MergedFile - Weeblyscore-in-chemistry.weebly.com/uploads/4/8/7/1/48719755/...Its final velocity before hitting the ground is 15 m s-1 at an angle of 20o from the ground. What is the

© DHS 2015 9646/Prelim/01/15 [Turn over

DUNMAN HIGH SCHOOL Preliminary Examinations Year 6 Higher 2

PHYSICS Paper 1 Multiple Choice

9646/01

September 2015

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, class and index number on the Answer Sheet in the spaces provided unless this has been

done for you.

DO NOT WRITE IN ANY BARCODES.

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 ducted for a wrong answer.

Any rough working should be done in this booklet.

The use of an approved scientific calculator is expected, where appropriate.

This document consists of 21 printed pages and 1 blank page.

CANDIDATE NAME

CLASS INDEX NUMBER

2

© DHS 2015 9646/Prelim/01/15

Data

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

-1

permeability of free space, μ0 = 4π × 10-7

H m-1

permittivity of free space, 𝜖0 = 8.85 × 10-12

F m-1

= (1/(36π)) × 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

3


Formulae

uniformly accelerated motion, s = ut + 1

2 at 2

v 2 = u 2 + 2as

work done on/by a gas, 0B0B0B0B0B0B0B0B0B0B0B0B0BW = p V

hydrostatic pressure, 1B1B1B1B1B1B1B1B1B1B1B1B1Bp = 𝜌gh

gravitational potential, 𝜙 = GM

r

displacement of particle in s.h.m., x = x0 sin 𝜔t

velocity of particle in s.h.m., v = v0 cos 𝜔t

v = 𝜔√x0 2 - x 2

mean kinetic energy of a molecule

of an ideal gas, E =

3

2kT

resistors in series, R = R 1 + R 2 + …

resistors in parallel, 1/R = 1/R 1 + 1/R 2 + ...

electric potential, V = Q

4π𝜀0r

alternating current/voltage, x = x0 sin 𝜔t

transmission coefficient, T exp(−2kd)

where k = √8π2m(U − E)

h2

radioactive decay, x = x0 exp(𝜆t)

decay constant, 𝜆 = 0.693

t12

4

© DHS 2015 9646/Prelim/01/15

1 Four students each made a series of measurements of a 1.000 kg mass. The table shows the results obtained.

Which student obtained a set of readings that is accurate but not precise?

student reading / kg

1 2 3 4 5

A 1.000 1.000 1.002 1.001 1.002

B 1.011 0.999 1.001 0.989 0.995

C 1.012 1.013 1.012 1.014 1.014

D 0.993 0.987 1.002 1.000 0.983

2 The initial velocity of a projectile is 10 m s-1 parallel to the ground. Its final velocity before hitting the ground is 15 m s-1 at an angle of 20o from the ground.

What is the change in velocity? A 3.6 m s-1 B 5.1 m s-1 C 6.6 m s-1 D 14.9 m s-1

3 A clay pigeon is launched vertically into the air from the ground.

A marksman lies 170 m away from the launching device on level ground. Just as the clay pigeon reaches its maximum height 60 m, the marksman fires a bullet aimed directly at the clay pigeon. The bullet leaves the rifle with a speed of 300 m s-1.

At what time after the bullet is fired is the clay pigeon hit? Assume air resistance is negligible.

A 0.17 s B 0.57 s C 0.60 s D 1.66 s

5


4 The graph shows how the horizontal displacement of a fairground car changes with time for part of its journey.

A simple accelerometer is made by sandwiching a rubber ring between two glass plates and introducing some coloured water insider the ring. The accelerometer is attached to the side of the car.

Diagram B corresponds to point X on the graph.

Which diagram shows the angle of water surface in the accelerometer at point Y?

A B C D

5 A trailer of mass 400 kg is pulled by a car of mass 1200 kg. The diagram shows the horizontal

forces acting on the trailer.

What is the net force acting on the car?

A 400 N B 600 N C 1200 N D 1800 N

6

© DHS 2015 9646/Prelim/01/15

6 A lead pellet is shot vertically upwards into a clay block that is stationary at the moment of impact but is able to rise freely after impact.

The pellet hits the block with an initial velocity of 200 m s-1. It embeds itself in the block and does not emerge.

How high above its initial position will the block rise? A 5.1 m B 5.6 m C 10 m D 102 m

7 A submarine is in equilibrium in a fully submerged position.

What causes the upthrust on the submarine? A The air in the submarine is less dense than sea water.

B The submarine displaces its own volume of sea water. C There is a difference in water pressure acting on the top and bottom of the submarine.

D The sea water exerts a greater upward force on the submarine than the weight of the steel.

7


8 The diagram shows a model of an arm. A force applied by the biceps muscle can hold the arm in equilibrium while it supports a load.

Which statement is correct when the arm is in equilibrium in the position shown? A The force from the biceps is bigger when the load is moved nearer to the pivot. B The force from the biceps is equal to W1 + W2.

C The resultant force on the biceps is zero.

D The force at the pivot is zero.

8

© DHS 2015 9646/Prelim/01/15

9 A trolley is pushed with a force of 3.0 N for 2.0 s along a frictionless track.

The graph shows the velocity of the trolley against time.

How much work is done by the force on the trolley? A 1.5 J B 3.0 J C 6.0 J D 9.0 J 10 A wire consists of a 3.0 m length of metal X joined to a 1.0 m length of metal Y. The cross-

sectional area of the wire is uniform.

A load hung from the wire causes metal X to stretch by 1.5 mm and metal Y to stretch by 1.0 mm.

The same load is then hung from a second wire of the same cross-section, consisting of 1.0 m of metal X and 3.0 m of metal Y.

What is the total extension of this second wire? A 2.5 mm B 3.5 mm C 4.8 mm D 5.0 mm

9


11 A motor of power 10 W is used to lift a load of 20 N. The efficiency of the motor is 25 %. How long does it take to lift the load through a vertical distance of 0.50 m? A 0.040 s B 0.25 s C 4.0 s D 39 s 12 A car of mass m moving at a constant speed v passes over a humpback bridge of radius of

curvature r.

Given that the car remains in contact with the road, what is the net force R exerted by the car

on the road when it is at the top of the bridge?

A 2mv

R mgr

B R mg

C 2mv

Rr

D 2mv

R mgr

13 Two stars of masses M and 2M move in circular motion about their common centre of mass. Which of the following statements is true? A Both stars move with the same radius.

B Both stars move with the same speed.

C Both stars move with the same angular velocity. D Such a motion is not possible. 14 Two points P and Q are at distances X and 2X from the centre of a planet respectively. X is

greater than the radius of the planet. The gravitational potential at P is -800 kJ kg1.

What is the work done on the mass when a 2.0 kg mass is taken from P to Q? A -800 KJ B -400 KJ C +400 KJ D +800 KJ

10

© DHS 2015 9646/Prelim/01/15

15 A mass is suspended from a vertical spring. The mass is displaced upwards from its equilibrium position and released.

equilibrium position

Which pair of graphs shows how the displacement x and the acceleration a of the mass change

with time t ?

