 8.50 kg mass is now given a slight displacement, x, down the slope.

By considering the forces now acting on the 5.00 kg mass and using F=ma, show that the acceleration of the 5.00 kg mass is given by the expression

a = - 40 x. [3] At equilibrium T = ke + mg With the displacement x,

M1 M1 M1 A0

Forces must be clearly labelled

5

[Turn over

(c) (i) Using your answer in part (b), prove that the motion of the 5.00 kg mass is simple harmonic.

a = - 40 x is similar in form to defining equation of SHM a = -2x

in the sense that acceleration of the mass is proportional to its displacement, and

its acceleration is opposite in direction to its displacement ( as denoted by the negative sign)

Hence the mass is moving in SHM [2]

B1 B1

(ii) Hence show that the period of the oscillating mass is given by the expression

√

[2]

M1 M1 A0

(d) The 8.50 kg mass is pulled 2.0 cm down the incline from its equilibrium position and is released from rest.

Find the speed of each mass when the 5.00 kg object is 21.0 cm above the floor.

speed = ………………………. m s-1 [2]

C1 A1

(e) Sketch, using the same axes below, the speed-time graphs of the 8.50 kg mass for the case of when the incline plane is smooth and when it is rough. Label your graphs S and R respectively. [2]

B1 – correct shapes, same period B1 – R has smaller amplitude (show decreasing amplitude)

6


3 A potentiometer is used to measure the small e.m.f. produced by a thermocouple, as

shown in Fig. 3.1. The metre wire has a resistance of 5 . The thermocouple has an e.m.f.

of 6.00 mV and an internal resistance 1 . The balance length is found to be 0.500 m.

Fig.3.1

(b) Moveable jockey J can be connected to any point along XY.

When contact J is connected to end Y, a current flow through the thermocouple. In Fig. 3.1, indicate using an arrow the direction of this current in the thermocouple. [1]

B1

(a) Given that the balance length is found to be 0.500 m, calculate the potential difference across the metre wire.

p.d. across 0.500 m wire = 6 mV By ratio, p.d. across metre wire = 1/0.5 x 6 mV = 12 mV

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

C1 A1

(b) Calculate the value of resistance R. In the upper loop, p.d. across wire :

( )

( )

R = 828

resistance R = ………………………. [2]

C1 A1

(c) A resistor of 2 is now connected across the terminals of the thermocouple of e.m.f. 6.00 mV, calculate the new balance length.

Terminal potential across thermocouple = 2/(2+1)x 6 mV = 4 mV P.d. across metre wire = 12 mV By ratio, new balance length L ,

L = 0.33 m

new balance length = ………………………. m [3]

C1 C1 A1

(b)

7

[Turn over

4 An X-ray spectrum is shown in Fig. 4.1.

Fig. 4.1

6

(a) Explain why there is a minimum wavelength for the emitted X-rays.

When the bombarding electrons interact with the target metal atoms, they can lose any amount of their initial kinetic energy due to the braking effect of the positive charges of the metal atom nuclei. If the electron loses all its energy in the interaction, a photon of EM radiation is produced with maximum energy, which corresponding gives the minimum wavelength in the Bremsstrahlung spectrum. [2]

B1 B1

(b) Explain why the series of peaks in Fig. 4.1 are called the characteristic X-ray spectrum.

The characteristic peaks are produced when the bombarding electrons knock out electrons of the metal atoms, creating vacancies which an atomic electron at a higher energy level can then transit into, and in the transition gives out photons of energy equal to the differences between the 2 energy levels. The energies of these photons are thus dependent on the type of metal atoms, and are characteristic of the atomic structure of the atoms. [2]

B1 B1

(c) A characteristic X-ray wavelength using a copper target is 1.54 x 10-10 m.

Calculate the energy change giving rise to this wavelength.

= 1.29 x 10-15 J

energy change = ………………………. J [2]

C1 A1

8


Section B

Answer two questions in this section

5 (a) The word ‘field’ is used in connection with electrostatics and gravitation.

