physics core ahl and option

Physics Core(Topic 1-8) AHL(Topic 9-14)

Option E,F

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Contents Topic 1: Physics and physical measurement ..................................................................................................................... 3

Topic 2: Mechanics ......................................................................................................................................................... 13

Topic 3: Thermal physics ................................................................................................................................................ 35

Topic 4: Oscillations and waves ..................................................................................................................................... 46

Topic 5: Electric currents ................................................................................................................................................ 61

Topic 6: Fields and forces ............................................................................................................................................... 72

Topic 7: Atomic and nuclear physics .............................................................................................................................. 87

Topic 8: Energy, power and climate change ................................................................................................................. 101

Topic 9: Motion in fields .............................................................................................................................................. 118

Topic 10: Thermal physics ............................................................................................................................................ 132

Topic 11: Wave phenomena ......................................................................................................................................... 141

Topic 12: Electromagnetic induction ............................................................................................................................ 157

Topic 13: Quantum physics and nuclear physics .......................................................................................................... 168

Topic 14: Digital technology ........................................................................................................................................ 181

Option E: Astrophysics ................................................................................................................................................. 184

Option F: Communications ........................................................................................................................................... 215

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Topic 1: Physics and physical measurement

1. The order of magnitude of the weight of an apple is

A. 10–4 N.

B. 10–2 N.

C. 1 N.

D. 102 N.

2. The number of heartbeats of a person at rest in one hour, to the nearest order of magnitude is

A. 101.

B. 102.

C. 103.

D. 105.

3. The ratio is approximately equal to

A. 10–15.

B. 10–8.

C. 10–5.

D. 10–2.

4. The volume of the Earth is approximately 1012 km3 and the volume of a grain of sand is approximately 1 mm3. The order of magnitude of the number of grains of sand that can fit in the volume of the Earth is

A. 1012.

B. 1018.

C. 1024.

D. 1030.

5. Which one of the following contains three fundamental units?

A. Metre Kilogram Coulomb

B. Second Ampere Newton

C. Kilogram Ampere Kelvin

D. Kelvin Coulomb Second

atoman ofdiameter nucleus a ofdiameter

4

6. Which one of the following lists a fundamental unit and a derived unit?

A. ampere second

B. coulomb kilogram

C. coulomb newton

D. metre kilogram

7. Sub-multiples of units may be expressed using a prefix. Which one of the following lists the prefixes in decreasing order of magnitude?

A. centi- micro- milli- nano-

B. milli- centi- nano- micro-

C. centi- milli- micro- nano-

D. milli- micro- centi- nano-

8. The resistive force F acting on a sphere of radius r moving at speed v through a liquid is given by

F = cvr

where c is a constant. Which of the following is a correct unit for c?

A. N

B. N s–1

C. N m2 s–1

D. N m–2 s

9. Which one of the following measurements is stated correctly to two significant digits?

A. 0.006 m

B. 0.06 m

C. 600 m

D. 620 m

10. When a voltage V of 12.2 V is applied to a DC motor, the current I in the motor is 0.20 A. Which one of the following is the output power VI of the motor given to the correct appropriate number of significant digits?

A. 2 W B. 2.4 W

C. 2.40 W D. 2.44 W

5

11. An object has an acceleration of 2.0 m sí2. Which of the following gives the change in the speed of the object after 7.00 s to the correct number of significant digits?

A. 14 m sí1 B. 14.0 m sí1 C. 14.00 m sí1 D. 14.000 m sí1

12. The reading of a constant potential difference is made four times by a student. The readings are

1.176 V 1.178 V 1.177 V 1.176 V

The student averages these readings but does not take into account the zero error on the voltmeter. The average measurement of the potential difference is

A. precise and accurate.

B. precise but not accurate.

C. accurate but not precise.

D. not accurate and not precise.

13. An ammeter has a zero offset error. This fault will affect

A. neither the precision nor the accuracy of the readings.

B. only the precision of the readings.

C. only the accuracy of the readings.

D. both the precision and the accuracy of the readings.

14. Both random and systematic errors are present in the measurement of a particular quantity. What changes, if any, would repeated measurements of this quantity have on the random and systematic errors?

Random Systematic

A. reduced reduced

B. reduced unchanged

C. unchanged reduced

D. unchanged unchanged

15. A student measures a distance several times. The readings lie between 49.8 cm and 50.2 cm. This measurement is best recorded as

A. 49.8 r 0.2 cm.

B. 49.8 r 0.4 cm.

C. 50.0 r 0.2 cm.

D. 50.0 r 0.4 cm.

6

16. When a force F of (10.0 r 0.2) N is applied to a mass m of (2.0 r 0.1) kg, the percentage uncertainty attached to the value of the calculated acceleration is

A. 2%. B. 5%. C. 7%. D. 10%.

17. The radius of a loop is measured to be (10.0 ± 0.5) cm. Which of the following is the best estimate of the uncertainty in the calculated area of the loop?

A. 0.25% B. 5% C. 10% D. 25%

18. The density of a metal cube is given by the expression where M is the mass and V is the volume

of the cube. The percentage uncertainties in M and V are as shown below.

M 12�

V 4.0�

The percentage uncertainty in the calculated value of the density is

A. 3.0�. B. 8.0�. C. 16�. D. 48�.

19. The mass of a body is measured with an uncertainty of 2.0� and its volume with an uncertainty of 10�. What is the uncertainty in the density of the body?

A. 0.2� B. 5.0� C. 12� D. 20�

20. The sides of a cube are each of length 1.00 m. Each side is measured with an uncertainty of 2�. The absolute uncertainty in the volume of the cube is

A. 0.02 m3. B. 0.06 m3. C. 0.2 m3. D. 0.6 m3.

21. The volume V of a cylinder of height h and radius r is given by the expression

V �ʌr2h.

In a particular experiment, r is to be determined from measurements of V and h. The uncertainties in V and in h are as shown below.

V 7%

h 3%

The approximate uncertainty in r is

A. 10%.

B. 5%.

C. 4%.

D. 2%.

VMȡ

7

22. An object falls from rest with an acceleration g. The variation with time t of the displacement s of the object is given by

The uncertainty in the value of the time is ±6� and the uncertainty in the value of g is ±4�. The best estimate for the uncertainty of the position of the object is

A. 5�.

B. 8�.

C. 10�.

D. 16�.

23. Which of the following graphs shows the best-fit line for the plotted points?

24. The time period T of oscillation of a mass m suspended from a vertical spring is given by the expression

T ��ʌ�

where k is a constant.

Which one of the following plots will give rise to a straight-line graph?

A. T2 against m

B. against

C. T against m

D. against m

.21 2gts

A. y

0

B. y

00 x 0 x

C. y

0

D. y

00 x 0 x

km

T m

T

8

25. The variation with time t of the speed v of an object is given by the expression

v = u + at

where u and a are constants.

A graph of the variation with time t of speed v is plotted. Which one of the following correctly shows how the constants may be determined from this graph?

26. Which of the following contains three scalar quantities?

A. mass charge speed

B. density weight mass

C. speed weight charge

D. charge weight density

27. Which one of the following includes three vector quantities?

A. velocity weight field strength

B. weight mass field strength

C. velocity energy weight

D. mass energy field strength

A. v

0

– u

0 t gradient = a

B. v

0

– u

0 t

gradient = 1 a

C. v

0 0 u t gradient = a

D. v

0 0 u t

gradient = 1 a

9

28. The diagram below shows two vectors, x and y.

Which of the vectors below best represents the vector c that would satisfy the relation c = x + y?

29. The diagram below shows two vectors X and Y.

Which of the following best represents the vector Z = X – Y.

30. Two objects X and Y are moving away from the point P. The diagram below shows the velocity vectors of the two objects.

Which of the following velocity vectors best represents the velocity of object X relative to object Y?

x

y

A. B.

C. D.

X

Y

A.Z

B.Z

C.

Z

D.

Z

P

Velocity vector for object Y

Velocity vector for object X

A. B.

C. D.

10

31. The diagram below shows a boat that is about to cross a river in a direction perpendicular to the bank at a speed of 0.8 m s–1. The current flows at 0.6 m s–1 in the direction shown.

The magnitude of the displacement of the boat 5 seconds after leaving the bank is

A. 3 m.

B. 4 m.

C. 5 m.

D. 7 m. 32. Two forces of magnitudes 7 N and 5 N act at a point. Which one of the following is not a possible value

for the magnitude of the resultant force?

A. 1 N

B. 3 N

C. 5 N

D. 7 N

Short answer questions

1. Use the method of rectangular resolution to find the resultant of the following set of forces: 1) 200 N to

the right; 2) 300 N @ 600 above the horizontal to the right. 3) 100 N @ 450 above the horizontal to the left; 4) 200 N vertically downward.

y

x6045

F1

F2

F3

F4

0.8 ms

Boat

Bank

Bank

–1 –1 0.6 ms

11

2. Data analysis question.

Gillian carried out an experiment to investigate the craters formed when steel balls are dropped into sand. To try and find the relationship between the diameter of the crater and the energy of impact of steel balls of the same diameter, she dropped a steel ball from different heights h into sand and measured the resulting diameter d of the crater. The data are shown plotted below.

(a) The uncertainty in the measurement of d is ±0.40 cm; the uncertainty in h is too small to be shown. Draw error bars for the data point (0.2, 0.047) and the data point (2.0, 0.10).

(2)

(b) Draw a best-fit line for the data points. (2)

(c) The original hypothesis, made by Gillian, was that the diameter of the crater is directly proportional to the energy of impact of the steel balls. Explain why the data does not support this hypothesis.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(d) Since Gillian’s data did not support her hypothesis, she researched to find alternative hypotheses. She found that there are two theories used to predict a relationship between d and h. In order to find which theory is best supported by the data, she processed the data in two separate ways. The processed data are shown below.

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(i) Draw a line of best-fit on each graph. (2)

(ii) State and explain which theory is best supported by the student’s data.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 11 marks)

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Topic 2: Mechanics

1. Which one of the following is a correct definition of displacement?

A. Distance from a fixed point

B. Distance moved from a fixed point

C. Distance from a fixed point in a given direction

D. Distance moved in a given direction

2. The minute hand of a clock hung on a vertical wall has length L.

The minute hand is observed at the time shown above and then again, 30 minutes later.

What is the displacement of, and the distance moved by, the end P of the minute hand during this time interval?

displacement distance moved

A. 2L vertically downwards ʌL

B. 2L vertically upwards ʌL

C. 2L vertically downwards 2L

D. 2L vertically upwards 2L

3. A particle moves from a point P to a point Q in a time T. Which one of the following correctly defines both the average velocity and average acceleration of the particle?

Average velocity Average acceleration

A.

B.

C.

D.

LP

TP and Q ofnt displaceme

TP toQ from speedin change

TP and Q ofnt displaceme

TP toQ fromy in velocit change

TP and Qbetween distance

TP toQ from speedin change

TP and Qbetween distance

TP toQ fromy in velocit change

14

4. A ball is thrown vertically upwards from the ground. The graph shows the variation with time t of the vertical displacement d of the ball.

Which of the following gives the final displacement after time T and the average speed between time t = 0 m aand time t = T?

Displacement Average speed

A. 0 0

B. 0

C. 2D

D. 2D 0

5. The graph below shows the variation with time t of the displacement s of an object moving along a straight-line.

The best estimate of the instantaneous speed of the object at t = 2.0 s is

A. 0.0 ms–1. B. 0.2 ms–1. C. 5.0 ms–1. D. 10.0 ms–1.

6. Four cars W, X, Y and Z are on a straight road. The graph below shows the variation with time t of the distance s of each car from a fixed point.

Which car has the greatest speed?

A. W

B. X

C. Y

D. Z

TD2

TD2

s / m

20.0

0.00.0 2.0 4.0 t / s

s

t

X

Y

Z

W

00

15

7. The diagram below shows the variation with time t of the velocity v of an object.

The area between the line of the graph and the time-axis represents

A. the average velocity of the object.

B. the displacement of the object.

C. the impulse acting on the object.

D. the work done on the object.

8. An object has initial speed u and acceleration a. After travelling a distance s, its final speed is v. The quantities u, v, a and s are related by the expression

v2 = u2 + 2as.

Which of the following includes the two conditions necessary for the equation to apply?

A. a has constant direction u and v are in the same direction

B. a has constant direction a, u and v are in the same direction

C. a has constant magnitude a has constant direction

D. a has constant magnitude u and v are in the same direction

9. A stone X is thrown vertically upwards with speed v from the top of a building. At the same time, a second stone Y is thrown vertically downwards with the same speed v as shown.

Air resistance is negligible. Which one of the following statements is true about the speeds with which the stones hit the ground at the base of the building?

A. The speed of stone X is greater than that of stone Y.

B. The speed of stone Y is greater than that of stone X.

C. The speed of stone X is equal to that of stone Y.

D. Any statement about the speeds depends on the height of the building.

v

t0

0

Building

X Y

v

v

16

10. A body starting from rest moves along a straight-line under the action of a constant force. After travelling a distance d the speed of the body is v.

The speed of the body when it has travelled a distance from its initial

position is

A. B.

C.

D.

11. The graph shows the variation with time t of the velocity v of an object.

Which one of the following graphs best represents the variation with time t of the acceleration a of the object?

12. The graph shows the variation with time t of the acceleration a of an object.

The object is at rest at time t = 0.

Which of the following is the velocity of the object at time t = 6.0 s?

A. 0.50 m s–1.

B. 2.0 m s–1.

C. 36 m s–1.

D. 72 m s–1.

initial position

d

v

2d

.4v .

2v

.2

v .22

v

0 0

0 0

0 0

0 0

a a

a a

t t

t t

A. B.

C. D.

v

t

0

20

15

10

5

a / ms ?

0 1 2 3 4 5 6 7 8 9 10t / s

a/ms-2

17

13. The graph below shows the variation with time t of the acceleration a of a spaceship.

The spaceship is at rest at t = 0.

The shaded area represents

A. the distance travelled by the spaceship between t = 0 and t = T.

B. the speed of the spaceship at t = T.

C. the rate at which the speed of the spaceship changes between t = 0 and t = T.

D. the rate at which the acceleration changes between t = 0 and t = T.

14. A raindrop falling through air reaches a terminal velocity before hitting the ground. At terminal velocity, the frictional force on the raindrop is

A. zero.

B. less than the weight of the raindrop.

C. greater than the weight of the raindrop.

D. equal to the weight of the raindrop.

15. A steel sphere is dropped from rest in oil. Which of the following graphs best represents the variation with time of the speed of the sphere?

a

00 T t

A. speed

0

B. speed

00 time 0 time

C. speed

0

D. speed

00 time 0 time

18

16. A boat is moving in the direction shown with a speed of 5 m sí1 as measured by Nico who is at rest on the beach. Aziz walks along the deck of the boat in the direction shown with a speed of 2 m sí1 measured relative to the boat.

If velocity is measured as positive in the direction shown, the velocity of Nico relative to Aziz is

A. í��P�Ví1. B. í��P�Ví1. C. + 3 m sí1. D. + 7 m sí1.

17. A car is heading due East at a speed of 10 m sí1. A bird is flying due North at a speed of 4 m sí1, as shown below.

Which one of the following vectors represents the velocity of the bird relative to a person in the car?

18. An object is moving at constant velocity. Which one of the following quantities must have zero magnitude?

A. Weight of object

B. Momentum of object

C. Kinetic energy of object

D. Resultant force on object

A.

C.

B.

D.

positive direction

Aziz 5 m s –1

Nico

N

S

E W

Bird 10 m s

4 m s

Car –1

–1

19

19. A horse pulls a boat along a canal at constant speed in a straight-line as shown below.

The horse exerts a constant force F on the boat. The water exerts a constant drag force L and a constant force P on the boat. The directions of F, L and P are as shown. Which one of the following best represents a free-body diagram for the boat?

20. Three forces of magnitude F1 = 3.0 N, F2 = 4.0 N and F3 = 6.0 N act at a point. The point is in equilibrium. The magnitude of the resultant of F1 and F2 is

A. 1.0 N. B. 5.0 N. C. 6.0 N. D. 7.0 N.

21. The graph below shows the variation with load F of the length L of a spring.

Which of the following expressions gives the force per unit extension (the spring constant) of the spring?

A. B. C. D.

boatL

P F

horse

direction of travel

A. B.

C. D.

F

L

P

F

L

P

F

L

P

F

L

P

F

00 L L L

F

F

2

1

1 2

1

1

LF

2

2

LF � �

2

12

LFF � � �

12

12

LLFF

��

20

22. A block of mass m is pulled along a horizontal, frictionless surface by a force of magnitude F. The force makes an angle T with the vertical.

The magnitude of the acceleration of the block in the horizontal direction produced by the force F is

A. B. C. D.

23. A trolley of mass 1.5 kg is pulled along a horizontal table by a force of 5.0N.

The frictional force acting on the trolley is 0.50N.