A B

x x t t

a a t t

C D

x x t t

a a t t

16 An object of mass 0.60 kg is held in place by two horizontal springs. It is displaced sideways

and undergoes simple harmonic motion of period 5.0 s. In each oscillation, it moves from left to right through a total distance of 0.30 m.

0.30 m

What is the total energy of the simple harmonic motion? A 4.3 × 10–3 J B 1.1 × 10–2 J C 1.7 × 10–2 J D 4.3 × 10–2 J

X

11


17 An immersion heater takes time t1 to raise the temperature of a mass M of liquid from T1 to its boiling point T2. In a further time t2, a mass m of the liquid is vaporised.

If the specific heat capacity of the liquid is c and heat losses to the atmosphere and to the

containing vessel are ignored, the specific latent heat of vaporisation is

A 2 1 2

1

( )Mc T T t

mt

B 2 1 2

1

( )mc T T t

Mt

C 1

2 1 2( )

mt

Mc T T t D 1 2

1

McT t

mt

18 A fixed mass of an ideal gas initially at room temperature and pressure is brought to half its

initial volume via the following processes independently:

(i) Compression at constant temperature. (ii) Compression at constant pressure. (iii) Adiabatic compression in a perfectly insulated chamber.

Which statement is correct?

A The work done on the gas is greatest for process (i). B The work done on the gas is greatest for process (ii).

C The work done on the gas is greatest for process (iii). D The work done on the gas is the same for all 3 processes as the final volume is the same.

12

© DHS 2015 9646/Prelim/01/15

19 The diagram shows a wave pulse at time t = 0. The pulse is travelling to the right at a speed of 4.0 m s-1.

Which graph correctly shows how the displacement of point X will vary over the next 4 seconds?

A B

D C

13


20 The solid line shows a diagram of a rope on which there is a progressive wave travelling to right. The dotted line shows the same rope 0.2 s later.

Which statement is correct? A The amplitude of the wave is about 0.2 m. B The frequency of the wave is about 0.6 Hz.

C The speed of the wave is about 30 m s-1.

D The wavelength of the portion shown is about 10 m.

21 Two radio telescopes separated by a distance d detected parallel waves of wavelength λ from

the same distant radio source.

What is the correct expression for the path difference between the waves received at the telescopes?

A d sin θ B d cos θ C sind

D

cosd

14

© DHS 2015 9646/Prelim/01/15

22 A strip of wet cardboard is fixed on the bottom of a microwave oven. The microwave oven is turned on for a short time. When the card is removed a pattern of dry spots is observed on the cardboard. This is because a standing wave is set up inside the oven.

The dry spots are measured and found to occur at 14 mm, 86 mm, 156 mm, 225 mm and 293 mm from the end of the strip.

From this information, what is the frequency of the microwaves?

A 2.2 GHz B 2.6 GHz C 4.3 GHz D 5.1 GHz 23 A constant electric field is to be maintained between two large parallel plates for which the

separation d can be varied.

Which graph shows how the potential difference V between the plates must be adjusted to

keep the field strength at a constant value?

24 An electron is projected at right angles to a uniform electric field E.

In the absence of other fields, in which direction is the electron deflected? A Into the plane of the paper B Out of the plane of the paper

C To the left D To the right

D C B A

15


25 Which statement describes the electrical potential difference between two points in a wire carrying a current?

A The force required to move a unit positive charge between the points.

B The ratio of the energy dissipated between the points to the current.

C The ratio of the power dissipated between the points to the current. D The ratio of the power dissipated between the points to the charge moved.

26 The diagram shows a model of an atom in which two electrons move round a nucleus in a

circular orbit. The electrons complete one full orbit in 1.0 x 10-15 s.

What is the current caused by the motion of the electrons in the orbit? A 1.6 x 10-34 A B 3.2 x 10-34 A C 1.6 x 10-4 A D 3.2 x 10-4 A

27 A cell of e.m.f. 2.0 V and negligible internal resistance is connected to the network of resistors

shown.

V1 is the potential difference between S and P. V2 is the potential difference between S and Q.

What is the value of V1 – V2?

A +0.50 V B +0.20 V C - 0.20 V D - 0.50 V

16

© DHS 2015 9646/Prelim/01/15

28 The diagram shows a circuit for measuring a small e.m.f. produced by a thermocouple.

There is zero current in the galvanometer when the variable resistor is set at 3.00 . What is the value of R?

A 195 B 495 C 995 D 1995 29 Three wires, X, Y and Z, each carrying the same current, are arranged in an equilateral triangle

as shown in the following diagram. The current in wires X and Y are directed out of the plane of the paper, while current in wire Z is directed into the plane of the paper.

The direction of magnetic field at the centre is

A B

C

D

X

Z Y

R

17


30 A horizontal power cable of length 2.0 m carries a steady current of 3.0 A into the plane of the diagram.

What is the force acting on the cable that is caused by the Earth’s magnetic field of flux density

4.0105 T, in a region where this field is at 65 to the horizontal?

A 100 N B 220 N C 240 N D 660 N 31 A rectangular coil moves in the direction parallel to a long straight current carrying conductor as

shown below.

The conductor carries a steady direct current. Which of the following statements is true?

A There is no induced current in the coil.

B The induced current flows clockwise in the coil.

C The magnitude of the induced current is proportional to 1

2.

D The magnitude of the induced current in the coil varies with the speed v at which the coil is

moving.

65

Earth’s magnetic field

I

v

long conductor with steady d.c.

rectangular

coil

18

© DHS 2015 9646/Prelim/01/15

32 In the following figure, a copper disc rotates uniformly between the pole-pieces of a powerful magnet (not shown in figure) in a clockwise direction. P and Q are metallic brushes making contact with the axle and the edge of the disc respectively.


A No current flows through R because P and Q are at the same horizontal level. B No current flows through R because the disc is rotating uniformly.

C A steady current flows from P, through R, to Q.

D Q is at a higher potential compared to P.

33 The diagram below shows a varying voltage signal.

What is the root mean square value of this signal?

A 1.65 mV B 1.77 mV C 2.38 mV D 2.54 mV

V / mV

t/s

2.0

3.0

0 1.0 2.0 3.0 4.0 5.0 6.0

P Q

R

rotation direction

magnetic field into the plane

of the paper

19


34 A resistive load R is connected across the secondary coil of a step-down transformer with turns ratio 100:1. When a sinusoidal source designed to supply a mean power of 400 W is connected across the primary coil, the current through the resistor is IS.

The transformer is now changed to one with turns ratio 50:1 and the load resistance is reduced to R/2. Assuming that the transformer is 100% efficient, and that the connecting wires have negligible resistance, what is the new current IR if it is supplied by the same 400 W source?

A 0.71 IS B 1.0 IS C 1.4 IS D 2.0 IS

35 The X-ray spectrum of a copper target is shown below.


A X-ray photons of energy 1.43 1015 J are produced mainly due to transitions of electrons.

B The positions of the peaks correspond to the energy levels of the copper atom.

C The smallest wavelength detected, 0.92 1010 m, is dependent on the target material.

D The metal target is struck by electrons with kinetic energy of 8100 eV.