(i) With reference to the above, explain what is meant by a field of force.

A region of space in which a force is experience by a body having a mass (for

gravitational field), or charge (for electric field). [1]

B1

(ii) An electrostatic field may be produced by a small charge and a gravitational field by a small mass.

Explain clearly

1. one way in which these fields behave similarly, and, 2. one way in which these fields behave differently.

Difference: The direction of the force on a mass is always along the gravitational field lines The direction of the force on a charge is along the electric field lines if the charge is positive, and in the opposite direction if the charge is negative [2]

Either or of each B1 B1

(b) Fig. 5.1 shows some equipotential lines around Mars. The mass of Mars is 6.4 x 1023 kg and the radius of Mars is 3.4 x106 m.

Fig. 5.1

(i) Define gravitational field strength at a point. Gravitational field strength at a point is the gravitational force per unit mass placed at that point in the field. [1]

9

[Turn over

(ii) Explain how Fig 5.1 shows that the gravitational field strength decreases as the distance from the surface of the Mars increases. Magnitude of field strength is given by potential gradient, which is illustrated by the closeness of the equipotential lines, and as the equipotential lines are more widely spaced out in Fig 5.1 as distance increases away from surface of Mars, it indicates that the gravitational field strength is weaker. [2]

(iii) A spacecraft at point X drops a satellite, of mass 90 kg, from rest onto the surface of Mars.

1. State and explain whether the mass gains or losses gravitational potential energy as it falls freely from point X to point Y.

The mass loses GPE as it falls from X to Y, as there is work done by the field force and it gains KE in the process

[2]

A1 B1

2. Calculate the change in gravitational potential energy as the satellite falls freely from point X to point Y.

( )[ ( )] = - 180 x 106 J change in gravitational potential energy = ………………………. J [2]

M1 A1

3. Hence, or otherwise, calculate the velocity of the satellite when it reaches point Y. Gain in KE of satellite when dropped from rest at X and moved to Y = lose in GPE of satellite in moving from X to Y

180 x 106

v = 2000 ms-1

velocity = ………………………. m s-1 [2]

M1 A1

(c) Fig. 5.2 below shows the variation of the gravitational potential with distance r from its centre, of planet Pluto, which has a radius of 1150 km.

Fig 5.2

10


(i) On Fig. 5.2, draw a tangent to the graph at r = 2500 km, and hence determine the

magnitude of the gravitational field strength at this location.

Tangent drawn correctly

Magnitude of Gravitational field strength = Gradient =

[ ( )

[ ] = 133

gravitational field strength = ………………………. N kg-1 [3]

M1 M1 A1

(ii) Use the graph of Fig. 5.2 to determine the escape velocity for an object at the surface of Pluto.

Loss in KE of object as it moves away from surface = gain in GPE

½ mv2 – 0 = 0 – (m ∆) ,

where ∆ = 0 – ( 0.77 106 J kg1)

Or,

(Ep + Ek)initial = (Ep + Ek)

2

2

10 0

2

2

m mv

v

At the surface of the planet, = 0.77 106 J kg1

v = 1240 m s1

escape velocity = ………………………. m s-1 [2]

M1 A1

(iii) 1. Helium-4 may be assumed to be an ideal gas.

Calculate the temperature of Helium-4 gas at which the r.m.s. speed of its atoms is equal to the escape velocity of Pluto.

Rms speed of a helium atom, √ √

√

( )( )

= 1240

T = 247 K

Or, 1/2 m <c2> = 3/2kT ,

m = mass of one helium atom = 4u

temperature = ………………………. K [2]

2. Hence suggest, with a reason, whether helium-4 is found on the surface of Pluto. Helium-4 is possibly found at surface of Pluto as temperature of Pluto is colder than 247 K ( as the furthest planet from Sun), and so the helium atoms will not have rms speeds high enough to escape its gravitational field. [1]

M1 A1 B1

11

[Turn over

6 (a) This part of the question is about the feasibility of using pressurised air to propel a vehicle.