The acceleration of the trolley is

A. 0.30 m s–2. B. 0.33 m s–2. C. 3.0 m s–2. D. 3.3 m s–2.

24. Two blocks having different masses slide down a frictionless slope.

Which of the following correctly compares the accelerating force acting on each block and also the accelerations of the blocks down the slope?

Accelerating force Acceleration

A. Equal Equal

B. Equal Different

C. Different Equal

D. Different Different

25. A light inextensible string has a mass attached to each end and passes over a frictionless pulley as shown.

The masses are of magnitudes M and m, where m < M. The acceleration of free fall is g. The downward acceleration of the mass M is

A. .

B. .

C. .

D. .

F

block

.mF .sin

mșF .cos

mșF .tan

mșF

force 5.0N

� �� mM

gmM��

� �M

gmM �

� �� mM

gmM��

� �mMMg�

pulley

string

mass m

mass M

21

26. A constant force of magnitude F acts on a body. The graph shows the variation with time t of the momentum p of the body.

The magnitude of the force F is

A. 1000 N. B. 200 N. C. 20 N. D. 0.05 N.

27. The velocity of a body of mass m changes by an amount 'v in a time 't. The impulse given to the body is equal to

A. m't. B. C. D. m'v.

28. A net force of magnitude F acts on a body for a time 't producing an impulse of magnitude Y. Which of the following is the magnitude of the rate of change of momentum of the body?

A. F B. F't C. Y D. Y't

29. The graph below shows the variation with time t of the magnitude of the net force F acting on a body moving along a straight-line.

The shaded area represents

A. the total work done by F.

B. the change in the kinetic energy of the body.

C. the change in the momentum of the body.

D. the change in the velocity of the body.

.tv'' .

tvm''

F

00 t

20

0 0

100

80

60

40

200

180

160

140

120

t / s

p /kg m s –1

1 2 3 4 5 6 7 8 9 10

22

30. Which of the following quantities are conserved in an inelastic collision between two bodies?

Total linear momentum of the bodies Total kinetic energy of the bodies

A. yes yes

B. yes no

C. no yes

D. no no

31. A ball of mass 2.0 kg falls vertically and hits the ground with speed 7.0 ms–1 as shown below.

before after

The ball leaves the ground with a vertical speed 3.0 ms–1.

The magnitude of the change in momentum of the ball is

A. zero. B. 8.0 Ns. C. 10 Ns. D. 20 Ns.

32. A ball of mass m, travelling in a direction at right angles to a vertical wall, strikes the wall with a speed v1. It rebounds at right angles to the wall with a speed v2��7KH�EDOO�LV�LQ�FRQWDFW�ZLWK�WKH�ZDOO�IRU�D�WLPH�ǻt. The magnitude of the force that the ball exerts on the wall is

A. .

B. m(v1 + v2�ǻt.

C. .

D. m(v1 – v2�ǻt.

33. The momentum of a system is conserved if

A. no external forces act on the system.

B. no friction forces act within the system.

C. no kinetic energy is lost or gained by the system.

D. the forces acting on the system are in equilibrium.

� �t

vvm'

� 21

� �t

vvm'

� 21

7.0 ms –1

–1 3.0 ms

23

34. Two spheres X and Y are moving towards each other along the same straight line with momenta of magnitude PX and PY respectively. The spheres collide and move off with momenta pX and pY respectively, as illustrated below.

Which one of the following is a correct statement of the law of conservation of momentum for this collision?

A. PX + PY = pX + pY

B. PX – PY = pX + pY

C. PX – PY = pX – pY

D. PX + PY = pX – pY

35. Two spheres of masses m1 and m2 are moving towards each other along the same straight-line with speeds v1 and v2 as shown.

The spheres collide. Which of the following gives the total change in linear momentum of the spheres as a result of the collision?

A. 0 B. m1v1 + m2v2 C. m1v1 í�m2v2 D. m2v2 í�m1v1

36. The diagram below shows a trolley of mass 4.0 kg moving on a frictionless horizontal table with a speed of 2.0 m s–1. It collides with a stationary trolley also of mass 4.0 kg.

Which of the following diagrams shows a possible outcome?

X XY Y

P pP px xY Y

Before collision After collision

positive direction

m 1 v1 v2 m2

4.0kg 4.0kg

2.0ms –1

24

37. A truck collides head on with a less massive car moving in the opposite direction to the truck. During the collision, the average force exerted by the truck on the car is FT and the average force exerted by the car on the truck is FC. Which one of the following statements is correct?

A. FT will always be greater in magnitude than FC.

B. FT will always be equal in magnitude to FC.

C. FT will be greater in magnitude than FC only when the speed of the car is less than the speed of the truck.

D. FT will be equal in magnitude to FC only when the speed of the truck is equal to the speed of the car.

38. A box of mass m is moved horizontally against a constant frictional force f through a distance s at constant speed v. The work done on the box is

A. 0. B. mgs. C. mv2. D. fs.

39. The point of action of a constant force F is displaced a distance d. The angle between the force and the direction of the displacement is ș, as shown below.

Which one of the following is the correct expression for the work done by the force?

A. Fd B. Fd sin ș C. Fd cos ș D. Fd tan ș

40. The graph below shows the variation with displacement d of the force F applied by a spring on a cart.

The work done by the force in moving the cart through a distance of 2 cm is

A. 10 × 10–2J.

B. 7 × 10–2J.

C. 5 × 10–2J.

D. 2.5 × 10–2J.

21

d

F

5

4

3

2

1

0 0 1 2 3

dm / 10 –2

F N /

25

41. A body of mass m and speed v has kinetic energy EK. A second body of mass moves at speed 2v.

The kinetic energy of this second body is

A. . B. EK. C. 2EK. D. 4EK.

42. An object of mass m1 has a kinetic energy K1. Another object of mass m2 has a kinetic energy K2. If the

momentum of both objects is the same, the ratio is equal to

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

43. The variation with time of the vertical speed of a ball falling in air is shown below.

During the time from 0 to T��WKH�EDOO�JDLQV�NLQHWLF�HQHUJ\�DQG�ORVHV�JUDYLWDWLRQDO�SRWHQWLDO�HQHUJ\�ǻEp. Which of the following statements is true?

A. ǻEp is equal to the gain in kinetic energy.

B. ǻEp is greater than the gain in kinetic energy.

C. ǻEp is equal to the work done against air resistance.

D. ǻEp is less than the work done against air resistance.

44. The diagram below represents energy transfers in an engine.

The efficiency of the engine is given by the expression

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

2m

2KE

2

1

KK

1

2

mm

2

1

mm

1

2

mm

2

1

mm

time

Speed

00 T

engineinput energy useful output energy

wasted energy

E E

E

IN

W

OUT

IN

W

EE

OUT

W

EE

IN

OUT

EE

W

OUT

EE

26

45. An engine takes in an amount E of thermal energy and, as a result, does an amount W of useful work. An amount H of thermal energy is ejected. The law of conservation of energy and the efficiency of the engine are given by which of the following?

Law of conservation of energy Efficiency

A. E = W + H W

B. E = W + H

C. E + H = W

D. E + H = W

46. An electric train develops a power of 1.0 MW when travelling at a constant speed of 50 ms–1. The net resistive force acting on the train is

A. 50 MN. B. 200 kN. C. 20 kN. D. 200 N.

47. Points P and Q are at distances R and 2R respectively from the centre X of a disc, as shown below.

The disc is rotating about an axis through X, normal to the plane of the disc. Point P has linear speed v and centripetal acceleration a. Which one of the following is correct for point Q?

Linear speed Centripetal acceleration

A. v a

B. v 2a

C. 2v 2a

D. 2v 4a

48. A particle P is moving in a circle with uniform speed. Which one of the following diagrams correctly shows the direction of the acceleration a and velocity v of the particle at one instant of time?

EW

HW

HEW–

Q

P 2R

R X

A. B.

C. D.

a

aa

a

v

v

v

v

P P

P P

27

49. The centripetal force that causes a car to go round a bend in the road is provided by

A. the force produced by the car engine acting on the wheels.

B. the friction between the tyres and the road.

C. the weight of the car.

D. the force exerted by the driver on the steering wheel.

50. The centripetal force F acting on a particle of mass m that is travelling with linear speed v along the arc of a circle of radius r is given by

A. F =

B. F = mv2r.

C. F = mr2v.

D. F =

51. A brick is placed on the surface of a flat horizontal disc as shown in the diagram below. The disc is rotating at constant speed about a vertical axis through its centre. The brick does not move relative to the disc.

Which of the diagrams below correctly represents the horizontal force or forces acting on the brick?

.2

mr

v

.2

rmv

28


52. Linear motion

(a) Define the term acceleration.

...................................................................................................................................

................................................................................................................................... (2)

(b) An object has an initial speed u and an acceleration a. After time t, its speed is v and it has moved through a distance s.

The motion of the object may be summarized by the equations

v = u + at,

s =

(i) State the assumption made in these equations about the acceleration a.

......................................................................................................................... (1)

(ii) Derive, using these equations, an expression for v in terms of u, s and a.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(c) The shutter speed of a camera is the time that the film is exposed to light. In order to determine the shutter speed of a camera, a metal ball is held at rest at the zero mark of a vertical scale, as shown below. The ball is released. The shutter of a camera is opened as the ball falls.

The photograph of the ball shows that the shutter opened as the ball reached the 196 cm mark on the scale and closed as it reached the 208 cm mark. Air resistance is negligible and the acceleration of free fall is 9.81 m s–2.

(i) Calculate the time for the ball to fall from rest to the 196 cm mark.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

� � .21 tuv�

0 cm

scale

196 cm

208 cm

camera

29

(ii) Determine the time for which the shutter was open. That is, the time for the ball to fall from the 196 cm mark to the 208 cm mark.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(Total 9 marks)

53. This question is about throwing a stone from a cliff.

Antonia stands at the edge of a vertical cliff and throws a stone vertically upwards.

The stone leaves Antonia’s hand with a speed v = 8.0ms–1.

The acceleration of free fall g is 10 m s–2 and all distance measurements are taken from the point where the stone leaves Antonia’s hand.

(a) Ignoring air resistance calculate

(i) the maximum height reached by the stone.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) the time taken by the stone to reach its maximum height.

...........................................................................................................................

........................................................................................................................... (1)

The time between the stone leaving Antonia’s hand and hitting the sea is 3.0 s.

(b) Determine the height of the cliff.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(Total 6 marks)

30

54. This question is about a balloon used to carry scientific equipment.

The diagram below represents a balloon just before take-off. The balloon’s basket is attached to the ground by two fixing ropes.

There is a force F vertically upwards of 2.15 × 103 N on the balloon. The total mass of the balloon and its basket is 1.95 × 102 kg.

(a) State the magnitude of the resultant force on the balloon when it is attached to the ground.

...................................................................................................................................

(1)

(b) Calculate the tension in either of the fixing ropes.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (3)

(c) The fixing ropes are released and the balloon accelerates upwards. Calculate the magnitude of this initial acceleration.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(d) The balloon reaches a terminal speed 10 seconds after take-off. The upward force F remains constant. Describe how the magnitude of air friction on the balloon varies during the first 10 seconds of its flight.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(Total 8 marks)

55. This question is about the collision between two railway trucks (carts).

(a) Define linear momentum.

.....................................................................................................................................

.....................................................................................................................................

balloon

basket

fixing rope fixing rope

50q 50q ground

31

In the diagram below, railway truck A is moving along a horizontal track. It collides with a stationary truck B and on collision, the two join together. Immediately before the collision, truck A is moving with speed 5.0 ms–1. Immediately after collision, the speed of the trucks is v.

The mass of truck A is 800 kg and the mass of truck B is 1200 kg.

(b) (i) Calculate the speed v immediately after the collision.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(ii) Calculate the total kinetic energy lost during the collision.

...........................................................................................................................

........................................................................................................................... (2)

(c) Suggest what has happened to the lost kinetic energy.

.....................................................................................................................................

..................................................................................................................................... (2)

(Total 8 marks)

56. This question is about estimating energy changes for an escalator (moving staircase).

The diagram below represents an escalator. People step on to it at point A and step off at point B.

B A

5.0 ms –1

Immediately before collision

Immediately after collision

B A

v

30m

40?A

B

32

(a) The escalator is 30 m long and makes an angle of 40° with the horizontal. At full capacity, 48 people step on at point A and step off at point B every minute.

(i) Calculate the potential energy gained by a person of weight 7.0 × 102 N in moving from A to B.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Estimate the energy supplied by the escalator motor to the people every minute when the escalator is working at full capacity.

...........................................................................................................................

...........................................................................................................................

(iii) State one assumption that you have made to obtain your answer to (ii).

...........................................................................................................................

...........................................................................................................................

The escalator is driven by an electric motor that has an efficiency of 70%.

(b) Using your answer to (a) (ii), calculate the minimum input power required by the motor to drive the escalator.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(Total 7 marks)

57. This question is about driving a metal bar into the ground.

Large metal bars can be driven into the ground using a heavy falling object.

33

In the situation shown, the object has a mass 2.0 × 103 kg and the metal bar has a mass of 400 kg.

The object strikes the bar at a speed of 6.0 m s–1. It comes to rest on the bar without bouncing. As a result of the collision, the bar is driven into the ground to a depth of 0.75 m.

(a) Determine the speed of the bar immediately after the object strikes it.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (4)

(b) Determine the average frictional force exerted by the ground on the bar.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(Total 7 marks) 58. This question is about the kinematics and dynamics of circular motion.

(a) A car goes round a curve in a road at constant speed. Explain why, although its speed is constant, it is accelerating.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

In the diagram below, a marble (small glass sphere) rolls down a track, the bottom part of which has been bent into a loop. The end A of the track, from which the marble is released, is at a height of 0.80 m above the ground. Point B is the lowest point and point C the highest point of the loop. The diameter of the loop is 0.35 m.

A

marble

ground B

C0.80 m

0.35 m

34

The mass of the marble is 0.050 kg. Friction forces and any gain in kinetic energy due to the rotating of the marble can be ignored. The acceleration due to gravity, g = 10 ms–2.

Consider the marble when it is at point C.

(b) (i) On the diagram opposite, draw an arrow to show the direction of the resultant force acting on the marble.

(ii) State the names of the two forces acting on the marble.

...........................................................................................................................

........................................................................................................................... (2)

(iii) Deduce that the speed of the marble is 3.0 ms–1.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(iv) Determine the resultant force acting on the marble and hence determine the reaction force of the track on the marble.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(Total 12 marks)

35

Topic 3: Thermal physics

1. Two different objects are in thermal contact with one another. The objects are at different temperatures. The temperatures of the two objects determine

A. the process by which thermal energy is transferred.

B. the heat capacity of each object.

C. the direction of transfer of thermal energy between the objects.

D. the amount of internal energy in each object.

2. The kelvin temperature of an object is a measure of

A. the total energy of the molecules of the object.

B. the total kinetic energy of the molecules of the object.

C. the maximum energy of the molecules of the object.

D. the average kinetic energy of the molecules of the object.

3. Two bodies are brought into thermal contact with each other. No thermal energy transfer takes place between the bodies. It may be deduced therefore, that the bodies must have the same

A. specific heat capacity. B. heat capacity.

C. temperature. D. internal energy.

4. Which two values of temperature are equivalent to the nearest degree when measured on the Kelvin and on the Celsius scales of temperature?

Kelvin scale Celsius scale

A. 40 313

B. 273 100

C. 313 40

D. 373 0

5. During an experiment, a solid is heated from 285 K to 298 K.

Which one of the following gives the rise in temperature, in deg C, and the final temperature, in °C, of the solid?

Rise in temperature in deg C Final temperature in °C

A. 13 571

B. 13 25

C. 286 571

D. 286 25

36

6. Which of the following is the internal energy of a system?

A. The total thermal energy gained by the system during melting and boiling.

B. The sum of the potential and the kinetic energies of the particles of the system.

C. The total external work done on the system during melting and boiling.

D. The change in the potential energy of the system that occurs during melting and boiling.

7. A container holds 20 g of neon (mass number 20) and also 8 g of helium (mass number 4).

What is the ratio helium of atoms ofnumber neon of atoms ofnumber ?

A. 0.4 B. 0.5 C. 2.0 D. 2.5

8. The molar mass of water is 18 g. The approximate number of water molecules in a glass of water is

A. 1022. B. 1025. C. 1028. D. 1031.

9. The heat capacity of a solid body is defined as

A. the thermal energy required to increase the body’s temperature by one degree.

B. the maximum thermal energy that must be supplied to melt the solid.

C. the total kinetic energy of the solid’s molecules.

D. the average kinetic energy of the solid’s molecules.

10. The specific heat capacity of an object is defined as the thermal energy required to raise the temperature of

A. the volume of the object by 1 K.

B. unit volume of the object by 1 K.

C. the mass of the object by 1 K.

D. unit mass of the object by 1 K.

11. The specific heat capacity of a metal block of mass m is determined by placing a heating coil in its centre, as shown in the diagram above.