Intensity

/ 1010 m 1.39 0.92

20

© DHS 2015 9646/Prelim/01/15

36 A photon of wavelength 555 nm is known to an accuracy of 0.01 nm.

What is the minimum uncertainty in the location of the photon?

A 5.3 10−24 m B 8.0 × 10−13 m C 2.5 10−3 m D 2.4 × 10−2 m

37 In a piece of n-type silicon semiconductor, A conduction is due to electrons only. B there is a net negative charge for the semiconductor. C the impurity element with which silicon is doped has fewer valence electrons than silicon. D the number of holes in the valence band is less than the number of electrons in the

conduction band at room temperature. 38 The diagram below is a representation of a p-n junction.

Which of the following statements is false?

A Group V ions can be found in region R.

B At room temperature, most electrons of the atoms in region S can gain enough energy to

jump into the conduction band. C The width of Q and R increases if region P and region S are connected to the lower and

higher potential terminals of a battery respectively. D Under forward-biased condition, holes flow from P to S, but electrons from S to P.

39 A stationary nucleus of mass number A undergoes radioactive decay and emits an alpha

particle. If the total energy released is E, what is the kinetic energy of the alpha particle?

A 4

EA

B 4A

EA

C 4

4E

A

D

4

AE

A

p-n junction p-type

n-type

P

Q

R

S

21


40 Radiation from a radioactive source enters an evacuated region in which there is a uniform magnetic field perpendicular to the plane of the diagram. This region is divided into two by a sheet of aluminium about 1 mm thick. The curved, horizontal path followed by the radiation is shown in the diagram below.

Which of the following correctly describes the type of radiation and its point of entry?

type of radiation point of entry

A alpha X

B alpha Y

C beta X

D beta Y

End of paper

22

© DHS 2015 9646/Prelim/01/15

Blank Page



PHYSICS Paper 2 Structured Questions Candidates answer on the Question Paper.

No Additional Materials are required.

9646/02

September 2015

1 hour 45 minutes


Write your class, index number and name on all the work you hand in.

Write in dark blue or black pen on both sides of the paper.

You may use a soft pencil for any diagrams, graphs or rough working.




Answer all questions.

At the end of the examination, fasten all your work securely together.

The number of marks is given in brackets [ ] at the end of each question or part

question.

For Examiner’s Use

1 7

2 6

3 9

4 9

5 8

6 6

7 15

8 12

Total 72


CANDIDATE NAME

CLASS INDEX NUMBER

2

© DHS 2015 9646/Prelim/02/15

Data


-1


H m-1


F m-1

= (1/(36π)) × 10-9

F m-1


C


J s


kg


kg


kg


mol-1


mol-1


J K-1


N m2

kg-2


3

© DHS 2015

9646/Prelim/02/15 [Turn over

Formulae


2 at 2

v 2 = u 2 + 2as

work done on/by a gas, 0B0B0B0B0B0BW = p V

hydrostatic pressure, 1B1B1B1B1B1Bp = 𝜌gh


r



v = 𝜔√x0 2 - x 2


of an ideal gas E =

3

2kT




4π𝜀0r




h2



t12

4

© DHS 2015 9646/Prelim/02/15

For Examiner’s

Use

1 A golf ball is hit from point A on the ground and moves through the air to point B. The path

of the ball is illustrated in Fig. 1.1.

The ground slopes downhill with constant gradient of angle 8.2° to the horizontal. The ball

has an initial velocity of 63 m s-1 at an angle of 14° to the horizontal. The acceleration due

to gravity is g and air resistance is ignored.

(a) State the acceleration, in terms of g, of the ball in the direction perpendicular to the

slope.

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

(b) Hence determine the time taken for the ball to travel from A to B.

time = ………………………………. s [2]

(c) Calculate the displacement from A to B.

displacement = ………………………………. m [2]

Fig. 1.1 (not to scale)

8.2°

5

© DHS 2015


For Examiner’s

Use

(d) Describe the difference between the displacement of the ball and the distance it travels

from A to B.

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

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

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

2 A 500 kg car is travelling at a constant speed of 14.0 m s-1 along a flat road that turns right

with a radius of 50.0 m as shown in Fig. 2.1.

(a) At the instant shown in Fig. 2.1, indicate and label all the forces acting on the car on

Fig. 2.2. [2]

Fig. 2.1

velocity into the

plane of page

r = 50.0 m

𝑣 = 14.0 m s-1

Top view Rear view

Rear view

Fig. 2.2

6

© DHS 2015 9646/Prelim/02/15

For Examiner’s

Use

(b) Determine the magnitude of the centripetal force required for the car to travel through

the turn.

force = ………………………………. N [2]

(c) A car travelling at a high speed could topple over while making a turn.

Use your answer in (a), state and explain whether a car will topple to the left or right

while turning right.

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

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

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

3 (a) One end of a string is attached to a wall. A student creates a single pulse in the string

that travels to the right as shown in Fig. 3.1.

(i) On Fig. 3.1, sketch the shape and size of the pulse after it has been reflected from

the wall. [1]

Fig. 3.1

7

© DHS 2015


For Examiner’s

Use

(ii) By reference to Newton’s third law, explain your sketch in (a)(i).

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

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

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

(b) The apparatus illustrated in Fig. 3.2 is used to demonstrate two source interference

using light.

Light of wavelength λ = 650 nm is incident normally on the double slit arrangement. The

interference fringes formed are viewed on a screen placed parallel to the plane of the

double slit with D = 1.2 m. The slit separation is 1.1 mm.

(i) Calculate the separation of the fringes.

separation = ………………………………. mm [2]


D = 1.2 m

screen

double

slit

a light

wavelength

λ = 650 nm

8

© DHS 2015 9646/Prelim/02/15

For Examiner’s

Use

(ii) State the effect, if any, on the separation and intensity of the fringes observed on

the screen when the following changes are made, separately, to the double slit

arrangement.

1. The width of each slit is increased but the slit separation remains constant.

..…………………………………………………………………………………………

..…………………………………………………………………………………………

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

2. Light is incident at a small angle to the normal of the plane of the double slit as shown in Fig. 3.3.

..…………………………………………………………………………………………

..…………………………………………………………………………………………

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


screen

double

slit

light

9

© DHS 2015


For Examiner’s

Use

4 A rectangular coil is rotating with a uniform angular velocity ω at 50 revolutions per second

in a uniform magnetic field of flux density 0.80 T. The number of turns and the cross

sectional area of the coil are 30 and 2.5 m2 respectively. The resistance of the resistor R is

40 Ω. The resistance of the rotating coil, connecting wires and slip rings are assumed to be

negligible. Fig. 4.1 shows the instant when the plane of the coil is in a horizontal position.

Throughout the rotation, the coil remains in the region of the uniform magnetic field.

(a) Explain why an e.m.f. is generated in the coil.

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

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

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

(b) On Fig. 4.1, draw arrows in the part of the circuit between the poles of the magnet to

indicate the direction of current. [1]

(c) Fig. 4.1 shows the position of the coil at time t = 0 s.

Write down an expression to show how the magnetic flux linkage, Φ in the coil changes

with time t.