(i) A cylinder contains 0.10 m3 of air at a pressure of 50 x 105 N m-2 at temperature 290 K. Molar mass of air is 0.030 kg mol-1.

1. Show that there are about 210 moles of air in the cylinder. [2]

( )( )

( )( )

M1 A1

2. Calculate the mass of air in the cylinder.

( )( ) = 6.22 kg

mass = ………………………. kg [2]

M1 A1

(ii) To obtain an estimate of the energy stored in the pressurised gas, consider the gas escaping into the atmosphere through a nozzle until the pressure in the cylinder has fallen to atmospheric pressure (1.0 x 105 N m-2). It can be assumed that the temperature of the gas remains constant in the process, while the pressure and volume varies as shown in Fig. 6.1.

Fig. 6.1

Volume / m3

Pressure /

105 Nm-2

12


1. Using Fig. 6.1, estimate the energy released as the air expands into the

atmosphere. [2]

Use of the method of counting squares under the graph 5 small square x 5 small square = 0.5 m3 x 5x105 N m-2 = 250 x 103J range = 2.80 x 106 J (2.50 to 3.0 acceptable)

M1 M1 A1

2. In reality, the air cools as it expands. Explain whether this means that the useful energy released is more or less than calculated in a(ii)1, as the air expands into the atmosphere.

Energy released will be less,

as when the air cools, pressure will be lower, as area under the graph in Fig 6.1 gets smaller too, and so does the energy released. [2]

B1 B1

(iii) It is proposed to utilise this energy to propel a vehicle.

1. The aerodynamic drag force on the vehicle is 44 N, when travelling at 10 ms-1. Calculate the power required to propel the vehicle at this steady speed.

P = Fv = 44 x 10

= 440 W

power = ………………………. W [2]

M1 A1

2. Calculate the maximum time the vehicle could travel at this steady speed on just one cylinder of pressurised air

Time = Energy / Power = 2.8 x 106 / (440 x 60 x 60 ) = 1.77 hours

(ecf on a (ii) 1 )

maximum travel time = ………………………. hrs [2]

C1 A1

(iv) To increase the energy available from the pressurised air, it is proposed to increase the initial pressure in the cylinder from 50 atmospheres to 300 atmospheres.

Suggest a possible disadvantage of this idea.

The cylinder needs to be stronger to withstand the higher pressure, and thus also gets heavier (lower cost effectiveness).

[1]

B1

(b) Pressure of an ideal gas, derived from the kinetic theory, is given by the equation

.

(i) State meanings of the symbols N, m and <c2>.

N is the total number of gas molecules, m is the mass of each molecule, <c2> is the mean-square speed of the gas molecules. [1]

B1

13

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(ii) Using the expression given in (b)(i) and the ideal gas equation, derive an expression which shows that the mean-square speed of a gas molecule is directly proportional to the thermodynamic temperature of the gas. Hence, calculate the root mean square

speed of oxygen molecules at a temperature of 27 C. (Assuming oxygen behaves ideally, and mass of one mole of oxygen molecules is 32 g.)

root mean square speed = ………………………. m s-1 [3]

(iii) Calculate the internal energy of a mole of oxygen at this temperature.

internal energy = ………………………. J [2]

M1 – correct expression derived M1 – correct substitution of T and mass A1

M1 A1

14


7 (a) A system consisting of two metal rods of same material and of length L = 1.500 m but of

different masses m = 0.90 kg and M = 1.00 kg, are connected by a smooth non-conducting cord of negligible mass. The system is hung over a smooth wooden support as shown in Fig. 7.1(a) and Fig. 7.1(b). A uniform magnetic field B is directed perpendicular to the rods and into the plane of the paper.