The block is heated for time t DQG�WKH�PD[LPXP�WHPSHUDWXUH�FKDQJH�UHFRUGHG�LV�ǻș��The ammeter and voltmeter readings during the heating are I and V respectively.

The specific heat capacity is best calculated using which one of the following expressions?

A. c = T'm

VIt B. c = T'm

VI

C. c = VI

m T'

D. c = VIt

m T'

A

V

metal block

thermometer

heater

37

12. The specific heat capacity c of a solid block of mass m is determined by heating the block and measuring its temperature. The graph below shows the variation of the temperature T of the block with the thermal energy Q transferred to the block.

The gradient of the line is equal to

A. .mc

B. .cm

C. mc. D. .1mc

13. Some liquid is contained in a shallow dish that is open to the atmosphere. The rate of evaporation of the liquid does not depend on

A. the temperature of the liquid.

B. the temperature of the atmosphere.

C. the depth of the liquid.

D. the pressure of the atmosphere.

14. Which of the following correctly shows the changes, if any, in the potential energy and in the kinetic energy of the molecules of a solid as it melts?

Potential energy Kinetic energy

A. Decreases Increases

B. Increases Stays the same

C. Stays the same Decreases

D. Stays the same Stays the same

15. A substance changes from solid to liquid at its normal melting temperature. What change, if any, occurs in the average kinetic energy and the average potential energy of its molecules?

Average kinetic energy Average potential energy

A. constant constant

B. increases constant

C. increases decreases

D. constant increases

16. The specific latent heat of vaporization of a substance is greater than its specific latent heat of fusion because

A. boiling takes place at a higher temperature than melting.

B. thermal energy is required to raise the temperature from the melting point to the boiling point.

C. the volume of the substance decreases on freezing but increases when boiling.

D. the increase in potential energy of the molecules is greater on boiling than on melting.

T

0 Q

38

17. The specific latent heat of vaporization of a substance is the quantity of energy required to

A. raise the temperature of a unit mass of a substance by one degree Celsius.

B. convert a unit mass of liquid to vapour at constant temperature and pressure.

C. convert a unit mass of solid to vapour at constant temperature and pressure.

D. convert a unit mass of liquid to vapour at a temperature of 100°C and a pressure of one atmosphere.

18. A substance is heated at a constant rate. The sketch graph shows the variation with time t of the temperature T of the substance.

In which region or regions of the graph must there be more than one phase of the substance present?

A. WX and YZ

B. WX only

C. WX, XY and YZ

D. XY only

19. Which of the following is not an assumption on which the kinetic model of an ideal gas is based?

A. All molecules behave as if they are perfectly elastic spheres.

B. The mean-square speed of the molecules is proportional to the kelvin temperature.

C. Unless in contact, the forces between molecules are negligible.

D. The molecules are in continuous random motion.

20. A gas is contained in a cylinder fitted with a piston as shown below.

When the gas is compressed rapidly by the piston its temperature rises because the molecules of the gas

A. are squeezed closer together.

B. collide with each other more frequently.

C. collide with the walls of the container more frequently.

D. gain energy from the moving piston.

21. The temperature of an ideal gas is reduced. Which one of the following statements is true?

A. The molecules collide with the walls of the container less frequently.

B. The molecules collide with each other more frequently.

C. The time of contact between the molecules and the wall is reduced.

D. The time of contact between molecules is increased.

W

X Y

Z

t= 0

pistongas

39

22. When a gas in a cylinder is compressed at constant temperature by a piston, the pressure of the gas increases. Consider the following three statements.

I. The rate at which the molecules collide with the piston increases.

II. The average speed of the molecules increases.

III. The molecules collide with each other more often.

Which statement(s) correctly explain the increase in pressure?

A. I only

B. II only

C. I and II only

D. I and III only


23. This question is about an experiment to measure the temperature of a flame.

(a) Define heat (thermal) capacity.

.....................................................................................................................................

.....................................................................................................................................

A piece of metal is held in the flame of a Bunsen burner for several minutes. The metal is then quickly transferred to a known mass of water contained in a calorimeter.

Bunsen burner

flame

water calorimetercontainer

lagging (insulation)

The water into which the metal has been placed is stirred until it reaches a steady temperature.

(b) Explain why

(i) the metal is transferred as quickly as possible from the flame to the water;

...........................................................................................................................

...........................................................................................................................

(ii) the water is stirred.

...........................................................................................................................

...........................................................................................................................

40

The following data are available:

heat capacity of metal = 82.7 J K–1

heat capacity of the water in the calorimeter = 5.46 × 102 J K–1

heat capacity of the calorimeter = 54.6 J K–1

initial temperature of the water = 288 K

final temperature of the water = 353 K

(c) Assuming negligible energy losses in the processes involved, use the data to calculate the temperature T of the Bunsen flame.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (4)

(Total 7 marks)

24. This question is about the change of phase (state) of ice.

A quantity of crushed ice is removed from a freezer and placed in a calorimeter. Thermal energy is supplied to the ice at a constant rate. To ensure that all the ice is at the same temperature, it is continually stirred. The temperature of the contents of the calorimeter is recorded every 15 seconds.

The graph below shows the variation with time t of the temperature ș�of the contents of the calorimeter. (Uncertainties in the measured quantities are not shown.)

20

15

10

5

0

–5

–10

–15

–20 0 25 50 75 100 125 150 175 200

��q C

t / s

41

(a) On the graph above, mark with an X, the data point on the graph at which all the ice has just melted.

(b) Explain, with reference to the energy of the molecules, the constant temperature region of the graph.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

The mass of the ice is 0.25 kg and the specific heat capacity of water is 4200 J kg–1 K–1.

(c) Use these data and data from the graph to

(i) deduce that energy is supplied to the ice at the rate of about 530 W.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(ii) determine the specific heat capacity of ice.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(iii) determine the specific latent heat of fusion of ice.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 12 marks)

42

25. Gases and liquids

(a) Describe two differences, in terms of molecular structure, between a gas and a liquid.

1. .........................................................................................................................

.........................................................................................................................

2. .........................................................................................................................

......................................................................................................................... (2)

(b) The temperature of an ideal gas is a measure of the average kinetic energy of the molecules of the gas. Explain why the average kinetic energy is specified.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(c) Define heat (thermal) capacity.

...................................................................................................................................

...................................................................................................................................

(d) Water is heated at a constant rate in a container that has negligible heat capacity. The container is thermally insulated from the surroundings.

The sketch-graph below shows the variation with time of the temperature of the water.

temperature / C°

A B

200 420 time / s

The following data are available:

initial mass of water = 0.40 kg initial temp of water = 20�C rate at which water is heated = 300 W specific heat capacity of water = 4.2 × 103 J kg–1Cí1

(i) State the reason why the temperature is constant in the region AB.

.........................................................................................................................

.........................................................................................................................

43

(ii) Calculate the temperature T at which the water starts to boil.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (5)

(e) All the water is boiled away 3.0 × 103 s after it first starts to boil. Determine a value for the specific latent heat L of vaporization of water.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(Total 13 marks) 26. This question is about modelling the thermal processes involved when a person is running.

When running, a person generates thermal energy but maintains approximately constant temperature.

(a) Explain what thermal energy and temperature mean. Distinguish between the two concepts.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (4)

The following simple model may be used to estimate the rise in temperature of a runner assuming no thermal energy is lost.

A closed container holds 70 kg of water, representing the mass of the runner. The water is heated at a rate of 1200 W for 30 minutes. This represents the energy generation in the runner.

(b) (i) Show that the thermal energy generated by the heater is 2.2 × 106 J.

...........................................................................................................................

44

...........................................................................................................................

........................................................................................................................... (2)

(ii) Calculate the temperature rise of the water, assuming no energy losses from the water. The specific heat capacity of water is 4200 J kgí1 Kí1.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(c) The temperature rise calculated in (b) would be dangerous for the runner. Outline three mechanisms, other than evaporation, by which the container in the model would transfer energy to its surroundings.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (6)

A further process by which energy is lost from the runner is the evaporation of sweat.

(d) (i) Describe, in terms of molecular behaviour, why evaporation causes cooling.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

45

(ii) Percentage of generated energy lost by sweating: 50% Specific latent heat of vaporization of sweat: 2.26 × 106 J kgí1

Using the information above, and your answer to (b) (i), estimate the mass of sweat evaporated from the runner.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(iii) State and explain two factors that affect the rate of evaporation of sweat from the skin of the runner.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(Total 25 marks)

46

Topic 4: Oscillations and waves

1. For a system executing simple harmonic motion, the restoring force acting on the system is proportional to the

A. displacement of the system from equilibrium.

B. amplitude of oscillation.

C. elastic potential energy.

D. frequency of oscillation.

2. The graphs show how the acceleration a of four different particles varies with their displacement x. Which of the particles is executing simple harmonic motion?

3. The graph shows how the displacement varies with time for an object undergoing simple harmonic motion.

Which graph shows how the object’s acceleration a varies with time t?

Cinry

47

4. An object at the end of a spring oscillates vertically with simple harmonic motion. The graph shows the variation with time t of the displacement x. The amplitude is x0 and the period of oscillation is T.

Which of the following is the correct expression for the displacement x?

A. tT

x S2cos0� B. tT

x S2cos0 C. tT

x S2sin0� D. tT

x S2sin0

5. Which of the following is the correct expression for the maximum acceleration of the object?

A. 02 xTS B. 02

2 xTS C. 02

24 xTS D. 0

24 xTS

6. The graph below shows how the displacement x of a particle undergoing simple harmonic motion varies with time t. The motion is undamped.

Which of the following graphs correctly shows how the velocity v of the particle varies with t?

48

7. The graph shows measurements of the height h of sea level at different times t in the Bay of Fundy.

Which of the following gives the approximate amplitude and period of the tides?

Amplitude Period

A. 6.5 m 6 hours

B. 13 m 12 hours

C. 6.5 m 12 hours

D. 13 m 6 hours

8. A particle oscillates with simple harmonic motion with period T.

At time t = 0, the particle has its maximum displacement. Which graph shows the variation with time t of the kinetic energy Ek of the particle?

9. A mass on the end of a horizontal spring is displaced from its equilibrium position by a distance A and released. Its subsequent oscillations have total energy E and time period T.

An identical mass is attached to an identical spring. The maximum displacement is 2A. Assuming this spring obeys Hooke’s law, which of the following gives the correct time period and total energy?

New time period New energy

A. T 4E

B. T 2E

C. T2 4E

D. T2 2E

49

10. The graph below represents the variation with time of the displacement of an oscillating particle.

The motion of the object is

A. over damped.

B. critically damped.

C. lightly damped.

D. not damped.

11. The shock absorbers of a car, in good working condition, ensure that the vertical oscillations of the car are

A. undamped. B. lightly damped. C. moderately damped. D. critically damped.

12. During one complete oscillation, the amplitude of a damped harmonic motion changes from 1.5 cm to 0.30 cm. The total energy at the end of the oscillation is E2 and the total energy at the beginning of the

oscillation is E1. The ratio 1

2

EE

is

A. 51 . B.

251 . C. 5. D. 25.

13. A force that varies sinusoidally is applied to a system that is lightly damped. Which of the following must be true of the force for resonance to occur?

A. It must always be in anti-phase with the oscillations of the system.

B. Its direction must always be in the direction of motion of the oscillations of the system.

C. Its frequency must be equal to the frequency of oscillation of the system.

D. Its amplitude must be equal to the amplitude of oscillation of the system.

14. Light travels from air into glass as shown below.

The refractive index of the glass is

A. qq

80sin30sin B.

qq

30sin80sin C.

qq

10sin60sin D.

qq

60sin10sin

15. What is the best estimate for the refractive index of a medium in which light travels at a speed of 2.7 × 108 m s–1?

A. 0.9 B. 1.0 C. 1.1 D. 2.7

50

16. Plane wavefronts are incident on a boundary between two media labelled 1 and 2 in the diagram. The diagram of the wavefronts is drawn to scale.

The ratio of the refractive index of medium 2 to that of medium 1 is

A. 0.50. B. 0.67. C. 1.5 . D. 2.0.

17. Which of the following correctly describes the change, if any, in the speed, wavelength and frequency of a light wave as it passes from air into glass?

Speed Wavelength Frequency

A. decreases decreases unchanged

B. decreases unchanged decreases

C. unchanged increases decreases

D. increases increases unchanged

18. A transverse wave travels from left to right. The diagram below shows how, at a particular instant of time, the displacement of particles in the medium varies with position. Which arrow represents the direction of the velocity of the particle marked P?

51

19. The diagram below is a snapshot of wave fronts of circular waves emitted by a point source S at the surface of water. The source vibrates at a frequency f = 10.0 Hz.

The speed of the wave front is

A. 0.15 cm s–1.B. 1.5 cm s–1.C. 15 cm s–1.D. 30 cm s–1.

20. Which of the following electromagnetic waves has a frequency greater than that of visible light?

A. Ultraviolet B. Radio C. Microwaves D. Infrared

21. Two waves meet at a point. The waves have a path difference of 4O . The phase difference between the

waves is

A. 8ʌ rad. B.

4ʌ rad. C.

2ʌ rad. D. ʌ�UDG�

22. Two waves meet at a point in space. Which of the following properties always add together?

A. Displacement B. Amplitude C. Speed D. Frequency

23. The two graphs show the variation with time of the individual displacements of two waves as they pass through the same point.

The displacement of the resultant wave at the point at time T is equal to

A. x1 + x2.

B. x1 – x2 .

C. A1 + A2.

D. A1 – A2.

52

24. Two coherent point sources S1 and S2 emit spherical waves.

Which of the following best describes the intensity of the waves at P and Q?

P Q

A. maximum minimum

B. minimum maximum

C. maximum maximum

D. minimum minimum 25. An orchestra playing on boat X can be heard by tourists on boat Y, which is situated out of sight of boat

X around a headland.

The sound from X can be heard on Y due to

A. refraction. B. reflection. C. diffraction. D. transmission.

26. A water surface wave (ripple) is travelling to the right on the surface of a lake. The wave has period T. The diagram below shows the surface of the lake at a particular instant of time. A piece of cork is floating in the water in the position shown.

Which is the correct position of the cork a time 4T later?

cork

A. B.

C. D.

53

27. Diagram 1 below shows the displacement of part of a medium through which a wave is travelling at time t = 0. Diagram 2 shows the displacement at a later time t = 4.0 s in which the wave has moved forward 10 cm. In this time, the point P on the wave has moved from a crest through zero displacement to a trough.

Diagram 1 Diagram 2

P

P

The wavelength of the wave is

A. 5.0 cm. B. 10 cm. C. 20 cm. D. 40 cm.

28. A pulse is sent down a string fixed at one end.

Which one of the following diagrams best represents the reflected pulse?

A.

C.

B.

D.


1. Simple harmonic motion

(a) A body is displaced from equilibrium. State the two conditions necessary for the body to execute simple harmonic motion.

1. .........................................................................................................................

.........................................................................................................................

2. .........................................................................................................................

......................................................................................................................... (2)

(b) In a simple model of a methane molecule, a hydrogen atom and the carbon atom can be regarded as two masses attached by a spring. A hydrogen atom is much less massive than the carbon atom such that any displacement of the carbon atom may be ignored.

The graph below shows the variation with time t of the displacement x from its equilibrium position of a hydrogen atom in a molecule of methane.

54

The mass of hydrogen atom is 1.7 ×10–27 kg. Use data from the graph above

(i) to determine its amplitude of oscillation.

......................................................................................................................... (1)

(ii) to show that the frequency of its oscillation is 9.1 × 1013 Hz.

.........................................................................................................................

......................................................................................................................... (2)

(iii) to show that the maximum kinetic energy of the hydrogen atom is 6.2 × 10–18 J.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(c) Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of oscillation f is given by the expression

,21

pmkf

S

where k is the force per unit displacement between a hydrogen atom and the carbon atom and mp is the mass of a proton.

(i) Show that the value of k is approximately 560 N m–1.

.........................................................................................................................

......................................................................................................................... (1)

(ii) Estimate, using your answer to (c)(i), the maximum acceleration of the hydrogen atom.

.........................................................................................................................

......................................................................................................................... (2)

55

2. Travelling waves

(a) Graph 1 below shows the variation with time t of the displacement d of a travelling (progressive) wave. Graph 2 shows the variation with distance x along the same wave of its displacement d.

(i) State what is meant by a travelling wave.

.........................................................................................................................

......................................................................................................................... (1)

(ii) Use the graphs to determine the amplitude, wavelength, frequency and speed of the wave.

Amplitude: ................................................................................................. (1)

Wavelength: ................................................................................................. (1)

Frequency: .................................................................................................

................................................................................................. (1)

Speed: .................................................................................................

................................................................................................. (1)

Refraction of waves

(b) The diagram below shows plane wavefronts incident on a boundary between two media A and B.

t / s

x / cm

4

2

0

–2

–4

4

2

0

–2

–4

0.0 0.1 0.2 0.3 0.4 0.5 0.6

2.4 2.0 1.6 1.2 0.8 0.4 0.0

Graph 1 d / mm

Graph 2 d / mm

56

medium Amedium B

The ratio .4.1isA medium ofindex refractiveB medium ofindex refractive

The angle between an incident wavefront and the normal to the boundary is 50�.