Φ = …………………………… Wb [1]

Fig. 4.1

10

© DHS 2015 9646/Prelim/02/15

For Examiner’s

Use

(d) (i) Complete Fig. 4.2 to show the variation with time t of the magnetic flux linkage Φ in

the coil. [1]

(ii) Complete Fig. 4.3 to show the variation with time t of the e.m.f., induced in the

coil. [2]

(e) Calculate the mean power dissipated in the resistor R.

power = ………………………………. W [2]

Φ / Wb

t / s 0.01 0.02 0.03

Fig. 4.2

/ V

t / s 0.01 0.02 0.03

Fig. 4.3

11

© DHS 2015


For Examiner’s

Use

5 Fig. 5.1 below shows some of the possible energy levels of an electron orbiting inside a

particular atom. The lowest possible energy level is Level 1. The diagram below is not

drawn to scale.

(a) Explain the significance of the energy levels having negative values.

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

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

(b) (i) The electron makes a transition from level 2 to level 1. Calculate the frequency of

the emitted photon.

frequency = ………………………………. Hz [1]

(ii) State and explain whether photons with frequency calculated in (b)(i) would be

emitted if photons with energy of 4.80 eV are incident on the atoms at the ground

state.

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

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

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


(Ground state)

12

© DHS 2015 9646/Prelim/02/15

For Examiner’s

Use

(iii) The atoms in their ground states are bombarded by electrons with energy of

7.60 eV, resulting in emission of photons. On Fig. 5.1, draw all the possible

transitions that are associated with these emitted photons. [1]

(c) Determine the de Broglie wavelength of the electrons in (b)(iii).

= ………………………………. m [2]

6 Iodine-131 is a fission product from Uranium-235, and can be released in nuclear weapon

tests and nuclear accidents. When Uranium-235 nuclei are fissioned by slow moving

neutrons, the following reaction takes place:

I235 1 131 102 1

92 0 53 39 0U n Y 3 n

(a) The binding energy per nucleon of U-235, I-131 and Y-102 are 7.6 MeV, 8.5 MeV and

8.6 MeV respectively.

Calculate the energy (in joules) released by 1.0 kg of Uranium-235 in the nuclear

reaction.

energy = ………………………………. J [3]

13

© DHS 2015


For Examiner’s

Use

(b) (i) Iodine-131 further decays into the stable Xenon-131 in two steps, with gamma

decay following rapidly after beta decay:

I131 13153 54 Xe

131 13154 54Xe Xe

The rest masses of Iodine-131 and the stable Xenon-131 are 130.9061246 u and

130.9050824 u respectively and the mass of the -particle is taken as 0.0005486 u.

Calculate the maximum possible energy of the gamma ray photon.

energy = ………………………………. J [2]

(ii) Suggest a reason why gamma ray photon is usually emitted with an energy lower

than that calculated in (b)(i).

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

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

7 For thousands of years, Man has studied the night sky and some ancient buildings provide

evidence of careful and patient astronomical observations by people of many different

cultures. As instrumentation has improved, so has the precision with which astronomical

observations could be made. Between 1576 and 1597, Brahé made comprehensive

observations of planetary positions and, on his death, these records became available to

Kepler.

Kepler was able to interpret the observations and deduced three laws, one of which had a

great impact on later discoveries. He deduced that, for a circular orbit of a planet around the

Sun, if T is the period of rotation and r is the radius of the orbit, then

T2 r3

As a result of Kepler's work, Newton formulated the law of gravitation.

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Use

(a) (i) State Newton’s law of gravitation.

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

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

(ii) By considering the gravitational force on a planet, show that, for a circular orbit of

the planet around the Sun,

G M

rπT

322 4

where 𝐺 is the gravitational constant and 𝑀 is the mass of the Sun. [2]

(b) The planet Jupiter has a number of moons. Data for some of these moons are given in

the table below.

Moon Period

T / days

Orbital radius

r / 109 m lg (T / days) lg (r / m)

Sinope 758 23.7 2.88 10.37

Leda 239 11.1 ……………… ………………

Callisto 16.7 1.88 1.22 9.27

Lo 1.77 0.422 0.25 8.63

Metis 0.295 0.128 - 0.53 8.11

Fig. 7.1

(i) Complete Fig. 7.1 for the moon Leda. [1]

(ii) Fig. 7.2 is a graph of some of the data in Fig. 7.1.

15

© DHS 2015


For Examiner’s

Use

Fig. 7.2

On Fig. 7.2,

1. plot the point calculated in (b)(i). [1]

2. draw the line of best fit for all the points. [1]

lg (r / m)

lg (T / days)

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

8.0 8.5 9.0 9.5 10.0 10.5 11.0

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© DHS 2015 9646/Prelim/02/15

For Examiner’s

Use

(c) (i) Determine the gradient of the line drawn in (b)(ii)2.

gradient = ………………………………. [2]

(ii) Hence explain whether the data in Fig. 7.1 support the expression T2 r3.

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

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

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

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

(d) Observation shows that the moon Ganymede orbits planet Jupiter with a period of 7.16

days. Use the graph in Fig. 7.2 to estimate the orbital radius of Ganymede.

orbital radius = ………………………………. m [2]

(e) Explain whether the graph in Fig. 7.2 could be used to determine the orbital radius of a

moon of another planet (e.g. Saturn) if the orbital period of the moon is known.

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

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

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

17

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Use

8 A thin card is inserted between two separate iron cores. A coil is wound around one core as

shown in Fig. 8.1.

Fig. 8.1

A current in the coil may induce an e.m.f. in another coil wound on the other core. The

induced e.m.f. V depends on the thickness t of the card.

A student suggests that

0

tV V e

where 𝑉0 is the induced e.m.f. without card between the cores and 𝜎 is a constant.

Design a laboratory experiment to test the relationship between 𝑉 and 𝑡 and determine the

value of 𝜎. You should draw a diagram showing the arrangement of your equipment.

In your account you should pay particular attention to

(a) the procedure to be followed,

(b) the measurements to be taken,

(c) the control of variables,

(d) the analysis of the data,

(e) the safety precautions to be taken.

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© DHS 2015 9646/Prelim/02/15

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Use

Diagram

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19

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Use

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© DHS 2015 9646/Prelim/02/15

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Use

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………………………………………………………………………………………………………….. [12]



PHYSICS Paper 3 Longer Structured Questions Candidates answer on the Question Paper.

No Additional Materials are required.

9646/03

September 2015

2 hours


Write your class, index number and name on all the work you hand in.

Write in dark blue or black pen on both sides of the paper.

You may use a soft pencil for any diagrams, graphs or rough working.




Section A

Answer all questions.

Section B

Answer any two questions.

You are advised to spend about one hour on each section

At the end of the examination, fasten all your work securely together.

The number of marks is given in brackets [ ] at the end of each question

or part question.