The ends of the smaller rod, A and B are connected to an accumulator. When a current flows through the rod, the system is in equilibrium as shown in Fig. 7.1(b).

(i) Define magnetic field strength.

(Also known as magnetic flux density)

Magnetic flux density B is defined as the force per unit length per unit current on a straight conductor placed perpendicularly to the magnetic field.

[2] (-1 mark for each missed key word)

B2

(ii) In Fig 7.1(a), draw an arrow to indicate the direction of the current in the smaller rod in order for the system to be in equilibrium. [1]

(iii) Draw a free body diagram for the smaller rod m. Label all the forces clearly. [2]

3 vectors drawn on rod m, Tension, Weight and Magnetic force (Or 4 vectors drawn, 2 x tension, weight and magnetic force) B1

Magnetic force vector is shortest B1

Fig. 7.1(a) Front view Fig. 7.1(b) Side view

Tension

Weight

Magnetic force

(ii) current in small rod such that mag force is downwards

(for equilibrium) B1

15

[Turn over

(iv) Calculate the magnetic force that keeps the system in equilibrium. Magnetic force = (1.00)(9.81) – (0.90)(9.81)

= 0.98 N

magnetic force = ………………………. N [2]

M1 A1

(v) If a current of magnitude 1.3 A flows in rod m, calculate the magnetic flux density B when the rod is in equilibrium.

BIL = 0.98 B(1.3)(1.5) = 0.98 B = 0.50 T

magnetic flux density B = ………………………. T [2]

M1 A1

(b) Two coils A and B are placed in a vertical line as shown in Fig. 7.2. Coil A is connected in series with a battery and a switch S. A milli-voltmeter is connected across terminals of coil B.

Fig. 7.2

(i) On Fig. 7.2, draw an arrow inside coil A to indicate the direction of the magnetic field in coil A when the switch is turned on. [1]

(ii) 1. State Faraday’s law of electromagnetic induction.

Faraday’s law of electromagnetic induction states that the magnitude of the induced e.m.f. is directly proportional to the rate of change of the magnetic flux-linkage through the circuit.

[1]

B1

2. Explain why, when current in coil A is switched on, the milli-voltmeter indicates an induced e.m.f. for a short period of time.

At the instant when switch is closed, current increases in coil A and so does the magnetic flux in coil A. This increasing magnetic flux in A gives rise to an increasing flux-linkage in coil B. By Faraday’s law, an e.m.f. is induced in B, indicated in the voltmeter. After a short time, current in A reaches its steady value, and so magnetic flux in A also stabilised. There is not further change in flux-linkage in coil B, and so no more e.m.f. induced, and the voltmeter reading drops to zero. [2]

B1 B1

(iii) 1. In Fig. 7.2, indicate using an arrow inside coil B, the direction of the magnetic field due to the induced current in coil B. [1]

(i) B1

(iii)1. B1

16


2. State Lenz’s law, and hence explain direction as chosen in (iii)1.

Lenz’s law states that the induced current produced in the conductor flows in a direction so as to oppose the change that is producing it.

By Lenz’ law, the current induced in coil B will be created such that it opposes the strengthening downwards magnetic field in coil A, and so the induced magnetic field in coil B will point upwards.

B1 B1

(c) Another coil of 500 turns of fine wire, each of area 4.0 x 10-4 m2 is placed with its plane normal to a magnetic field. The ends of the coil are connected together. The magnitude of the magnetic flux density varies with time as show in Fig. 7.3.

Fig. 7.3

(i) Determine the magnitude of the e.m.f. induced in the coil during the first 3 ms.

magnitude of induced e.m.f. = ………………………. V [2]

M1 A1

(ii) Sketch a graph in Fig. 7.4 to show how the induced e.m.f. varies with time over the 6 ms internal shown in Fig. 7.3. Indicate numerical values where applicable in your graph. [2]

Fig. 7.4

END OF PAPER

B1 – correct shape wrt timings B1 – correct Y-axis values indicated

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