(i) Calculate the angle between a refracted wavefront and the normal to the boundary.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (3)

(ii) On the diagram above, construct three wavefronts to show the refraction of the wave at the boundary.

(3) (Total 11 marks)

3. This question is about waves.

(a) With reference to the direction of energy transfer through a medium, distinguish between a transverse wave and a longitudinal wave.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(b) A wave is travelling along the surface of some shallow water in the x-direction. The graph shows the variation with time t of the displacement d of a particle of water.

57

Use the graph to determine for the wave

(i) the frequency,

...........................................................................................................................

........................................................................................................................... (2)

(ii) the amplitude.

........................................................................................................................... (1)

(c) The speed of the wave in (b) is 15 cm s–1. Deduce that the wavelength of this wave is 2.0 cm.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(d) The graph in (b) shows the displacement of a particle at the position x = 0.

On the axes below, draw a graph to show the variation with distance x along the water surface of the displacement d of the water surface at time t = 0.070 s.

(3)

–10

10

8

6

4

2

0

–2

–4

–6

–8

0 0.05 0.25 0.2 0.15 0.1 0.3 t / s

d / mm

58

(e) The wave encounters a shelf that divides the water into two separate depths. The water to the right of the shelf is deeper than that to the left of the shelf.

shelf

deep watershallow water

direction oftravel of wave

wave fronts

30 q

The angle between the wavefronts in the shallow water and the shelf is 30°. The speed of the wave in the shallow water is 15 cm s–1 and in the deeper water is 20 cm s–1. For the wave in the deeper water, determine the angle between the normal to the wavefronts and the shelf.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(Total 14 marks)

4. This question is about oscillations and waves.

(a) A rectangular piece of wood of length l floats in water with its axis vertical as shown in diagram 1.

The length of wood below the surface is d. The wood is pushed vertically downwards a distance A such that a length of wood is still above the water surface as shown in diagram 2. The wood is then released and oscillates vertically. At the instant shown in diagram 3, the wood is moving downwards and the length of wood beneath the surface is d + x.

(i) On diagram 3, draw an arrow to show the direction of the acceleration of the wood. (1)

59

(ii) The acceleration a of the wood (in m s–2) is related to x (in m) by the following equation.

a = xl

14�

Explain why this equation shows that the wood is executing simple harmonic motion.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) The period of oscillation of the wood is 1.4 s. Show that the length l of the wood is 0.70 m.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(b) The wood in (a), as shown in diagram 2, is released at time t = 0. On the axes below, sketch a graph to show how the velocity v of the wood varies with time over one period of oscillation.

(1)

(c) The distance A that the wood is initially pushed down is 0.12 m.

(i) Calculate the magnitude of the maximum acceleration of the wood.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

60

(ii) On your sketch graph in (b) label with the letter P one point where the magnitude of the acceleration is a maximum.

(1)

(d) The oscillations of the wood generate waves in the water of wavelength 0.45 m. The graph shows how the displacement D, of the water surface at a particular distance from the wood varies with time t.

Using the graph, calculate the

(i) speed of the waves.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) ratio of the displacement at t = 1.75 s to the displacement at t = 0.35 s.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) ratio of the energy of the wave at t = 1.75 s to the energy at t = 0.35 s

...........................................................................................................................

........................................................................................................................... (1)

(Total 15 marks)

61

Topic 5: Electric currents

1. Which one of the following is a correct definition of electric potential difference between two points?

A. The power to move a small positive charge between the two points.

B. The work done to move a small positive charge between the two points.

C. The power per unit charge to move a small positive charge between the two points.

D. The work done per unit charge to move a small positive charge between the two points.

2. The work done on a positive point charge of magnitude 3.0 nC as it is moved at constant speed from one point to another is 12 nJ. The potential difference between the two points is

A. 0.0 V. B. 0.25 V. C. 4.0 V. D. 36 V.

3. Which of the following is the correct value of the electronvolt, measured in SI Units?

A. 1.6 × 10–19 N B. 1.6 × 10–19 J C. 9.1 × 10–31 N D. 9.1 × 10–31 J

4. In the circuit below, n charge carriers pass the point P in a time t. Each charge carrier has charge q.

The current in the circuit is given by the expression

A. tq . B.

tnq . C.

nqt . D. nqt.

5. The variation with potential difference V of the current I in an electric lamp is shown below.

I

Ip

p00 V V

P

At point P, the current is Ip, the potential difference is Vp and the gradient of the tangent to the curve is G. What is the resistance of the lamp at point P?

A. G1

B. G C.

p

p

VI

D.

p

p

IV

6. The graph below shows the current/voltage characteristics of a filament lamp.

The resistance of the filament at 4.0 V is

A. ��ȍ�%� ��ȍ�&� ��ȍ�'� ��ȍ�

P

62

7. Which of the following is a correct statement of Ohm’s law?

A. The resistance of a conductor is always constant.

B. The current in a conductor is always proportional to the potential difference across the conductor.

C. The resistance of a conductor increases with increasing temperature.

D. The resistance of a conductor is constant only if the temperature of the conductor is constant.

8. The graph below shows the variation with voltage V of the current I in three resistors X, Y and Z.

Which of the following corresponds to resistors for which the resistance increases with increasing current?

A. X only B. Z only

C. X and Z D. Y and Z

9. Which graph best represents the relationship between the current I and the voltage V of a filament lamp.

A. V

0

B. V

00 I 0 I

C. V

0

D. V

00 I 0 I

10. A battery is connected in series with a resistor R. The battery transfers 2 000 C of charge completely round the circuit. During this process, 2 500 J of energy is dissipated in the resistor R and 1 500 J is expended in the battery.

The emf of the battery is

A. 2.00 V. B. 1.25 V. C. 0.75 V. D. 0.50 V.

11. Which one of the following shows a correct circuit, using ideal voltmeters and ammeters, for measuring the I-V characteristic of a filament lamp?

I

0V0

X

Y

Z

A

A

A

A

A.

C.

B.

D.

V

V

V

V

63

12. ,Q�WKH�FLUFXLW�VKRZQ��WKH�YROWPHWHU�KDV�D�UHVLVWDQFH�RI��Nȍ�DQG�the battery has an emf of 6.0 V and negligible internal resistance.

The reading on the voltmeter is

A. 2.0 V. B. 3.0 V.

C. 4.0 V. D. 6.0 V.

13. In the circuits below, the cells each have the same emf and zero internal resistance. All the resistors have the same resistance.

Circuit X Circuit Y Circuit Z

Which of the following gives the current through the cells in order of increasing magnitude?

Lowest current Highest current

A. X Y Z

B. Z X Y

C. Y Z X

D. Y X Z

14. In the two circuits X and Y below, each cell has an emf E and negligible internal resistance. Each resistor has a resistance R.

circuit X circuit Y

E E

RR

R

The power dissipated in circuit X is P.

The best estimate for the power dissipated in circuit Y is

A. .4P

B. .2P

C. 2P. D. 4P.

15. A conductor of constant resistance dissipates 6.0 W of power when the potential difference across it is 12 V. The power that will be dissipated in this conductor when the potential difference across it is 24 V is

A. 6.0 W. B. 12 W. C. 24 W. D. 48 W.

V

6.0 V

10 k: 20 k:

20 k:

64

16. In the circuit below, resistors X, Y and Z are connected in series with a 9.0 V supply.

0

X Y Z

+9.0 V

3000 W3000 W

V

Resistors X and Z are fixed resistors of resistance 3000 :. The resistance of resistor Y may be varied between zero and 3000 :.

Which of the following gives the maximum range of potential difference V across the resistors X and Y?

A. 0 to 6.0 V B. 3.0 V to 6.0 V C. 4.5 V to 6.0 V D. 4.5 V to 9.0 V

17. A resistor of resistance 1.0 : is connected in series with a battery. The current in the circuit is 2.0 A. The resistor is now replaced by a resistor of resistance of 4.0 :. The current in this circuit is 1.0 A.

2.0 A

1.0 W

1.0 A

4.0 W

The best estimate for the internal resistance of the battery is

A. 1.0 :. B. 2.0 :. C. 4.0 :. D. 5.0 :.

18. In the circuit below, the battery has negligible internal resistance. Three identical lamps L, M and N of constant resistance are connected as shown.

The filament of lamp N breaks. Which of the following shows the subsequent changes to the brightness of lamp L and lamp M?

Lamp L Lamp M

A. stays the same decreases

B. increases stays the same

C. increases decreases

D. decreases increases

65

19. In the circuit below, which meter is not correctly connected?

A. 1 B. 2 C. 3 D. 4

20. A copper wire, of electric resistance R, has a length L and a cross-section area S. Another copper wire has a length 2L and a

cross-section area of 2S . Which of the following is the resistance of

this wire?

A. 4R

B.

2R

C. 2R D. 4R

21. Two resistors, made of the same material, are connected in series to a battery. The length of resistor X is twice that of resistor Y, and X has twice the cross-sectional area of Y.

Which of the following gives Y of resistanceX of resistance ?

A. 41

B.

21

C. 1 D. 4

22. The tungsten filament of a lamp has a cross-sectional area A and length L. For a potential difference V across the filament, the current in the filament is I. The resistivity of the tungsten equals

A. LIAV

. B. AVLI

. C. AILV

. D. LVAI

23. In the circuit below, which of the following will cause the greatest increase in the reading of the voltmeter?

A. An increase in temperature

B. An increase in light intensity

C. A decrease in temperature

D. A decrease in light intensity

24. The circuit shows a light-dependent resistor (LDR) in series with a resistor and a cell. The emf of the cell is İ��7KH�LQWHUQDO�UHVLVWDQFH�RI�WKH�FHOO�LV�QHJOLJLEOH�

When light shines on the LDR, the potential difference across the resistor will

A. stay the same. B. decrease.

C. LQFUHDVH�EXW�DOZD\V�EH�OHVV�WKDQ�İ�

D. LQFUHDVH�DQG�H[FHHG�İ�

A

V

A

V

1

2

3

4

66

25. Which of the following correctly gives the resistance of an ideal ammeter and resistance of an ideal voltmeter?

Ammeter Voltmeter

A. infinite infinite

B. zero zero

C. zero infinite

D. infinite zero


1. This question is about electrical resistance.

(a) A heating coil is to be made of wire of diameter 3.5 × 10–4 m. The heater is to dissipate 980 W when connected to a 230 V d.c. supply. The material of the wire has resistivity 1.3 × 10–6 ȍ�P�DW�WKH�ZRUNLQJ�WHPSHUDWXUH�RI�WKH�KHDWHU�

(i) Define electrical resistance.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Calculate the resistance of the heating coil at its normal working temperature.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) Show that the length of wire needed to make the heating coil is approximately 4 m.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(b) Three identical electrical heaters each provide power P when connected separately to a supply S which has zero internal resistance. On the diagram below, complete the circuit by drawing two switches so that the power provided by the heaters may be either P or 2P or 3P.

(2)

(Total 7 marks)

67

2. This question is about electric circuits.

(a) (i) Define emf and state Ohm’s law.

emf: ....................................................................................................

....................................................................................................

Ohm’s law: ....................................................................................................

.................................................................................................... (2)

(ii) The graph below shows the I-V characteristic of a particular electrical component.

00

V

I

State show the resistance of the component is determined from the graph.

.........................................................................................................................

......................................................................................................................... (1)

(b) In the circuit below an electrical device (load) is connected in series with a cell of emf 2.5 V and internal resistance r. The current I in the circuit is 0.10 A.

load

I = 0.10A

e.m.f. = 2.5V

r

The power dissipated in the load is 0.23 W.

Calculate

(i) the total power of the cell;

.........................................................................................................................

......................................................................................................................... (1)

68

(ii) the resistance of the load;

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(iii) the internal resistance r of the cell.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(c) A second identical cell is connected into the circuit in (b) as shown below.

load

I = 0.15A

The current in this circuit is 0.15 A. Deduce that the load is a non-ohmic device.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (4)

(Total 12 marks)

3. This question is about electrical energy and associated phenomena.

Current electricity

A cell of electromotive force (emf) E and internal resistance r is connected in series with a resistor R, as shown below.

R

rE

69

The cell supplies 8.1 × 103 J of energy when 5.8 × 103 C of charge moves completely round the circuit. The current in the circuit is constant.

(i) Calculate the emf E of the cell.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) 7KH�UHVLVWRU�5�KDV�UHVLVWDQFH��ȍ��7KH�SRWHQWLDO�GLIIHUHQFH�EHWZHHQ�LWV�WHUPLQDOV�LV� 1.2 V. Determine the internal resistance r of the cell.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(iii) Calculate the total energy transfer in the resistor R.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(iv) Describe, in terms of a simple model of electrical conduction, the mechanism by which the energy transfer in the resistor R takes place.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (5)

(Total 12 marks)

4. This question is about electric circuits.

Susan sets up the circuit below in order to measure the current-voltage (I-V) characteristic of a small filament lamp.

A

V3.0 V

S

70

The supply is a battery that has an emf of 3.0 V and the ammeter and voltmeter are considered to be ideal. The lamp is labelled by the manufacturer as “3 Volts, 0.6 Watts”.

(a) (i) Explain what information this labelling provides about the normal operation of the lamp.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Calculate the current in the filament of the lamp when it is operating at normal brightness.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

Susan sets the variable resistor to its maximum value of resistance. She then closes the switch S and records the following readings.

Ammeter reading = 0.18 A Voltmeter reading = 0.60 V

She then sets the variable resistor to its zero value of resistance and records the following readings.

Ammeter reading = 0.20 A Voltmeter reading = 2.6 V

(b) (i) Explain why, by changing the value of the resistance of the variable resistance, the potential difference across the lamp cannot be reduced to zero or be increased to 3.0 V.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Determine the internal resistance of the battery.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

71

(c) Calculate the resistance of the filament when the reading on the voltmeter is

(i) 0.60 V.

...........................................................................................................................

........................................................................................................................... (1)

(ii) 2.6 V.

...........................................................................................................................

........................................................................................................................... (1)

(d) Explain why there is a difference between your answers to (c)(i) and (c)(ii).

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(e) Using the axes below, draw a sketch-graph of the I-V characteristic of the filament of the lamp. (Note: this is a sketch-graph; you do not need to add any values to the axes.)

I

V0

0 (1)

The diagram below shows an alternative circuit for varying the potential difference across the lamp.

The potential divider XZ has a potential of 3.0 V across it. When the contact is at the position Y, the resistance of XY equals the resistance of YZ which equals ��ȍ��7KH�UHVLVWDQFH�RI�WKH�ODPS�LV��ȍ�

(f) Calculate the potential difference across the lamp.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (4)

(Total 18 marks)

3.0 V

X

Y

Z

72

Topic 6: Fields and forces

1. Newton’s law of gravitation for the force F between two point objects of masses M and m, separated by a distance d may be written as

Fd2 is proportional to Mm.

The expression may also be used for the force of attraction between the Sun and the Earth, although they are not point masses. This is because

A. the gravitational constant G is not involved in the expression.

B. the force between the Sun and the Earth is very large.

C. the separation of the Sun and the Earth is much greater than their radii.

D. the mass of the Earth is much less than the mass of the Sun.

2. In Newton’s universal law of gravitation the masses are assumed to be

A. extended masses. B. masses of planets. C. point masses. D. spherical masses.

3. Gravitational field strength at a point may be defined as

A. the force on a small mass placed at the point.

B. the force per unit mass on a small mass placed at the point.

C. the work done to move unit mass from infinity to the point.

D. the work done per unit mass to move a small mass from infinity to the point.

4. The acceleration of free fall of a small sphere of mass 5.0 × 10–3 kg when close to the surface of Jupiter is 25 ms–2. The gravitational field strength at the surface of Jupiter is

A. 2.0 × 10–4 N kg–1.B. 1.3 × 10–1 N kg–1.C. 25 N kg–1.D. 5.0 × 103 N kg–1.

5. The mass of Mars is approximately 0.1 times the mass of Earth and its diameter is approximately 0.5 times that of Earth.

What is the approximate gravitational field strength on the surface of Mars?

A. 2N kg–1 B. 4N kg–1 C. 25N kg–1 D. 50N kg–1

6. Planet X has radius R and mass M. Planet Y has radius 2R and mass 8M.

Which one of the following is the correct value of the ratio

? Yplanet of surfaceat strength field nalgravitatio Xplanet of surfaceat strength field nalgravitatio

A. 4 B. 2 C. 21

D.

41

73

7. Two identical spherical conductors X and Y are mounted on insulated stands. X carries a charge of +8.0 nC and Y carries a charge of –2.0 nC.

The two conductors are brought into contact and are then separated. Which of the following gives the charge on each conductor?