For Examiner’s Use

Section A

1 6

2 10

3 10

4 6

5 8

Section B

6 20

7 20

8 20

Total 80


CANDIDATE NAME

CLASS INDEX NUMBER

2

© DHS 2015 9646/Prelim/03/15

Data


-1


H m-1


F m-1

= (1/(36π)) × 10-9

F m-1


C


J s


kg


kg


kg


mol-1


mol-1


J K-1


N m2

kg-2


3

© DHS 2015


Formulae


2 at 2

v 2 = u 2 + 2as

work done on/by a gas, 0B0B0B0B0B0B0B0B0B0B0B0B0BW = p V

hydrostatic pressure, 1B1B1B1B1B1B1B1B1B1B1B1B1Bp = 𝜌gh


r



v = 𝜔√x0 2 - x 2


of an ideal gas E =

3

2kT




4π𝜀0r




h2



t12

4

© DHS 2015 9646/Prelim/03/15

For Examiner’s

Use Section A

Answer all the questions in the spaces provided.

1 (a) Define, for a wave, what is meant by displacement. ………………………………………………………………………………………………......... ………………………………………………………………………………………………… [1]

(b) Fig. 1.1 shows the variation with time t of the displacement xA of wave A as it passes

through a point P.

Fig. 1.1

Fig. 1.2 shows the variation with time t of the displacement xB of wave B as it passes

through point P.

Fig. 1.2

(i) Calculate the frequency of the waves. frequency = ……………. Hz [1]

t / ms

xA / mm

xB / mm

t / ms

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For Examiner’s

Use (ii) State the phase difference between the waves. phase difference = ……………….. [1]

(iii) Calculate the amplitude of the resultant wave at P. amplitude = .………… mm [2]

(iv) State the minimum displacement of the resultant wave at P. minimum displacement = .………… mm [1]

2 (a) Distinguish between electric potential and electric potential energy.

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

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

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

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

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© DHS 2015 9646/Prelim/03/15

For Examiner’s

Use (b) A cable used for the transmission in an electrical distribution system has a circular

cross-section of radius 0.012 m. Fig. 2.1 is a full-scale drawing showing the

electric field surrounding the cable together with lines of equal potential at an

instant when the potential of the cable is +564000V.

Fig. 2.1 (to scale)

(i) State the relation between electric field strength and potential gradient.

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

(ii) Use Fig. 2.1 to estimate the potential gradient near the surface of the cable.

potential gradient = …………………. V m-1 [3]

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For Examiner’s

Use (iii) Explain why a cable of a larger radius, but at the same potential, will have a

smaller electric field at its surface.

……………………………………………………………………………………………….

……………………………………………………………………………………………….

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

(iv) On Fig. 2.2, sketch the electric field lines near a cable of square cross-section. [3]

Fig. 2.2

cable

8

© DHS 2015 9646/Prelim/03/15

For Examiner’s

Use 3 (a) A car headlamp is marked 12 V, 72 W. It is switched on for a 20 minute journey.

Calculate

(i) the current in the lamp,

current = ……………….. A [1]

(ii) the charge which passes through the lamp during the journey,

charge = ……………… C [1]

(iii) the energy supplied to the lamp during the journey,

energy = ………………… J [1]

(iv) the working resistance of the lamp.

resistance = …………….. Ω [1]

(b) Two of the headlamps referred to in part (a) are connected into the circuit shown in

Fig. 3.1, in which one source of e.m.f. (the generator of the car) is placed in parallel

with the car battery and the two lamps. Both lamps are on and are working normally.

.

Fig. 3.1

R

9

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For Examiner’s

Use

The battery has an e.m.f. of 12.0 V and negligible internal resistance. The generator

has an e.m.f. of 15.0 V and negligible internal resistance. The generator is in series

with a variable resistor R.

(i) The value of R is adjusted so that there is no current in the battery when the

lamps are on.

Calculate

1 . the current in the generator,

current = ……………… A [1]

2. the value of the resistance of R.

resistance of R = …………….Ω [2]

(ii) Calculate the current in the battery when both lamps are switched off, the value of

R remaining the same as in (i).

current = ………………… A [2]

(c) Suggest one advantage which the circuit, as shown in Fig. 3.1, has over a single

power source.

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

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

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

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Use 4 A charged particle of mass 2.66 10-23 g and charge –4.8 10-19 C is travelling with a

velocity of 2.38 105 m s-1 in a vacuum. It then enters a region of uniform magnetic field of

flux density 0.40 T as shown in Fig. 4.1. The magnetic field is normal to the path of the

charged particle and is out of the plane of the paper.

(a) Calculate the radius of the path of the particle in the magnetic field.

radius = …………... m [3]

(b) On Fig. 4.1 draw to scale the path of the particle as it passes through, and beyond, the

region of the magnetic field. [3]

path of charged particle Region of magnetic

field out of the plane of paper

Fig. 4.1

to scale

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For Examiner’s

Use 5 An isotope of Americium, 241

95 Am , undergoes spontaneous, random nuclear decay with a

half-life of 432.2 years.

(a) Explain the significance of the 432.2 years.

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

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

(b) Explain what is meant by a

(i) spontaneous decay,

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

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

(ii) random decay.

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

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

(c) Calculate the decay constant of 241

95 Am .

1decay constant ................................... s [1]

(d) Determine the activity of 1.00 gram of 241

95 Am .

activity ................................... Bq [3]

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© DHS 2015 9646/Prelim/03/15

For Examiner’s

Use Section B

Answer two questions from this Section in the spaces provided.

6 (a) The Earth may be assumed to be a uniform sphere of radius of 6370 km and mass of 5.98 x 1024 kg. An object of mass 1.00 kg is placed on the Equator. Calculate (i) the angular velocity of the object,

angular velocity = ………..………………. rad s−1 [1]

(ii) the speed of the object,

speed = ………..………………. m s−1 [1]

(iii) the centripetal acceleration of the object,

centripetal acceleration = ………..………………. m s−2 [1]

(iv) the gravitational force exerted on the object by the Earth.

gravitational force = ………..………………. N [2]

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Use (b) The object in (a) is suspended from a spring balance fixed to the ceiling of a laboratory,

as shown in Fig. 6.1. There are two forces acting on the object, namely the gravitational force FG by the Earth and the support force Fs by the spring.

(i) Draw a labelled force diagram to show the forces on the object. [2]

(ii) Using your answers to (a)(iii) and (iv), calculate the magnitude of Fs.

Fs = ………..………………. N [2] (c) Define gravitational potential at a point.

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

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

North

pole

Fig. 6.1

Axis of

rotation

Equator

object

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For Examiner’s

Use (d) The gravitational potential at distance r from point mass M is given by the expression

GM

r

where G is the gravitational constant.

Explain the significance of the negative sign in this expression.

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

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

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

(e) A spherical planet may be assumed to be an isolated point mass with its mass concentrated at its centre. A small mass m is moving near to, and normal to, the surface of the planet. The mass moves away from the planet through a short distance h.

Show that the change in gravitational potential energy EP of the mass is given by the expression

EP = mgh

where g is the acceleration of free fall. [4]

(f) The planet in (e) has mass M and diameter 6.8 x 103 km. The product GM for this planet

is 4.3 x 1013 N m2 kg−1. Calculate the escape speed of a body of mass 3.0 kg from the surface of the planet.

escape speed = ………..………………. m s−1 [2]

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Use (g) Give two reasons why the actual value to escape from the field of the planet is different

from that calculated in (f). …………………………………………………………………………………………………......