Charge on X Charge on Y

A. 0.0 nC 0.0 nC

B. +8.0 nC –2.0 nC

C. +5.0 nC +5.0 nC

D. +3.0 nC +3.0 nC

8. The diagram below shows a positively charged rod brought near an isolated uncharged metal plate.

As a result of bringing the rod near to the plate,

A. the metal plate will gain a charge dependent on the separation of the rod and the plate.

B. the metal plate will remain uncharged.

C. the metal plate will gain a negative charge.

D. the metal plate will gain a positive charge.

9. An isolated, uncharged metal conductor is brought close to a positively charged insulator.

+ + + ++ + + +insulating handle

conductor

insulator

The conductor is earthed (grounded) for a short time and then the insulator is removed.

Which of the following best represents the charge distribution on the surface of the conductor as a result of these actions?

—

—— —— —— —

—————

———A.

D.C.

B.

insulated stands conductor X conductor Y

+8.0nC –2.0nC

+

+

+

+

+

+++

rod

plate

74

10. X and Y are two identical conducting spheres separated by a distance d. X has a charge +6 ȝC and Y has a charge –2 ȝC. The electric force between them is + F (ie attractive). The spheres are touched together and are then returned to their original separation d. The force between them now is

A. +F. B. –F. C. .3F

� D. .3F

�

11. Three equal point charges X, Y and Z are fixed in the positions shown.

The distance between q1 and q2 and the distance between q2 and q3 is 1.0 m. The electric force between the charges at X and Y is F. The electric force between the charges at X and Z is

A. .2F B. .

2F

C. F. D. 2F.

12. The electric field strength at a point may be defined as

A. the force exerted on unit positive charge placed at that point.

B. the force per unit positive charge on a small test charge placed at that point.

C. the work done on unit positive charge to move the charge to that point from infinity.

D. the work done per unit positive charge to move a small test charge to that point from infinity.

13. Two positive point charges P and Q are held a certain distance apart.

X P Y Q Z

+ +

At which point(s) could the electric field strength, due to the charges, be zero?

A. X only B. Y only C. Z only D. X and Z only

14. Two point charges of magnitude +2Q DQG�íQ are fixed at the positions shown below. At which point is the electric field due to the two charges most likely to be zero?

+2Q –Q

A. B. C. D.

15. The diagram below shows two parallel conducting plates that are oppositely charged.

The line XY is perpendicular to the plates.

Which of the following diagrams shows the variation along the line XY of the magnitude E of the electric field strength between the plates?

Z q3

1.0 m

X 1.0 m

90qY

q1

q2

+++ + +

– – –––

X

Y

E

E

E

E

X

X

X

X

Y

Y

Y

Y

distance

distance

distance

distance

A. B.

C. D.

75

16. The Earth’s magnetic field may be compared with that of a bar magnet.

Which of the following diagrams correctly shows the orientation of the bar magnet in this model?

geographical north pole



geographical north poleA. B.

C. D.

NN

N

N

S

S

S

S

17. A current-carrying solenoid is placed with its axis pointing east-west as shown below. A small compass is situated near one end of the solenoid.

axis ofsolenoid

N

EW

S

The axis of the needle of the compass is approximately 45° to the axis of the solenoid. The current in the solenoid is then doubled. Which of the following diagrams best shows the new position of the compass needle?

W

W

W

W

E

E

E

E

A.

C.

B.

D.

18. A long, straight current-carrying wire is placed normal to the plane of the page. The current in the wire is into the plane of the page.

Which of the following diagrams best represents the magnetic field around the wire?

A. B.

C. D.

76

19. Two long, vertical wires X and Y carry currents in the same direction and pass through a horizontal sheet of card.

X Y

Iron filings are scattered on the card. Which one of the following diagrams best shows the pattern formed by the iron filings? (The dots show where the wires X and Y enter the card.)

A. B.

C. D.

20. A strip of aluminium foil is held between the poles of a strong magnet, as shown below.

magnet

aluminium foil

direction of current

When a current is passed through the aluminium foil in the direction shown, the foil is deflected. In which direction is this deflection?

A. Vertically downwards

B. Vertically upwards

C. Towards the North pole of the magnet

D. Towards the South pole of the magnet

77

21. A magnetic force acts on an electric charge in a magnetic field when

A. the charge is not moving.

B. the charge moves in the direction of the magnetic field.

C. the charge moves in the opposite direction to the magnetic field.

D. the charge moves at right angles to the lines of the magnetic field.

22. The diagram below shows a charged particle about to enter a region of uniform magnetic field directed into the page.

magnetic fieldcharged particle

Which of the following correctly describes the change, if any, in the kinetic energy and the momentum of the particle in the magnetic field?

Kinetic energy Momentum

A. Changed Changed

B. Changed Unchanged

C. Unchanged Changed

D. Unchanged Unchanged

23. The currents in two parallel wires are I and 3I in the directions shown in the diagram below.

The magnetic force on wire 2 due to the current in wire 1 is F. The magnitude of the force on wire 1 due to the current in wire 2 is

A. .3F

B. .2F

C. F. D. 3F.

24. The diagram below shows three parallel wires P, Q and R that are equally spaced.

The currents in the wires are each of the same magnitude I and are in the directions shown. The resultant force on wire Q due to the current in wire P and in wire R is

A. perpendicular and into the plane of the paper.

B. perpendicular and out of the plane of the paper.

C. in the plane of the paper to the right.

D. in the plane of the paper to the left.

wire 1

I

wire 2

3I

I I I

wire P wire Q wire R

78

25. A straight conductor is in the plane of a uniform magnetic field as shown.

current I

magnetic field

The current in the conductor is I and the conductor is at an angle ș to the magnetic field. The force per unit length on the conductor due to the current in the magnetic field is P. Which is the correct expression for the magnitude of the magnetic field strength?

A. I

P Tsin B. I

P Tcos

C. TsinI

P

D.

TcosIP

26. A positively charged particle enters a region of uniform magnetic field. The direction of the particle’s velocity is parallel to the direction of the magnetic field as shown in the diagram below.

charged particle

region of uniform magnetic field

Which of the following diagrams correctly shows the path of the charged particle while in the region of magnetic field?

A. B.

C. D.

27. An electron is travelling in the direction shown and enters a region of uniform magnetic field.

direction ofmagnetic field

region of uniformmagnetic field

direction of travel ofthe electron

e–

On entering the field the direction of the force acting on the electron is

A. into the plane of the paper.

B. out of the plane of the paper.

C. towards the top of the page.

D. towards the bottom of the page.

79

28. Three positive point charges of equal magnitude are held at the corners X, Y and Z of a right-angled triangle. The point P is at the midpoint of XY. Which of the arrows shows the direction of the electric field at point P?

29. The radius of a charged spherical conductor is R. Which of the following graphs best shows how the magnitude of the electrical field strength E varies with distance r from the centre of the sphere?

30. Which of the following gives the acceleration of an electron of electric charge e and mass m in a uniform electric field of strength E?

A. E B. Ee C. mEe

D.

Eem

31. Which diagram best represents the electric field due to a negatively charged conducting sphere?

80


1. This question is about gravitational fields.

(a) Define gravitational field strength.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(b) The gravitational field strength at the surface of Jupiter is 25 N kg–1 and the radius of Jupiter is 7.1 × 107 m.

(i) Derive an expression for the gravitational field strength at the surface of a planet in terms of its mass M, its radius R and the gravitational constant G.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(ii) Use your expression in (b)(i) above to estimate the mass of Jupiter.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(Total 6 marks)

2. This question is about the electric field due to a charged sphere and the motion of electrons in that field.

The diagram below shows an isolated, metal sphere in a vacuum that carries a negative electric charge of 9.0 nC.

–

(a) On the diagram draw arrows to represent the electric field pattern due to the charged sphere. (3)

(b) The electric field strength at the surface of the sphere and at points outside the sphere can be determined by assuming that the sphere acts as though a point charge of magnitude 9.0 nC is situated at its centre. The radius of the sphere is 4.5 × 10–2 m. Deduce that the magnitude of the field strength at the surface of the sphere is 4.0 × 104 Vm–1.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (1)

81

An electron is initially at rest on the surface of the sphere.

(c) (i) Describe the path followed by the electron as it leaves the surface of the sphere.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Calculate the initial acceleration of the electron.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(iii) State and explain whether the acceleration of the electron remains constant, increases or decreases as it moves away from the sphere.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iv) At a certain point P, the speed of the electron is 6.0 × 106 ms–1. Determine the potential difference between the point P and the surface of the sphere.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 13 marks)

3. This question is about electric charge at rest.

(a) Define electric field strength at a point in an electric field.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

82

Four point charges of equal magnitude, are held at the corners of a square as shown below.

The length of each side of the square is 2a and the sign of the charges is as shown. The point P is at the centre of the square.

(b) (i) Deduce that the magnitude of the electric field strength at point P due to one of the point

charges is equal to 22akQ .

...........................................................................................................................

........................................................................................................................... (2)

(ii) On the diagram above, draw an arrow to represent the direction of the resultant electric field at point P.

(1)

(iii) Determine, in terms of Q, a and k, the magnitude of the electric field strength at point P.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 8 marks)

4. (a) On the diagram below, draw the magnetic field pattern around a long straight current-carrying conductor.

current-carrying wire

(3)

2a

2a

+ Q + Q

–Q –Q

P

83

The diagram below shows a coil consisting of two loops of wire. The coil is suspended vertically.

6.0 cm

0.20 cm

Each loop has a diameter of 6.0 cm and the separation of the loops is 0.20 cm. The coil forms part of an electrical circuit so that a current may be passed through the coil.

(b) (i) State and explain why, when the current is switched on in the coil, the distance between the two loops changes.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

When there is a current I in the coil, a mass of 0.10 g hung from the free end of the coil returns the separation of the loops to the original value of 0.20 cm.

The circumference C of a circle of radius r is given by the expression

C = 2ʌU.

(ii) Calculate the current I in the coil. You may assume that each loop behaves as a long straight current-carrying wire.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (5)

(Total 11 marks)

5. This question is about motion of a charged particle in a magnetic field.

A charged particle is projected from point X with speed v at right angles to a uniform magnetic field. The magnetic field is directed out of the plane of the page. The particle moves along a circle of radius R and centre C as shown in the diagram below.

84

region of magnetic fieldout of plane of page

Y

R C

v

Xcharged particle

(a) On the diagram above, draw arrows to represent the magnetic force on the particle at position X and at position Y.

(1)

(b) State and explain whether

(i) the charge is positive or negative;

......................................................................................................................... (1)

(ii) work is done by the magnetic force.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(c) A second identical charged particle is projected at position X with a speed 2v in a direction

opposite to that of the first particle. On the diagram above, draw the path followed by this particle. (2)

(Total 6 marks) 6. This question is about the force between current-carrying wires.

Diagram 1 below shows two long, parallel vertical wires each carrying equal currents in the same direction. The wires pass through a horizontal sheet of card. Diagram 2 shows a plan view of the wires looking down onto the card.

sheet of card

eye

diagram 1 diagram 2

85

(a) (i) Draw on diagram 1 the direction of the force acting on each wire. (1)

(ii) Draw on diagram 2 the magnetic field pattern due to the currents in the wire. (3)

(b) The card is removed and one of the two wires is free to move. Describe and explain the changes in the velocity and in acceleration of the moveable wire.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(Total 7 marks)

7. This question is about force fields.

(a) Outline what is meant by a field of force.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) Five particles A to E are each placed in a different type of field. Complete the table to identify the nature of the field in which each particle is situated.

Particle Charge on particle

Initial direction of motion of particle

Direction of force on particle Type of field

A uncharged stationary in direction of field .....................................

B negative along direction of field

opposite to direction of field .....................................

C positive normal to direction of field

normal to direction of field .....................................

D positive normal to direction of field

in direction of field .....................................

E uncharged opposite to direction of field

in direction of field .....................................

(5) (Total 7 marks)

86

8. This question is about gravitational and electric fields.

(a) The equation for the magnitude of the gravitational field strength due to a point mass may be written as below.

Y = 2s

KX

The equation for the magnitude of the electric field strength can also be written in the same form.

In the table identify the symbols used in the equation.

Symbol Gravitational field quantity Electrical field quantity

Y

K

X

s (4)

(b) The magnitude of the electrostatic force between the proton and electron in a hydrogen atom is FE. The magnitude of the gravitational force between them is FG.

Determine the ratio G

E

FF

.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 7 marks)

87

Topic 7: Atomic and nuclear physics

1. The Geiger-Marsden alpha particle scattering experiment provides evidence for the existence of

A. atomic nuclei.

B. neutrons.

C. protons.

D. nuclear energy levels.

2. In the Geiger-Marsden experiment, Į�particles are scattered by gold nuclei. The experimental results indicate that most Į�particles are

A. scattered only at small angles.

B. scattered only at large angles.

C. absorbed in the target.

D. scattered back along the original direction.

3. The atomic line spectra of elements provides evidence for the existence of

A. photons.

B. electrons.

C. quantized energy states within nuclei.

D. quantized energy states within atoms.

4. Which one of the following correctly gives the number of electrons, protons and neutrons in a neutral atom of the nuclide Cu65

29 ?

Number of electrons Number of protons Number of neutrons

A. 65 29 36

B. 36 36 29

C. 29 29 65

D. 29 29 36

5. The number of nucleons in a nucleus is the number of

A. particles in the nucleus.

B. neutrons in the nucleus.

C. protons in the nucleus.

D. protons plus neutrons in the nucleus.

6. Isotopes provide evidence for the existence of

A. protons. B. electrons. C. nuclei. D. neutrons.

88

7. Ag-102, Ag-103 and Ag-104 are three isotopes of the element silver.

Which one of the following is a true statement about the nuclei of these isotopes?

A. All have the same mass.

B. All have the same number of nucleons.

C. All have the same number of neutrons.

D. All have the same number of protons.

8. Which of the following identifies the significant interaction(s) between nucleons inside the nucleus?

A. Nuclear only B. Coulomb only

C. Nuclear and Coulomb D. Gravitational, nuclear and Coulomb

9. The nucleus of an atom contains protons. The protons are prevented from flying apart by

A. the presence of orbiting electrons.

B. the presence of gravitational forces.

C. the presence of strong attractive nuclear forces.

D. the absence of Coulomb repulsive forces at nuclear distances.

10. The unified mass unit is defined as

A. the mass of one neutral atom of 126 C.

B. 121 of the mass of one neutral atom of 12

6 C.

C. 61 of the mass of one neutral atom of 12

6 C.

D. the mass of the nucleus of 126 C.

11. Which of the following best describes why alpha-particles travel only a short distance in air?

A. They undergo radioactive decay.

B. They undergo elastic collisions with air molecules.

C. They ionize air molecules.

D. They are attracted by the nuclei of air molecules.

12. A nucleus of the isotope potassium-40 � �K4019 decays to form a nucleus argon-40 � �Ar40

18 Which one of the following correctly identifies the other two particles resulting from this decay?

A. Eí and v B. Eí and v

C. E+ and v D. E+ and v

89

13. The nucleus P3015 undergoes radioactive decay to the nucleus Si.30

14 The particles emitted in the decay are

A. a positron and an antineutrino.

B. an electron and an antineutrino.

C. a positron and a neutrino.

D. an electron and a neutrino.

14. In a laboratory when aluminium nuclei are bombarded with Į-particles, the following reaction may take place.

nPAlHe 10

3015

2713

42 �o�

This reaction is an example of

A. nuclear fission. B. nuclear fusion.

C. natural radioactive decay. D. artificial transmutation.

15. K-capture is a process that occurs when a nucleus captures an electron from the innermost shell of electrons surrounding the nucleus.

When K-capture occurs in iron-55 ( 5526 Fe), the nucleus is changed into a manganese (Mn) nucleus. Which

equation represents this change?

A. ( 5526 Fe) + 0

1H�ĺ� 5527 Mn

B. ( 5526 Fe) +1

1H�ĺ� 5627 Mn

C. ( 5526 Fe) + 0

1� H�ĺ� 5525 Mn

D. ( 5526 Fe) + 1

1� H�ĺ� 5625 Mn

16. When the isotope aluminium-27 is bombarded with alpha particles, the following nuclear reaction can take place.

neutronXAlHe 2713

42 �o�

Which of the following correctly gives the atomic (proton) number and mass (nucleon) number of the nucleus X?

Proton number Nucleon number

A. 15 30

B. 16 31

C. 30 15

D. 31 16

90

17. The binding energy per nucleon of the nucleus Li73 is approximately 5 MeV. The total energy required

to completely separate the nucleons of this nucleus is approximately

A. 15 MeV. B. 20 MeV.

C. 35 MeV. D. 50 MeV.

18. The graph below illustrates the variation with nucleon number (mass number) N of the binding energy per nucleon E of nuclei.

Which of the labelled nuclei is the most stable?

A

B

C

D

E

N

19. A freshly-prepared sample of cobalt-64 ( Co6427 ��GHFD\V�E\�WKH�HPLVVLRQ�RI�Ȗ-ray photons. The decay may

be represented by the nuclear equation

CoCo 6427

6427 o + energy.

After this decay, the binding energy per nucleon has

A. increased in magnitude because energy has been emitted from the nucleus.

B. decreased in magnitude because energy has been emitted from the nucleus.

C. stayed constant because the number of nucleons in the nucleus is unchanged.

D. stayed constant because the proton number is unchanged.

20. Two light nuclei of masses m1 and m2 fuse in a nuclear reaction to form a nucleus of mass M. Which of the following expressions correctly relates the masses of the nuclei?

A. M ! m1 + m2

B. M � m1 + m2

C. M = m1 + m2

D. M = m1 í�m2

91

21. The equation of a nuclear reaction is shown below.

nHeHH 10

32

21

21 �o�

The reaction is an example of

A. artificial transmutation.

B. fission.

C. natural radioactivity.

D. fusion.

22. The graph below shows the variation with mass (nucleon) number of the average binding energy per nucleon.

IV

IIII

II

mass number0

average bindingenergy per

nucleon

Which direction indicates a fission reaction with a release of energy?

A. I

B. II

C. III

D. IV

23. The rest-mass of a nucleus of lithium-7 � �Li73 is mL. The rest-mass of a proton is mP and the rest-mass of

a neutron is mN. The speed of light in free space is c.

Which of the following is a correct expression for the binding energy of a lithium-7 nucleus?

A. (3mP + 4mN – mL)c2

B. (3mP + 4mN + mL)c2

C. (4mP + 3mN – mL)c2

D. (3mP + 7mN – mL)c2

92

24. The source of the Sun’s energy is

A. fission.

B. radioactivity.

C. fusion.

D. ionization.

25. Radioactive decay is a random process. This means that

A. a radioactive sample will decay continuously.

B. some nuclei will decay faster than others.

C. it cannot be predicted how much energy will be released.

D. it cannot be predicted when a particular nucleus will decay.

26. A sample of a radioactive isotope of half-life 21T initially contains N atoms. Which one of the following

gives the number of atoms of this isotope that have decayed after a time ?321T

A. N81

B. N31

C. N32

D. N87

27. The initial activity (rate of decay) of a sample of mass 25 Pg of a radioactive isotope is A0. The half-life of the isotope is .

21T Which of the following gives the initial activity and half-life of a sample of mass 50

Pg of this isotope?

Activity Half-life

A. A0 21T

B. 2A0 21T

C. A0 212T

D. 2A0 212T

93

28. A nuclide X has a half-life of 10 s. On decay the stable nuclide Y is formed. Initially a sample contains only atoms of X.

After what time will 87.5% of the atoms in the sample have decayed into nuclide Y.

A. 9.0 s

B. 30 s

C. 70 s

D. 80 s

29. A sample of material contains 64 Pg of a radioactive isotope. After sixty minutes 2.0 Pg of the isotope remain. The half-life of this isotope is

A. 10 minutes.

B. 12 minutes.

C. 15 minutes.

D. 20 minutes.


30. This question is about atomic spectra.

An electron undergoes a transition from an atomic energy level of 3.20 × 10–15 J to an energy level of 0.32 × 10–15 J. Determine the wavelength of the emitted photon.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

.............................................................................................................................................. (Total 3 marks)

31. This question is about nuclear binding energy.

(a) (i) Define nucleon.

........................................................................................................................... (1)

(ii) Define nuclear binding energy of a nucleus.

...........................................................................................................................

........................................................................................................................... (1)

94

The axes below show values of nucleon number A (horizontal axis) and average binding energy per nucleon E (vertical axis). (Binding energy is taken to be a positive quantity).

9

8

7

6

5

4

3

2

1

00 25 50 75 100 125 150 175 200 225 250

A

E / MeV

(b) Mark on the E axis above, the approximate position of

(i) the isotope Fe5626 (label this F).

(1)

(ii) the isotope H21 (label this H).

(1)

(iii) the isotope U23892 (label this U).

(1)

(c) Using the grid in part (a), draw a graph to show the variation with nucleon number A of the average binding energy per nucleon E.

(2)

(d) Use the following data to deduce that the binding energy per nucleon of the isotope He32 is 2.2

MeV.

nuclear mass of He32 = 3.01603 u

mass of proton = 1.00728 u mass of neutron = 1.00867 u

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

95

In the nuclear reaction nHeHH 10

32

21

21 �o� energy is released.

(e) (i) State the name of this type of reaction.

........................................................................................................................... (1)

(ii) Use your graph in (c) to explain why energy is released in this reaction.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 13 marks)

32. This question is about radioactivity and nuclear energy.

(a) Define the following terms,

(i) Isotope

...........................................................................................................................

........................................................................................................................... (1)

(ii) Radioactive half-life

...........................................................................................................................

........................................................................................................................... (1)

Thorium-227 (Th-227) results from the decay of the isotope actinium-227.

(b) (i) Complete the following reaction equation.

�o ThAc 22790

22789

(1)

Th-227 has a half-life of 18 days and undergoes D-decay to the isotope Ra-223 (Ra-223). A sample of Th-227 has an initial activity of 32 arbitrary units.

(ii) Using the axes below, draw a graph to show the variation with time t (for t = 0 to t = 72 days) of the activity A of Th-227.

(2)

32

24

16

8

00 18 36 54 72

activity /arbitrary units

time / days

96

(iii) Determine from your graph, the activity of thorium after 50 days.

........................................................................................................................... (1)

(iv) Outline the experimental procedure to measure the activity of Th-227.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

In the decay of a Th-227 nucleus, a Ȗ-ray photon is also emitted.

(c) Use the following data to deduce that the energy of the Ȗ-ray photon is 0.667 MeV.

mass of Th-227 nucleus = 227.0278 u mass of Ra-223 nucleus = 223.0186 u mass of helium nucleus = 4.0026 u energy of Į-particle emitted =5.481 MeV unified atomic mass unit (u) = 931.5 MeV c–2

You may assume that the Th-227 nucleus is stationary before decay and that the Ra-223 nucleus has negligible kinetic energy.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(Total 11 marks)

33. Radioactive decay

(a) The nucleon number (mass number) of a stable isotope of argon is 36 and of a radioactive isotope of argon is 39.

(i) State what is meant by a nucleon.

.........................................................................................................................

......................................................................................................................... (1)

(ii) Explain, in terms of the number of nucleons and the forces between them, why argon-36 is stable and argon-39 is radioactive.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (4)

97

(b) A particular nucleus of argon-39 undergoes the decay shown by the nuclear reaction equation below.

��o ȕKAr3918

(i) State the proton (atomic) number and the nucleon (mass) number of the potassium (K) nucleus.

Proton number: .........................................................................................

Nucleon number: ......................................................................................... (2)

(ii) Use the following data to determine the maximum energy, in J, of the Eí particle in the decay of a sample of argon-39.

Mass of argon-39 nucleus = 38.96431 u

Mass of K nucleus = 38.96370 u

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (3)

(c) The graph below shows the variation with time t of the activity A of a sample of argon-39.

1750

1600

1450

1300

1150

1000

850

700

550

400

250

1001211109876543210

time / 10 years

activity / Bq

2

Use the graph to determine the half-life of argon-39. Explain your reasoning.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

98

(Total 12 marks) 34. This question is about nuclear power production.

(a) The purpose of a nuclear power station is to produce electrical energy from nuclear energy. The diagram below is a representation of the principal components of a nuclear reactor pile used in a certain type of nuclear power station that uses uranium as a fuel.

The function of the moderator is to slow down the neutrons produced in a reaction such as that described above.

Explain,

(i) why it is necessary to slow down the neutrons.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (3)

(ii) the function of the control rods.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(b) With reference to the concept of fuel enrichment in a nuclear reactor explain,

(i) the advantage of enriching the uranium used in a nuclear reactor.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (3)

(ii) from an international point of view, a possible risk to which fuel enrichment could lead.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

99

(c) A particular nuclear reactor uses uranium-235 as its fuel source. When a nucleus of uranium-235 absorbs a neutron, the following reaction can take place.

n2SrXenU 10

9038

14454

10

23592 ��o�

The following data are available. rest mass of U235

92 = 2.1895 × 105 MeV c–2

rest mass of Xe14454 = 1.3408 × 105 MeV c–2

rest mass of Sr9038 = 8.3749 × 104 MeV c–2

rest mass of n10 = 939.56 MeV c–2

(i) Show that the energy released in the reaction is approximately 180 MeV.

.........................................................................................................................

......................................................................................................................... (1)

(ii) State the form in which the energy appears.

......................................................................................................................... (1)

(d) The energy released by 1 atom of carbon-12 during combustion is approximately 4 eV.

(i) Using the answer to (c)(i), estimate the ratio

.12-carbon ofdensity energy 235-uranium ofdensity energy

.........................................................................................................................

......................................................................................................................... (3)

(ii) Suggest, with reference to your answer in (d)(i), one advantage of uranium-235 compared with fossil fuels.

.........................................................................................................................

......................................................................................................................... (1)

(e) When a uranium-238 nucleus absorbs a neutron the following reaction can take place.

UnU 23992

10

23892 o�

The isotope uranium-239 is radioactive and decays with a half-life of 23 minutes to form an isotope of neptunium-239 (Np-239).

(i) Define radioactive half-life and explain what is meant by an isotope.

Radioactive half-life:

.........................................................................................................................

.........................................................................................................................

100

Isotope:

.........................................................................................................................

......................................................................................................................... (2)

(ii) Complete the reaction equation for this decay.

oU23992

(3)

(iii) The isotope neptunium-239 undergoes radioactive E� decay to form an isotope of plutonium. Outline one advantage and one disadvantage of this decay in relation to nuclear power production.

Advantage:

.........................................................................................................................

Disadvantage:

......................................................................................................................... (4)

(Total 25 marks)

101

Topic 8: Energy, power and climate change

1. Degraded energy is energy that is

A. stored in the Earth’s atmosphere.

B. available from non-renewable energy sources.

C. converted into work in a cyclical process.

D. no longer available for the performance of useful work.

2. The Sankey diagram of a fossil-fuelled power station is shown below.

Which of the following best identifies the thermal energy removed by water and the useful electrical energy output of the station?

Thermal energy removed Useful electrical energy output

A. 2 1

B. 2 3

C. 3 1

D. 1 2

3. World energy resources include coal, nuclear fuel and geothermal energy. Which of the following lists these resources in order of primary energy use in the world?

A. nuclear, geothermal, coal

B. nuclear, coal, geothermal

C. coal, geothermal, nuclear

D. coal, nuclear, geothermal

4. Which of the following correctly shows a renewable and a non-renewable source of energy?

Renewable Non-renewable

A. oil geothermal

B. wind biofuels

C. ocean waves nuclear

D. natural gas coal

5. Which of the following energy sources results from the solar energy incident on Earth?

A. Nuclear fission B. Wind energy C. Nuclear fusion D. Geothermal energy

6. A coal-fired power station has a power output of P DQG�LWV�HIILFLHQF\�LV�İ��,W�EXUQV�D�PDVV�RI�FRDO�M every second. The best estimate of the energy density of the coal used is

A. 3İ0� � � B. P

MH

C.

MPH

D.

MPH

7. Which of the following fuels has the highest energy density?

A. Coal B. Gas C. Oil D. Uranium

102

8. Which of the following is the best estimate for the overall efficiency of a typical coal power station?

A. 5 % B. 30 % C. 60 % D. 90 %

9. The efficiency of a modern natural gas power station is approximately

A. 10 %. B. 50 %. C. 5 %. D. 90 %.

10. The design of a nuclear power station includes an electrical generator. The function of the generator is to convert

A. nuclear energy to kinetic energy.

B. kinetic energy to thermal energy.

C. thermal energy to electrical energy.

D. kinetic energy to electrical energy.

11. Which of the following correctly describes both the role of the moderator and of the control rods in a nuclear reactor?

Moderator Control rods

A. slows down the neutrons maintain a constant rate of fission

B. cools down the reactor extract thermal energy

C. cools down the reactor maintain a constant rate of fission

D. slows down the neutrons extract thermal energy

12. Critical mass refers to the amount of fissile material that

A. will allow fission to be sustained.

B. is equivalent to 235 g of uranium.

C. will produce a growing chain reaction.

D. is the minimum mass necessary for fission to take place.

13. In a nuclear power station, uranium is used as the energy source and plutonium-239 is produced. Which of the following is true?

A. Plutonium-239 is produced by nuclear fusion.

B. A moderator is used to absorb plutonium-239.

C. Control rods are used to slow down plutonium-239.

D. Plutonium-239 can be used as a fuel in another type of nuclear reactor.

14. Which of the following correctly shows the energy change in a photovoltaic cell and in a solar heating panel?

Photovoltaic cell Solar heating panel

A. VRODU�ĺ�HOHFWULFDO VRODU�ĺ�WKHUPDO

B. HOHFWULFDO�ĺ�WKHUPDO VRODU�ĺ�HOHFWULFDO

C. VRODU�ĺ�HOHFWULFDO HOHFWULFDO�ĺ�WKHUPDO

D. HOHFWULFDO�ĺ�WKHUPDO VRODU�ĺ�WKHUPDO

103

15. Water is contained in a tidal basin behind a dam. The water has a depth h at high tide and zero at low tide, as shown in the diagram.

The gravitational potential energy of the water stored in the basin between a high tide and a low tide is proportional to

A. h . B. h. C. h2. D. h3.

16. The power per unit length P of an oscillating water column (OWC) is due to the action of a surface wave of amplitude A. Which of the following correctly relates P and A, and correctly identifies the nature of the energy of the water column?

Relation between P and A Nature of energy

A. P v A kinetic

B. P v A kinetic and potential

C. P v A2 kinetic

D. P v A2 kinetic and potential

17. A wind turbine produces a power P when the wind speed is v. Assuming that the efficiency of the turbine is constant, the best estimate for the power produced when the wind speed becomes 2v is

A. 2P. B. 4P. C. 6P. D. 8P.

18. Surface X has a temperature TX and emissivity İx. Surface Y has a temperature TY and emissivity İy. The two surfaces emit radiation at the same rate.

What is the ratio Y

X

TT

?

A. 41

x

y

¸̧¹

·¨̈©

§

H

H

B.

41

y

x¸¸¹

·¨¨©

§

HH

C.

4

x

y

¸̧¹

·¨̈©

§

H

H

D.

4

y

X¸¸¹

·¨¨©

§

HH

19. The diagram shows the variation with wavelength of the power per unit wavelength I radiated from an area of 1 m2 of two different bodies.

Which of the following is a correct comparison of the temperature and of the emissivity of the two bodies?

Temperature Emissivity

A. same same

B. same different

C. different same

D. different different

104

20. What is the phenomenon that best explains why greenhouse gases absorb infrared radiation?

A. Resonance B. Interference C. Refraction D. Diffraction

21. Greenhouse gases

A. reflect infrared radiation but absorb ultraviolet radiation.

B. reflect ultraviolet radiation but absorb infrared radiation.

C. transmit infrared radiation but absorb ultraviolet radiation.

D. transmit ultraviolet radiation but absorb infrared radiation.

22. The diagram shows an energy balance climate model for a planet.

The intensities of the reflected and radiated radiation are given in terms of the incident intensity I. Which of the following is the albedo of this planet?

A. 0.15 B. 0.25 C. 0.40 D. 0.60

23. In which of the following places will the albedo be greatest?

A. A forest B. A grassland C. An ocean D. A polar ice cap

24. Large areas of rainforests are cut down and burned every year. The result of these actions is

A. reduced albedo.

B. reduced carbon fixation.

C. increased evaporation rate.

D. increased mass of atmospheric methane.

25. What is the unit of surface heat capacity?

A. J kg–1 K–1 B. J K–1 C. J m–2 K–1 D. J m–3 K–1

26. Most climate scientists agree that the enhanced greenhouse effect is due to

A. cyclical changes of the Earth’s orbit.

B. volcanic activity.

C. the burning of fossil fuels.

D. increased solar activity.

105

27. The volume of the Pacific Ocean is V DQG�WKH�YROXPH�H[SDQVLYLW\�RI�VHDZDWHU�LV�Ȗ��,I�WKH�DYHUDJH�WHPSHUDWXUH�RI�WKH�3DFLILF�2FHDQ�LQFUHDVHV�E\�¨T, what would be the fractional increase in volume of the Pacific Ocean?

A. ȖV ¨T B. TV'J

C. Ȗ¨T D.

T'J


28. This question is about fossil fuels.

(a) A Sankey diagram for the generation of electrical energy using fossil fuel as the primary energy source is shown.

(i) State what is meant by a fuel.

...........................................................................................................................

........................................................................................................................... (1)

(ii) State two examples of fossil fuels.

1. .......................................................................................................................

2. ....................................................................................................................... (2)

(iii) Explain why fossil fuels are said to be non-renewable.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iv) Use the Sankey diagram to estimate the efficiency of production of electrical energy and explain your answer.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

106

(b) Despite the fact that fossil fuels are non-renewable and contribute to atmospheric pollution there is widespread use of such fuels. Suggest three reasons for this widespread use.

1. ..................................................................................................................................

......................................................................................................................................