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

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

7 (a) Fig. 7.1 shows the variation with time t of displacement x of the bob for a particular

pendulum.

(i) Use information from Fig. 7.1 to determine the

1. amplitude,

amplitude = .......................... m [1]

2. frequency,

frequency = ........................... Hz [1]

3. maximum velocity of the bob.

maximum velocity = …………………. m s-1 [2]

x/cm

t/s 0

10

5

-5

-10

1.0 2.0 3.0 0

Fig. 7.1

16

© DHS 2015 9646/Prelim/03/15

For Examiner’s

Use (ii) The mass m of the pendulum bob is 20 g.

1. Sketch a labelled graph of the variation with time of the kinetic energy of the

pendulum bob. [2]

2. Calculate the maximum force exerted on the bob.

maximum force = ....................................... N [2]

3. On Fig. 7.2, sketch a graph to show the variation with time, t of the force F

exerted on the bob. [2]

F/N

t/s 0 1.0 2.0 3.0

Fig. 7.2

1.0 0 2.0 3.0 t/s

17

© DHS 2015


For Examiner’s

Use

(b) State what is meant by a

(i) free oscillation, ……………………………………………………………………………………………….. ………………………………………………………………………………………… [1] (ii) damped oscillation,

………………………………………………………………………………………………. ………………………………………………………………………………………… [1] (iii) forced oscillation.

………………………………………………………………………………………………. ………………………………………………………………………………………….. [1] (c) A car component of mass 0.0460 kg rattles at a resonant frequency of 35.5 Hz.

Fig. 7.3 shows how the amplitude of the oscillation varies with frequency. (i) Calculate the energy stored in the oscillation of the component when oscillating

1. at the resonant frequency,

energy = .............................................. J [3]

0

2

4

6

8

10

12

10 20 30 40 50 60 70 80 0

frequency/Hz

amplitude/mm

Fig. 7.3

18

© DHS 2015 9646/Prelim/03/15

For Examiner’s

Use 2. at a frequency of 20.0 Hz.

energy = .............................................. J [2] (ii) Draw on Fig. 7.3 to show how the amplitude of the oscillation varies with

frequency if the component is supported on a rubber mounting. [2]

8 (a) The variation with time t of temperature for 0.200 kg of a substance, initially solid, is shown in Fig. 8.1. The substance is heated at a uniform rate of 200 W in a copper container of negligible heat capacity. The room temperature is 25 oC.

(i) Define specific latent heat of fusion.

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

t / min 1

/ oC

2 3

30

40

20

10 4 0

Fig. 8.1

19

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For Examiner’s

Use (ii) Calculate the specific latent heat of fusion of the substance.

specific latent heat of fusion = ………………… J kg-1 [2] (iii) State and explain whether your calculation in (a)(ii) is an overestimate or

underestimate.

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

(b) In a diesel engine a fixed amount of gas can be considered to undergo a cycle of four

stages. The cycle is shown in Fig. 8.2.


The four stages are A B a compression with a rise in pressure and temperature from an initial

temperature of 300 K, B C an expansion at constant pressure while fuel is being burnt, C D a further expansion with a drop in both temperature and pressure, D A a return to the starting point.

Volume /10-5 m3

57.0

Pressure /105 Pa

A

B C

D

2.0

1.85

1.00

3.1 36.0

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© DHS 2015 9646/Prelim/03/15

For Examiner’s

Use Some numerical values of temperature, pressure and volume are given on Fig. 8.2.

(i) Using Fig. 8.2, determine the work done by the gas during the stages 1. B C,

work done = ……….J [1]

2. D A.

work done = ………...J [1]

(ii) Calculate the temperature of the gas at point B.

temperature = ………………… K [2]

(iii) Using your answers in (b)(i), complete Fig. 8.3 for the four stages of the cycle.

Stage of cycle heat supplied

to gas /J

work done

on gas /J

increase in internal

energy of the

system /J

A B 0 235

B C 246

C D 0 –333

D A

Fig. 8.3

[4]

21

© DHS 2015


For Examiner’s

Use (c)

Fig. 8.4

A thermally insulated container is divided into two sections by a thermally insulating and frictionless partition. The partition is initially held in place as shown in Fig. 8.4. X contains an ideal gas of volume 2.00 x 10-3 m3 and pressure 2.50 x 105 Pa at a temperature of 450 K. Y contains the same gas of volume 4.50 x 10 -3 m3 and pressure 1.50 x 105 Pa at a temperature of 300 K.

(i) Calculate the amount of gas, in moles, in X and Y separately.

amount of gas in X = …………… mol [1] amount of gas in Y = …………… mol [1]

(ii) The partition is now released and allowed to move towards the right to the

equilibrium position. Using the First Law of Thermodynamics, state and explain

how the temperature of the gas in X changes.

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

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

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

(iii) The partition is then removed so that gas in X and Y is allowed to mix. Given that

the internal energy of an ideal gas is 3

2nRT , calculate the final temperature of the

gas in the container.

temperature = ……………. K [3]

X Y

22

© DHS 2015 9646/Prelim/03/15

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Use Blank Page

Page 1 of 14

DHS Mark Scheme Syllabus

Year 6 Preliminary Examinations H2 Physics 2015 9646

Paper 1

Question Number

Key Question Number

Key

1 B 21 B

2 C 22 A

3 C 23 C

4 A 24 C

5 C 25 C

6 A 26 D

7 C 27 C

8 C 28 C

9 A 29 B

10 B 30 C

11 C 31 A

12 D 32 D

13 C 33 C

14 D 34 C

15 C 35 A

16 B 36 C

17 A 37 D

18 C 38 B

19 B 39 B

20 B 40 D

Page 2 of 14

Paper 2

1 (a) (+ or -) g cos(8.2°) A1 [1]

(b) s = ut + ½ at2 (apply to direction perpendicular to slope)

0 = 63sin(14°+8.2°) – ½ g cos(8.2°)t C1 t = 4.9 s A1 [2]

(c) s = ut + ½ at2 (apply to direction along slope) = 63cos(14°+8.2°)t + ½ g sin(8.2°)t2 C1 = 302 m = 300 m A1 [2]

(d) Distance is the actual path travelled. B1

Displacement is the straight line between A and B or minimum distance

between A and B. B1 [2]

2 (a) Correct normal forces and weight, length of normal forces = weight B1

Correct direction of frictional forces B1 [2]

(b) Centripetal force = mv2/r

= (500)(14.0)2/50.0 C1 = 1960 N A1 [2]

(c) As speed increases, the frictional forces increases (to provide a greater centripetal force).