2. ..................................................................................................................................

......................................................................................................................................

3. ..................................................................................................................................

...................................................................................................................................... (3)

(Total 10 marks)

29. This question is about fossil fuels and the greenhouse effect.

(a) State two reasons why most of the world’s energy consumption is provided by fossil fuels.

1. ..................................................................................................................................

......................................................................................................................................

2. ..................................................................................................................................

...................................................................................................................................... (2)

(b) A power station has an output power of 500 MW and an overall efficiency of 27 %. It uses natural gas as a fuel that has an energy density of 56 MJ kg–1.

(i) Define energy density.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Determine the rate of consumption of natural gas in the power station.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(c) Outline why the enhanced greenhouse effect may result in an increase in the temperature of the Earth’s surface.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

107

(d) (i) The solar intensity at the position of the Earth is 1380 W m–2. The average albedo of Earth is 0.300. State why an average value of albedo is quoted.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Show that the average reflected intensity from the Earth is about 100 W m–2.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(e) 2QH�RI�WKH�H[SHFWHG�UHVXOWV�RI�JOREDO�ZDUPLQJ�LV�DQ�LQFUHDVHG�VHD�OHYHO��7KH�LQFUHDVH�LQ�YROXPH�ǻV IRU�D�WHPSHUDWXUH�LQFUHDVH�ǻT LV�JLYHQ�E\�ǻV �ȖVǻT. Show, using the following data, that the resulting rise in sea level is about 0.5 m.

Temperature increase = 2.0 °C Surface area of oceans on Earth = 3.6 × 108 km2 Average ocean depth = 3.0 km Ȗ = 8.8 × 10–5 K–1

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 16 marks)

30. This question is about power production and global warming.

(a) In any cyclical process designed to continuously convert thermal energy to work, some energy is always degraded. Explain what is meant by degraded energy.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

108

(b) A nuclear power station uses uranium-235 (U-235) as fuel. Outline the

(i) processes and energy changes that occur through which thermal energy is produced.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(ii) role of the heat exchanger of the reactor and the turbine in the generation of electrical energy.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(c) Identify one process in the power station where energy is degraded.

...................................................................................................................................... (1)

(d) The maximum power output of the Drax coal-fired power station in the UK is 4.0 GW. Determine the minimum mass of pure U-235 that would be required by a nuclear power station to provide the same maximum annual energy output as the Drax power station.

Energy density of U-235 = 82 TJ kg–1 1 year = 3.2 × 107 s

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(e) The Drax power station produces an enormous amount of carbon dioxide, a gas classified as a greenhouse gas. Outline, with reference to the vibrational behaviour of molecules of carbon dioxide, what is meant by a greenhouse gas.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

109

(f) It has been suggested that the production of greenhouse gases by coal-fired power stations has increased global warming. One piece of evidence to support this suggestion is the increase in sea-level due to an increase in temperature of the oceans. Over the past 100 years it is suggested that sea-levels have risen by 6.4 × 10–2 m due to volume expansion.

Using the following data, determine the average rise in temperature in the top levels of the oceans in the last 100 years.

Mean depth of oceans that is affected by global warming = 4.0 × 102 m Coefficient of volume expansion of sea water = 5.1 × 10–5 K–1

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 18 marks)

31. This question is about solar heating panels.

(a) A village consists of 120 houses. It is proposed that solar panels be used to provide hot water to the houses.

The following data are available.

average power needed per house to heat water = 3.0 kW average surface solar intensity = 650 W m–2 efficiency of energy conversion of a solar panel = 18 %

Calculate the minimum surface area of the solar panels required to provide the total power for water heating.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(b) Suggest two disadvantages of using solar power to provide energy for heating water.

1: ..................................................................................................................................

......................................................................................................................................

2: ..................................................................................................................................

...................................................................................................................................... (2)

(Total 5 marks)

110

32. This question is about a pumped-storage power station.

(a) The diagram, not to scale, shows a pumped-storage power station used for the generation of electrical energy.

Water stored in the tank is allowed to fall through a pipe to a lake via a turbine. The turbine is connected to an electrical generator. The pumped-storage ac generator system is reversible so that water can be pumped from the lake to the tank.

The tank is 50 m deep and has a uniform area of 5.0 × 104 m2. The height from the bottom of the tank to the turbine is 310 m. The density of water is 1.0 × 103 kg m–3.

(i) Show that the maximum energy that can be delivered to the turbine by the falling water is about 8 × 1012 J.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(ii) The flow rate of water in the pipe is 400 m3 s–1. Calculate the power delivered by the falling water.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(b) The energy losses in the power station are shown in the following table.

Source of energy loss Percentage loss of energy

friction and turbulence of water in pipe 27

friction in turbine and ac generator 15

electrical heating losses 5

(i) Calculate the overall efficiency of the conversion of the gravitational potential energy of water in the tank into electrical energy.

...........................................................................................................................

........................................................................................................................... (1)

111

(ii) Sketch a Sankey diagram to represent the energy conversion in the power station.

(2)

(c) The electrical power produced at the power station is transmitted by cables to the consumer.

(i) Outline how the energy losses in transmission are minimized.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(ii) State one advantage and one disadvantage that a pumped-storage system has compared to a tidal water storage system.

Advantage: .......................................................................................................

...........................................................................................................................

Disadvantage: ...................................................................................................

........................................................................................................................... (2)

(Total 13 marks)

33. This question is about wave power.

(a) Outline how the energy of a wave can be converted to electrical energy.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) A wave on the surface of water is assumed to be a square-wave of height 2A, as shown.

The wave has wavelengWK�Ȝ��VSHHG�v and has a wavefront of length L. For this wave,

112

(i) show that the gravitational potential energy EP stored in one wavelength of the wave is given by

EP = 21 A2ȜJȡ/

where ȡ is the density of the water and g is the acceleration of free fall.

...........................................................................................................................

........................................................................................................................... (3)

(ii) deduce that the gravitational wave power P per unit length of the wavefront is given by

P = 21 A2YJ�ȡ

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(c) The density of sea-water is 1.2 × 103 kg m–3. Using the expression in (b)(ii), estimate the gravitational power per metre length available in a wave of height 0.60 m.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(d) In practice a water wave is approximately sinusoidal in cross-section. Outline whether a sine wave of the same height as in (b) transfers a greater or a smaller amount of power than that derived in (b)(ii).

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 11 marks)

34. This question is about the energy balance of the Earth.

(a) The intensity of the Sun’s radiation at the position of the Earth is approximately 1400 W m–2.

Suggest why the average power received per unit area of the Earth is 350 W m–2.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

113

(b) The diagram shows a simplified model of the energy balance of the Earth’s surface.

The diagram shows radiation entering or leaving the Earth’s surface only.

The average equilibrium temperature of the Earth’s surface is TE and that of the atmosphere is TA = 242 K.

(i) Using the data from the diagram, state the emissivity of the atmosphere.

........................................................................................................................... (1)

(ii) Show that the intensity of the radiation radiated by the atmosphere towards the Earth’s surface is 136 W m–2.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)

(iii) By reference to the energy balance of the Earth’s surface, calculate TE.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(c) (i) Outline a mechanism by which part of the radiation radiated by the Earth’s surface is absorbed by greenhouse gases in the atmosphere.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

114

(ii) Suggest why the incoming solar radiation is not affected by the mechanism you outlined in (c)(i).

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) Carbon dioxide (CO2) is a greenhouse gas. State one source and one sink (object that removes CO2) of this gas.

Source: ..............................................................................................................

Sink: .................................................................................................................. (2)

(Total 13 marks) 35. This question is about the greenhouse effect.

(a) The graph shows part of the absorption spectrum of nitrogen oxide (N2O) in which the intensity of absorbed radiation A is plotted against frequency f.

(i) State the region of the electromagnetic spectrum to which the resonant frequency of nitrogen oxide belongs.

........................................................................................................................... (1)

(ii) Using your answer to (a)(i), explain why nitrogen oxide is classified as a greenhouse gas.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

115

(b) Define emissivity and albedo.

Emissivity: ...................................................................................................................

......................................................................................................................................

Albedo: ........................................................................................................................

...................................................................................................................................... (3)

(c) The diagram shows a simple energy balance climate model in which the atmosphere and the surface of Earth are two bodies each at constant temperature. The surface of the Earth receives both solar radiation and radiation emitted from the atmosphere. Assume that the Earth’s surface behaves as a black body.

The following data are available for this model.

average temperature of the atmosphere of Earth = 242 K emissivity, e of the atmosphere of Earth = 0.720 DYHUDJH�DOEHGR��Į�RI�WKH�DWPRVSKHUH�RI�(DUWK = 0.280 solar intensity at top of atmosphere = 344 W m–2

average temperature of the surface of Earth = 288 K

Use the data to show that the

(i) power radiated per unit area of the atmosphere is 140 W m–2.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) solar power absorbed per unit area at the surface of the Earth is 248 W m–2.

...........................................................................................................................

........................................................................................................................... (1)

116

(d) It is hypothesized that, if the production of greenhouse gases were to stay at its present level then the temperature of the Earth’s atmosphere would eventually rise by 6.0 K.

Calculate the power per unit area that would then be

(i) radiated by the atmosphere.

...........................................................................................................................

........................................................................................................................... (1)

(ii) absorbed by the Earth’s surface.

...........................................................................................................................

........................................................................................................................... (1)

(e) Estimate, using your answer to (d)(ii), the increase in temperature of Earth’s surface.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 14 marks) 36. This question is about wind power. The maximum theoretical wind power P for air of speed v moving normally through area A Where ȡ is the density of air is given by

3

2AvP U

(a) (i) Air of density 1.3 kg m–3 and speed of 9.0 m s–1 is incident on a wind turbine having blades of diameter 15 m. Calculate the maximum wind power incident on the turbine.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

(ii) State why it is impossible in practice to extract all of the power P in (i) from the air.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

117

(iii) State two reasons why wind turbines are not placed close to one another. 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

(b) A nuclear power station has an output power of 200 MW. It is proposed to replace the power station with a series of wind turbines each with an energy output of 750 kW. State and discuss one advantage and one disadvantage such a change might bring if this proposal was to take place. Advantage: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Disadvantage: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

118

Topic 9: Motion in fields

1. A ball is thrown horizontally from the top of a cliff. Air resistance is negligible. Which of the following diagrams best represents the subsequent path of the ball?

2. A stone is thrown at an angle to the horizontal. Ignoring air resistance, the horizontal component of the initial velocity of the stone determines the value of

A. range only. B. maximum height only.

C. range and maximum height. D. range and time of flight.

3. A stone is projected horizontally from the top of a cliff. Neglecting air resistance, which one of the following correctly describes what happens to the horizontal component of velocity and to the vertical component of velocity?

Horizontal component of velocity Vertical component of velocity


B. Decreases Constant

C. Constant Constant

D. Constant Increases

4. A ball rolls off a horizontal table with velocity v. It lands on the ground a time T later at a distance D from the foot of the table as shown in the diagram below. Air resistance is negligible.

A second heavier ball rolls off the table with velocity v. Which one of the following is correct for the heavier ball?

Time to land Distance from table

A. T D

B. T less than D

C. less than T D

D. less than T less than D

A.

C.

B.

D.

v

table

D

119

5. A projectile is fired from the ground at time t = 0. It lands back on the ground at time t = T. Which of the following sketch graphs best shows the variation with time t of the vertical speed VV and horizontal speed VH of the projectile? Air resistance is negligible.

6. Two identical metal spheres X and Y are released at the same time from the same height above the horizontal ground. Sphere X falls vertically from rest. Sphere Y is projected horizontally as shown below.

Air resistance is negligible.

Which of the following statements is correct?

A. Sphere X hits the ground before sphere Y because it travels a shorter distance.

B. Sphere Y hits the ground before sphere X because its initial velocity is greater.

C. The spheres hit the ground at the same time because horizontal motion does not affect vertical motion.

D. The spheres hit the ground at the same time because they have equal weights.

7. The diagram below shows the trajectory of a ball thrown into the air. There is no air resistance.

Which arrow gives the direction of the resultant force on the ball at the point X?

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

8. A particle is projected horizontally with speed v from a height H. It lands a horizontal distance R from the point of launch as shown in the diagram below.

A second particle is projected horizontally from the same height with speed 2v. Neglecting air resistance the horizontal distance travelled by this particle is

A. R. B. C. 2R. D. 4R.

speed

speed

speed

speed

T

T

T

T

t

t

t

t

0

0

0

0

0

0

0

0

A. B.

C. D.

VH

VH

VHVH

VV VV

VV

VV

.2R

ground

X Y

trajectory of ballX

A B

C

D

v

H

R

120

9. Which one of the following statements correctly defines the gravitational potential at a point P in a gravitational field?

A. The work done per unit mass in moving a small mass from point P to infinity.

B. The work done per unit mass in moving a small mass from infinity to point P.

C. The work done in moving a small mass from infinity to point P.

D. The work done in moving a small mass from point P to infinity.

10. An isolated point object has mass M. A second small point object of mass m is placed a distance x from the larger mass.

Which one of the following is a correct expression for the gravitational potential energy of the mass m?

A.

B.

C.

D.

11. The centres of two isolated spherical stars each of mass M and radius R are separated by a distance d as shown in the diagram below.

The distance d is very large compared to R. Point X is mid-way between the stars. The gravitational potential at point X due to the two stars is

A.

B.

C.

D. zero.

12. Which of the following diagrams best represents the gravitational equipotential surfaces due to two equal spherical masses?

13. The escape speed from a planet is defined as the speed at which an object must leave the planet’s surface to

A. escape completely from the gravitational field of the planet.

B. enter a geostationary orbit about the planet.

C. escape from the atmosphere of the planet.

D. overcome the gravitational force of the planet.

xGM

�x

GMm�

2xGM

� 2xGMm

�

X

M

R

M

R

d

.4d

GM� .2

RGM

� .d

GM�

121

14. The escape speed of an object of mass m from a planet of mass M and radius r depends on the gravitational constant and

A. M and r. B. m and r. C.M only. D. M, m, and r.

15. A planet is in a circular orbit of radius r about a star. The period of the planet in its orbit is T. A second planet orbits the same star in a circular orbit of radius rS.

Which of the following is a correct expression for the period of the second planet in its orbit about the star?

A.

B.

C.

D.

16. Two satellites, X and Y, move in circular orbits about the Earth. The orbital period of satellite X is eight times that of satellite Y.

The ratio

A. 2. B. 4. C. 8. D. 16.

17. A powered spaceship is moving directly away from a planet as shown below.

At point P the motors of the spaceship are switched off but the spaceship remains under the influence of the planet. Which one of the following graphs best represents the variation with time t of the velocity v of the spaceship after it passes point P?

18. Which one of the following graphs best shows the variation of the total energy E of a satellite orbiting the Earth with distance r from the centre of the Earth? (The radius of the Earth is R.)

23

S Trr¸¹

·¨©

§ Trr 2

3

S ¸¹

·¨©

§ 32

S Trr¸¹

·¨©

§ 23

S Trr¸¹

·¨©

§

isY satellite of radius orbitalX satellite of radius orbital

B. E

r0

0

r = R

A. E

r0

0

r = R

D. E

r0

0

r = R

C. E

r0

0

r = R

planet Spaceship

P

v v

v v

t t

t t

0 0

0 0

0 0

0 0

A. B.

C. D.

122

19. A satellite is in orbit about Earth. The satellite moves to an orbit closer to Earth. Which of the following correctly gives the change in the potential energy and the kinetic energy of the satellite?

change in potential energy change in kinetic energy


B. Decreases Decreases

C. Increases Increases

D. Increases Decreases

20. A spacecraft orbits Earth. An astronaut inside the spacecraft feels “weightless” because

A. the gravitational field in the spacecraft is negligible.

B. the Earth exerts equal forces on the spacecraft and the astronaut.

C. the spacecraft and the astronaut have the same acceleration towards the Earth.

D. the spacecraft and the astronaut exert equal and opposite forces on each other.

21. Which of the following correctly describes the nature of electric potential and electric field strength?

Potential Field strength

A. Scalar Scalar

B. Scalar Vector

C. Vector Scalar

D. Vector Vector

22. The diagram shows the electric field lines produced by an electrostatic focussing device.

Which one of the following diagrams best shows the corresponding equipotential lines? The electric field lines are shown as broken lines on each of the diagrams.

A. B.

C. D.

123

23. The diagram below shows two lines of equipotential in a region of a uniform electric field. Line X has a potential of +50 V and line Y has a potential of +100V. The distance between X and Y is 2.0 cm.

Which one of the following correctly gives the direction of the electric field and its strength?

Direction Strength / V cm–1

A. X ĺY 25

B. X ĺ Y 100

C. Y ĺX 25

D. Y ĺ X 100

24. An isolated conducting sphere of radius r is positively charged.

Which one of the following graphs best shows the variation with distance x from the centre of the sphere of the electric potential V?