Taking moment about CG of car, M1

the anticlockwise moment will increase and the car topples to the left. A1 [2]

3 (a) (i) Pulse of similar shape and inverted. B1 [1]

(ii) The string exerts an upward force on the wall, and M1

the wall exerts a downward force on the string by N3L, M1

creating an inverted pulse. A0 [2]

(b) (i) x =λD/a

= (650 x 10-9) (1.2) / (1.1 x 10-3) M1 = 0.71 mm A1 [2]

Weight

Friction 1 Friction 2

Normal 1 Normal 2

Page 3 of 14

(ii)1 Same separation B1

Bright areas brighter but dark areas no change B1 [2] (note: fewer fringes observed)

2 Same separation B1

Same brightness for fringes B1 [2] (note: locations of the bright fringes will change, depend on the phase difference between the waves coming from both slits)

4 (a) Cutting of magnetic flux of the magnet by sides of the rotating coil B1

Area perpendicular to the magnetic field changes as the coil rotates B1

Based on Faraday’s law, emf is induced. A0 [2]

(b)

A1 [1]

(c) Angular velocity, ω = 2πf = 2π( 50) = 100π

Magnetic Flux linkage, Φ = NBA sin ωt

= (30) (0.80) (2.5) sin (100πt)

= 60 sin (100πt) A1 [1]

(d) (i) A sine wave with period = 0.020 s and amplitude = 60 Wb B1

(ii) same frequency and amplitude = 6000π V = 19000 V B1

Correct phase with respect to fig. 4.2. B1 [3]

(e) Vrms = 6000π/√2 C1

Pmean = Vrms2 / R = 4.4 x 106 W A1 [2]

5 (a) Energy at infinity = 0 (energy increases at higher level) B1

Work done on electron to bring it to higher level/

work got out as electron move to lower level B1 [2]

(b) (i)

1 2

1915

34

10.38 ( 5.72) 4.66

4.66 1.6 101.12 10 Hz

6.63 10

hf E E

eV

f

A1

(ii) No, photons would not be emitted. A1

Energy of incident photon not equal

to energy difference between ground and any higher level. M1 [3]

Page 4 of 14

(iii)

B1

(c) λ = ℎ

𝑝=

ℎ

√2𝑚𝐸

=6.63×10−34

√2×9.11×10−31×7.60×1.6×10−19 C1

= 4.5 × 10−10 m A1 [2]

6 (a) Energy released when one U-235 atom fissions

= 131 x 8.5 + 102 x 8.6 – 235 x 7.6

= 204.7 MeV C1

No. of U-235 atoms in 1.0 kg of Uranium = 231.0

x 6.02 x 100.235

C1

Total energy released = 204.7 x 231.0

x 6.02 x 100.235

x 1.6 x 10-13

= 8.39 x 1013 J A1 [3]

(b) (i) E = (130.9061246 – 0.0005486 – 130.9050824) x 1.66 x 10-27 x (3.0 x 108)2 C1 = 7.37 x 10-14 J A1

(ii) Any one of the followings : B1 [3]

Emission of neutrino OR

KE of Xe and/or 𝛽 particle.

7 (a) (i) The mutual force of attraction between any two point masses is

directly proportional to the product of the masses and inversely

proportional to the square of their separation, and it acts along the

line joining the two point masses. B2

Page 5 of 14

(ii) Gravitational force provides the centripetal force M1

𝑮𝑴𝒎

𝒓𝟐 = 𝒎𝒓𝝎𝟐

𝑮𝑴𝒎

𝒓𝟐 = 𝒎𝒓 (𝟐𝝅

𝑻)

𝟐

M1

𝑻𝟐 =𝟒𝝅𝟐

𝑮𝑴𝒓𝟑 A0 [4]

(b) (i)

Moon

Period

T / days

Orbital radius

r / 109 m

log10 (T / days) log10 (r / m)

Sinope 758 23.7 2.88 10.37

Leda 239 11.1 2.38 10.05

Callisto 16.7 1.88 1.22 9.27

Lo 1.77 0.422 0.25 8.63

Metis 0.295 0.128 -0.53 8.11

Correct answers for Leda B1

(b) (ii) 1 plot to half square precision B1

(b) (ii) 2 Line of best fit plotted with balance points on both sides B1 [3]

(c) (i) gradient = Δ𝑦

Δ𝑥=

3.000−(−0.700)

10.450−8.000 M1

= 1.5 A1

(c) (ii) Since the graph in (b) (ii) is a straight line with gradient = 1.5,

10 10log 1.5logT r C , where C is a constant B1

10 10log 1.5logT cr (assume C = 1.5 log10 c where c is a constant)

Page 6 of 14

10 102log 3logT cr

32

10 10log logT cr B1

32 crT where c is a constant

Thus 2 3 T r

The data supports the relationship in (a) A0 [4]

Note: M is now the mass of the planet and the moons orbit the planet.

(d) Period of Ganymede, T = 7.16 days, so 10log 0.85T C1

From graph, 10 10log 0.85 log 9.025T r (read to half the smallest square)

Thus orbital radius of Ganymede r = 9.025 910 1.06 10 m A1 [2]

(e) Mass of planet is not the same. M1

The graph cannot be used. A1 [2]

Note: The gradient of the graph is expected to be the same (1.5) but the intercept with the

10log T axis will be different.

Page 7 of 14

8 Aim

Verify relationship between V and t

AND determine 𝜎

Defining problem

t independent / vary t

V dependent / measure V

Keep magnitude of peak current / rms current in primary coil constant P1

Method to keep current constant – rheostat (or variable power supply) and ammeter correctly

positioned in primary circuit and explained. Diagram and text required. P2

Measurement

Diagram showing two independent labelled coils wound on iron cores M1

AC power supply / Signal generator connected to one coil M2

Measure t (thickness of card) with vernier calipers / micrometer M3

Voltmeter / oscilloscope connected to other coil in a workable circuit M4

Data Analysis

ln(V) = ln(𝑉0) - σt Plot graph of ln(V) against t

Relationship valid if straight line obtained with y-intercept ln(𝑉0)

A1

𝝈 = - gradient A2

Safety

Prevent coil overheating

e.g. switch off when not in use

Prevent injury from hot coil

e.g. do not touch hot coil, use gloves

(“small currents” not allowed) S1

Additional detail

Use coil of many turns on secondary /large current in primary

to have measurable V D1

Use laminated cores or use insulated wires for turns. D2

Keep frequency of power supply constant or keep the number of turns

on each coil constant. D3

Measurement of V0 stating that no card is present. D4

Discuss of compression of card/ measure t when secured. D5

max 3 [12]

Page 8 of 14

Paper 3

1 (a) Distance (of a point on wave) from rest / equilibrium position. B1

(b) (i) f = 1/(6.0 x 10-3) = 170 Hz A1

(ii) π/2 rad or 90° A1

(iii) displacement of wave 1 is 90° out of phase with that of wave 2.

Use vector addition to find amplitude of resultant wave.

Or slide a ruler along the x-axis and determine the resultant displacement,

amplitude = max resultant displacement (at t = 0.9 to 1.1 s)

Or key in the resultant wave equation and use GC to obtain

amplitude = 2.4 mm

(iv) minimum displacement = -2.4 mm A1 [6]

2 (a) The work done per unit positive charge in moving a small test charge from infinity to that point. B1

work done in moving a charge from infinity to that point. B1 [2] (b) (i) Electric field strength is the negative of the potential gradient. B1

(ii)

6 1

Read potential values correctly B1

564000 550000 M1

0.003

4.7 x 10 V m A1

dV

dr

(iii) Larger radius, the charges on the cable are less concentrated.

Or same potential larger radius, so field lines more spaced out B1

(iv) Field lines are at right angle to conducting surface B1

Correct curvature of field lines B1

Field lines concentrating at the corners of the square cross section B1

Note : The shape of the cable would not make much difference to the pattern a long way

from the cable

3 (a) (i) 72

6.0 A A112

PI

V

(ii) (6.0)(1200) 7200 C A1Q It

1.4

2.0

Resultant = √(1.42+2.02) C1

= 2.4 mm A1

Page 9 of 14

(iii) 4(72)(1200) 8.64 10 J A1 E Pt

(iv) 12

2.0 A16.0

R V

I

(b) (i) 1. 6.0 6.0 12 AgI A1

2. 15 12 12 M1

0.25 A1

R R

R

V

(ii) 15 12 (0.25) M1

12 A A1

R

V I

I

(c) If the engine is not switched on, the car battery can still power the headlights. B1

4 Magnetic force provides centripetal force B1

Bqv sin 90o =r

mv 2

, θ = 900 since vB. M1

r = Bq

mv=

26 5

19

(2.66 10 )(2.38 x10 )

(0.40)(4.8 10 )

= 0.033 m = 3.3 cm A1

Page 10 of 14

Circular path turning anticlockwise in magnetic field region A2

Straight line tangential to circle upon exiting from magnetic field A1

5 (a) time for initial number of Americium-241 nuclei / activity

to reduce to one half of its initial value. B1

(b) (i) rate of decay is not affected by external or environmental factors (such as pressure, temperature) B1

(ii) nucleus has constant probability of decay per unit time B1 and the time of decay of a nucleus cannot be predicted. B1

Magnetic

Field

Region

drawn

to Scale

1: 1

Page 11 of 14

(c)

1/2

11 1

11 1

ln2

ln2

432.2 yrs

ln2

432.2 365 24 3600 s

5.086 10 s

5.09 10 s (3 s.f.) A1

t

(d) 241 grams of 241

95 Am contain 6.02 × 1023 atoms.

23 -1 21

-1

11 -1 21

11

Number of undecayed atoms,

1.00 g6.02 10 mol 2.4979 10 M1

241 g mol

M1

5.086 10 s 2.4979 10

1.27 10 Bq A1

N

A N

6 (a) (i) 5 12 2

7.27X10 rad.sT 24X60X60

A1

(ii) 5 3 1v r 7.27x10 x6370x10 463ms A1

(iii) 2 5 2 3 2 2a r (7.27x10 ) x6370x10 3.37x10 ms . A1

(iv)

11 24

G 2 3 2

GMm 6.67x10 x598x10 x1.00F M1

r (6370x10 )

9.83N A1

(b) (i)

(ii) F = ma

FG − Fs = ma

9.83 − Fs = 1.00 x 3.37x10-2 [C1]

Fs= 9.80 N [A1]

FG Fs

Correct Direction [B1]

Correct Magnitude [B1]

Page 12 of 14

(c) Work done in bringing unit mass from infinity (to the point) [B1]

(d) Gravitational force is (always) attractive [B1]

either Gravitational potential is taken as zero at infinity

or Work is done by mass/ work got out as it moves from infinity [B1]

(e) ∆EP = m ∆ [C1] = −GMm(1/r2 – 1/r1)

= GMm(1/r1 – 1/r2)

= GMm(r2 – r1) / (r1r2) [B1]

where r2 – r1 = h

if h is small, then r2 ≈ r1, then r1r2 = r2 [B1]

Since g = GM/r2 [B1]

∆EP = m gh [A0]

(f) Increase in GPE = Decrease in KE

GPEf – GPEi = KEi – KEf

0 – (−GMm/ri) = ½ mv2 – 0

GMm/ri = ½ mv2

GM/ri = ½ v2

(4.3 x 1013) / (3.4 x 106) = ½ v2 [C1]

v = 5.0 x 103 ms−1 [A1]

(Use of diameter instead of radius to give 3.6 x 103 ms−1 score 2 marks)

(g) any two: [B2]

Field of other planets

Atmospheric air resistance

Rotation of the planet

Planet is not a perfect sphere

Speed at infinity not zero.

7 (a) (i) 1. amplitude = 0.080 m A1

2. T = 2.0 s, f = 0.50 Hz A1

3. Max velocity = w xo = (2π/2)(0.080) M1

= 0.251 m s-1 A1 (ii) Correct values of maximum kinetic energy (6.32 x 10-4 J) and time B1

Correct shape for at least 3.5 s B1

Page 13 of 14

(iii) 1. F = m xo ω2

= 0.020 × 0.080 × (2π/2)2 M1 = 0.0158 N A1

2. Correct values of amplitude (0.0158N) and time B1

Correct shape for at least 3.5 s B1

(b) (i) an oscillation in which frictional forces are zero (negligible) OR

no change in amplitude OR

no loss in energy of the oscillation B1

(ii) a oscillation where the amplitude is decreasing OR

where frictional forces exist OR

where the energy of the oscillation is decreasing B1

(iii) an oscillation where the amplitude is maintained by energy being supplied by an

external source B1

(c) (i) 1. at the resonant frequency ω = 2πf = 2π × 35.5 = 223 rad s-1 M1

xo = 0.0114 m M1

E = ½m x02 ω2= ½ × 0.046 × 0.01142 × 2232 = 0.149 J A1

2. amplitude read correctly as 0.0026 m M1

giving energy as ½ × 0.046 × 0.00262 × (40π)2 = 0.00246 J A1

(ii) same starting point and lower graph peak B1

maximum amplitude at lower frequency within original shape B1

8 (a) (i) (thermal) energy/ heat required to convert unit mass of solid to liquid

without any change in temperature B1

(ii) Q = mL

200 × (1.5 × 60) = 0.200 × L M1

L = 9.00 × 104 J kg−1 A1

(iii) Some thermal energy is lost to surroundings M1

So calculated L is an overestimate of the actual value. A1

(b) (i) 1. W = p ∆V = 57.0 × 105 Pa x (3.1 – 2.0) × 10–5 m-3 = 62.7 J A1

2. W = 0. A1

Page 14 of 14

(ii) 5 5

5 5

M1

(57.0 10 )(2.0 10 )(300)950K A1

(1.00 10 )(36.0 10 )

A A B B

A B

B B AB

A A

P V P V

T T

P V TT

P V

Stage of

cycle

heat supplied

to gas /J

work done

on gas /J

increase in internal

energy of the

system /J

A B 0 235 235 [A]

B C 246 –63 [C] 183 [B]

C D 0 –333 –333 [A]

D A –85 [D] 0 [C] –85 [D]

A, B, C, D 1 mark each.

(c) (i)

5 3

5 3

2.50 10 2.00 10 8.31 450

0.134 mol A1

1.50 10 4.50 10 8.31 300

0.271 mol A1

X

X

Y

Y

n

n

n

n

(ii) Work done by gas in X and no heating B1

So internal energy and hence temperature decreases. B1

(iii)

0 M1

3 30

2 2

0.134 450 0.271 300 0 M1

350 K

X Y

X f X Y f Y

f f

f

U U

n R T T n R T T

T T

T

A1

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