25. Which one of the following statements about electric potential gradient is correct?

A. Electric potential gradient is numerically equal to the gradient of the electric field.

B. Electric potential gradient at a point is numerically equal to the electric field strength at that point.

C. When one joule of work is done in moving one coulomb of charge between two points, the electric potential gradient between the points is one volt per metre.

D. When one joule of work is done in moving one coulomb of charge to a point, the electric potential gradient at that point is one volt per metre.

26. The diagram below shows the electric field lines in a region of space. A positively charged particle moves from P to Q.

Which of the following is correct?

Change in potential energy of particle Change in potential between P and Q

A. decreases zero

B. decreases negative

C. increases zero

D. increases negative

V

V

V

V

0

0

0

0

0

0

0

0

r

r

r

r

x

x

x

x

A.

C.

B.

D.

+50 V +100 V

X Y

2.0 cm

P Q

124


27. This question is about trajectory motion.

Antonia stands at the edge of a vertical cliff and throws a stone upwards at an angle of 60° to the horizontal.

The stone leaves Antonia’s hand with a speed v = 8.0 m s–1. The time between the stone leaving Antonia’s hand and hitting the sea is 3.0 s.

The acceleration of free fall g is 10 m s–2 and all distance measurements are taken from the point where the stone leaves Antonia’s hand.

Ignoring air resistance calculate

(a) the maximum height reached by the stone.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

(b) the horizontal distance travelled by the stone.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(Total 5 marks)

Sea

v = 8.0ms –1

60°

125

28. Linear motion

At a sports event, a skier descends a slope AB. At B there is a dip BC of width 12 m. The slope and dip are shown in the diagram below. The vertical height of the slope is 41 m.

The graph below shows the variation with time t of the speed v down the slope of the skier.

The skier, of mass 72 kg, takes 8.0 s to ski, from rest, down the length AB of the slope.

(a) Use the graph to

(i) calculate the kinetic energy EK of the skier at point B.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(ii) determine the length of the slope.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (4)

A

B C D

41m

slope

(not to scale)

1.8m

dip 12m

25.0

20.0

15.0

10.0

5.0

0.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0

v / ms –1

t / s

126

(b) (i) Calculate the magnitude of the change 'EP in the gravitational potential energy of the skier between point A and point B.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(ii) Use your anwers to (a)(i) and (b)(i) to determine the ratio

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(iii) Suggest what this ratio represents.

.........................................................................................................................

......................................................................................................................... (1)

(c) At point B of the slope, the skier leaves the ground. He “flies” across the dip and lands on the lower side at point D. The lower side C of the dip is 1.8 m below the upper side B.

(i) Calculate the time taken for an object to fall, from rest, through a vertical distance of 1.8 m. Assume negligible air resistance.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(ii) The time calculated in (c)(i) is the time of flight of the skier across the dip. Determine the horizontal distance travelled by the skier during this time, assuming that the skier has the constant speed at which he leaves the slope at B.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(Total 15 marks)

� �.

P

KP

EEE

'�'

127

29. This question is about gravitation.

(a) (i) Define gravitational potential at a point in a gravitational field.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(ii) Explain why values of gravitational potential have negative values.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

The Earth and the Moon may be considered to be two isolated point masses. The masses of the Earth and the Moon are 5.98 × 1024kg and 7.35 × 1022 kg respectively and their separation is 3.84 × 108 m, as shown below. The diagram is not to scale.

(b) (i) Deduce that, at point P, 3.46 × 108m from Earth, the gravitational field strength is approximately zero.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (3)

(ii) 7KH�JUDYLWDWLRQDO�SRWHQWLDO�DW�3�LV�í��î��6 J kg–1. Calculate the minimum speed of a space probe at P so that it can escape from the attraction of the Earth and the Moon.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (3)

(Total 10 marks)

Earth Moonmass 5 98 10. kg 24 mass 7 35 10. kg22

P

3 84 10. m8

128

30. Gravitation

The diagram below illustrates the planet Saturn.

Saturn has several rings, each of which consists of many small particles that orbit the planet. Saturn may be considered to be a sphere with its mass M concentrated at its centre.

(a) Deduce that, for a particle in one ring moving in a circular orbit of radius R, the linear speed v of the particle in its orbit is given by the expression

GM = Rv2.

Explain your reasoning.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(b) One ring, the A ring, has an outer diameter of 2.72 × 108 m. The mass of Saturn is 5.69 × 1026 kg. A particle orbits on the outer edge of this ring. Determine the time for the particle to complete one orbit of Saturn.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (3)

(c) Another particle of mass m is orbiting at a distance r from the centre of Saturn.

(i) State a formula, in terms of G, M, m and r for the gravitational potential energy EP of the particle.

......................................................................................................................... (1)

(ii) The gravitational potential energy of this particle decreases. Suggest and explain the change, if any, in the linear speed of the particle.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

Saturn

2.72 10 8m

A ring

129

(d) Explain the concept of escape speed.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(e) A planet has radius R and the acceleration of free fall at its surface is g. The planet may be considered to be a sphere with its mass concentrated at its centre.

Deduce that the escape speed ves is given by the expression

Explain your working and state one assumption that is made in the derivation.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (4)

(f) Calculate the escape speed for a spherical planet of radius 1.7 × 103 km having an acceleration of free fall at its surface of 1.6 m s–2.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(g) The mean kinetic energy EK, in joule, of helium-4 atoms at thermodynamic temperature T is given by the expression

EK = 2.1 × 10–23 T.

Determine the surface temperature of the planet such that helium-4 atoms on the surface of the planet have the escape speed calculated in (f).

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(h) Suggest one reason why, at temperatures below that calculated in (g), helium will escape from the planet.

...................................................................................................................................

................................................................................................................................... (1)

(Total 19 marks)

� �.2es gRv

130

31. This question is about the electric potential due to a charged sphere.

(a) Define electric potential at a point in an electric field.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (3)

The diagram below shows an isolated, metal sphere in a vacuum that carries a negative electric charge of 9.0 nC.

(b) On the diagram above draw

(i) arrows to represent the electric field pattern in the region outside the charged sphere. (3)

(ii) lines to represent three equipotential surfaces in the region outside the sphere. The potential differences between the lines are to be equal in value.

(2)

(c) Explain how the lines representing the equipotential surfaces that you have sketched indicate that the strength of the electric field is decreasing with distance from the centre of the sphere.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(d) The electric field strength at all points inside the conductor is zero. On the axes below, draw a graph to show the variation with distance r from the centre of the sphere of the potential V. The dotted line is drawn at r = a where a is the radius of the sphere. (Note: this is a sketch graph; you do not need to add values to the axes.)

(2)

–

00

V

ra

131

(e) The electric field strength at the surface of the sphere and at points outside the sphere may be determined by assuming that the sphere acts as though a point charge of magnitude 9.0 nC is situated at its centre. The radius of the sphere is 4.5 × 10–2 m. Deduce that the potential at the surface of the sphere is –1800 V.

.....................................................................................................................................

..................................................................................................................................... (1)

An electron is initially at rest at the surface of the sphere.

(f) (i) Describe the path followed by the electron as it leaves the surface of the sphere.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Determine the speed of the electron when it reaches a point a distance 0.30 m from the centre of the sphere.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(Total 18 marks)

132

Topic 10: Thermal physics

1. Two identical boxes X and Y each contain an ideal gas.

Box X Box Y

n moles

temperature T

pressure PX

2n moles

temperature

pressure PY

In box X there are n moles of the gas at temperature T and pressure PX. In box Y there are 2n moles of

the gas at temperature and pressure PY.

The ratio is

A. . B. . C. 2. D. 3.

2. The equation of state for an ideal gas, pV = nRT, describes the behaviour of real gases

A. only at low pressures and large volumes.

B. only at high temperatures.

C. only at large volumes and large pressures.

D. at all pressures and volumes.

3. The equation of state of an ideal gas is

pV = nRT.

In this equation, the constant n is the number of

A. atoms in the gas. B.molecules in the gas. C.particles in the gas. D.moles of the gas.

4. An ideal gas is kept in a container of fixed volume at a temperature of 30�C and a pressure of 6.0 atm. The gas is heated at constant volume to a temperature of 330�C.

The new pressure of the gas is about

A. 0.60 atm. B. 3.0 atm. C. 12 atm. D. 66 atm.

3T

3T

Y

X

PP

32

23

pressure 6.0 atm

temperature 30 C°

gas

new pressure

temperature 330 C°

gas

133

5. The graph below shows the variation with absolute temperature T of the pressure p of one mole of an ideal gas having a volume V. R is the molar gas constant.

Which of the following is the best interpretation of the intercept on the temperature axis and the gradient of the graph?

Intercept on temperature axis / K Gradient of graph

A. – 273

B. 0

C. 0

D. – 273

6. When a gas in a thermally insulated cylinder is suddenly compressed, the change of state is

A. adiabatic. B. isothermal. C. isobaric. D. isochoric.

7. The diagram shows the variation with volume V of pressure p during one complete cycle of a heat engine.

The work done is represented by the area

A. A. B. B. C. (B + A). D. (B – A).

8. The first law of thermodynamics may be expressed in terms of the quantities below.

'U, the increase in the internal energy of the system Q, the energy transferred to the system by heating W, the work done on the system

Which one of the following is a correct statement of the law?

A. W = 'U + Q

B. W �í'U í�Q

C. W = 'U í�Q

D. W �í'U + Q

p

T

VR

VR

RV

RV

B

Ap

V

1

23

00

134

9. The graph below shows the variation with volume of the pressure of a system.

The work done in compressing the gas from R to P is

A. 5.0 × 105 J. B. 4.5 × 105 J. C. 3.0 × 105 J. D. 0.

10. A sample of an ideal gas is held in an insulated container and it undergoes an adiabatic change. The graph below shows the change in pressure p with change in volume V as the gas changes from X to Y.

Which of the following describes correctly the work done and the change in the internal energy of the gas?

Work done Internal energy

A. on the gas increases

B. on the gas decreases

C. by the gas decreases

D. by the gas increases

11. The graph below shows the variation with volume V of the pressure p of a gas during one cycle of an engine.

During which operations, PQ, QR, RS and SP does the gas do external work?

A. PQ only

B. RS only

C. QR and RS only

D. PQ and RS only

5

4

3

2

1

00 1 2 3 4 5 6

Volume / m

Pressure / 10 Pa5

3

P

Q

R

p

V

Y

X

S

R

P

Q

V

p

135

12. The entropy of a system is a measure of the system’s

A. disorder. B. mean energy. C. temperature. D. total energy.

13. The second law of thermodynamics states that the entropy of the universe is

A. increasing. B. decreasing. C. zero. D. constant but not zero.

14. An operating refrigerator with its door open is placed in a thermally insulated room.

The refrigerator operates for a long period of time. Which of the following correctly gives the change in temperature and the entropy of the air in the room?

Temperature Entropy

A. Increases Increases

B. Increases Decreases

C. Decreases Decreases

D. Decreases Increases

15. A well-insulated container is divided into two equal volumes by a wall. In one half there is an ideal gas and the other is a vacuum as shown below.

The wall is now removed. Which one of the following correctly gives the changes, if any, that take place in the internal energy and entropy of the gas?

Internal energy Entropy

A. stays the same stays the same

B. stays the same increases

C. decreases stays the same


gas vacuum gas

136

16. Boiling water in a beaker is heated continuously. Steam escapes into the surroundings.

Which of the following correctly lists the entropy changes of the boiling water and the surroundings?

boiling water surroundings

A. increases constant

B. increases increases

C. decreases constant



17. Expansion of a gas

An ideal gas at an initial pressure of 4.0 ×105 Pa is expanded isothermally from a volume of 3.0 m3 to a volume of 5.0 m3.

(a) Calculate the final pressure of the gas.

...................................................................................................................................

................................................................................................................................... (1)

(b) On the axes below draw a sketch graph to show the variation with volume V of the pressure p during this expansion.

(3)

(c) Use the sketch graph in (b) to

(i) estimate the work done by the gas during this process;

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

p / 10 Pa� 5

6

4

2

0 0 2 4 6 / m 3

137

(ii) explain why less work would be done if the gas were to expand adiabatically from the same initial state to the same final volume.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (1)

(Total 7 marks)

18. This question is about thermodynamic processes.

(a) State what is meant by the concept of internal energy of an ideal gas.

...................................................................................................................................

................................................................................................................................... (1)

(b) The diagram below shows the variation with volume of the pressure of a fixed mass of an ideal gas.

The change from B to C is an isothermal change at 546 K. At point A, the pressure of the gas is 1.01 × 105 Pa, the volume of the gas is 22.0 m3 and the temperature of the gas is 273 K.

(i) State the temperature of the gas at point C;

......................................................................................................................... (1)

(ii) Calculate the volume of the gas at point C.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(c) For the change from B to C, 31.5 × 105 J of thermal energy is transferred to the gas.

(i) State the work done in the change from A to B.

......................................................................................................................... (1)

pressure

0

B

A C

0 volume

138

(ii) Determine the work done during the change C to A.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(iii) Explain whether the work in (ii) is done by the gas or on the gas.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(iv) Determine the work done by the gas during one cycle ABCA.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(Total 11 marks)

19. This question is about thermodynamic processes.

(a) Distinguish between an isothermal process and an adiabatic process as applied to an ideal gas.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

An ideal gas is held in a container by a moveable piston and thermal energy is supplied to the gas such that it expands at a constant pressure of 1.2 × 105 Pa.

The initial volume of the container is 0.050 m3 and after expansion the volume is 0.10 m3. The total energy supplied to the gas during the process is 8.0 × 103 J.

(b) (i) State whether this process is either isothermal or adiabatic or neither.

........................................................................................................................... (1)

pistonthermal energy

139

(ii) Determine the work done by the gas.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (1)

(iii) Hence calculate the change in internal energy of the gas.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 6 marks)

20. Thermodynamics

The graph below shows the variation with volume V of the pressure p for two isothermal changes of two ideal gases X and Y. The gases have the same number of moles. The dots indicate two particular states of the gases, (pX, VX) and (pY, VY).

V

(a) State what is meant by an isothermal change.

...................................................................................................................................

................................................................................................................................... (1)

pX Y

00 V V

pX

pY

X Y

140

(b) Explain whether gas X in the state (pX, VX) is at a higher or lower temperature than gas Y in the state (pY, VY).

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(c) Gas Y is compressed adiabatically from state (pY, VY) until it reaches the pressure pX.

(i) Explain whether the temperature of gas Y will increase, decrease or stay the same during this process.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (3)

(ii) On the graph opposite, draw a line to represent this adiabatic compression of gas Y. (3)

(d) On the graph opposite, shade the area that represents the work done when gas X is compressed isothermally from volume VY to volume VX.

(2) (Total 11 marks)

21. This question is about entropy changes.

(a) State what is meant by an increase in entropy of a system.

.....................................................................................................................................

..................................................................................................................................... (1)

(b) State, in terms of entropy, the second law of thermodynamics.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(c) When a chicken develops inside an egg, the entropy of the egg and its contents decreases. Explain how this observation is consistent with the second law of thermodynamics.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(Total 5 marks)

141

Topic 11: Wave phenomena

1. Standing waves in an open pipe come about as a result of

A. reflection and superposition. B. reflection and diffraction.

C. superposition and diffraction. D. reflection and refraction.

2. Which one of the following is correct for transfer of energy along a standing wave and for amplitude of vibration of the standing wave?

Transfer of energy along a standing wave

Amplitude of vibration of the standing wave

A. None Constant amplitude

B. None Variable amplitude

C. Energy is transferred Constant amplitude

D. Energy is transferred Variable amplitude

3. A string with both ends fixed is made to vibrate in the second harmonic mode as shown by the dashed lines in the diagram below.

The solid line shows a photograph of the string at a particular instant of time. Two points on the string have been marked P and Q.

Which of the following correctly compares both the period of vibration of P and Q and the average speed of P and Q?

Period Average speed

A. same same

B. same different

C. different same

D. different different

4. For a standing wave, all the particles between two successive nodes have the same

A. amplitude only. B. frequency only. C. amplitude and frequency. D. frequency and energy.

P

Q

142

5. The diagram below represents the fundamental (first harmonic) standing wave of sound inside a pipe.

Which of the following correctly represents the displacement of the air at P and Q?

6. A pipe, open at both ends, has a length L. The speed of sound in the air in the pipe is v. The frequency of vibration of the fundamental (first harmonic) standing wave that can be set up in the pipe is

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

7. A tube is filled with water and a vibrating tuning fork is held above its open end.

The tap at the base of the tube is opened. As the water runs out, the sound is loudest when the water level is a distance x below the top of the tube. A second loud sound is heard when the water level is a distance y below the top. Which one of the following is a correct expression for the wavelength O of the sound produced by the tuning fork?

A. O = yB. O = 2xC. O = y í�xD. O = 2(y í�x)

8. The diagrams below show two standing wave patterns that are set up in a stretched string fixed at both ends. The frequency of pattern 1 is f1 and that of pattern 2 is f2.

The ratio is

A. . B. . C. 3. D. 6.

9. A vibrating tuning fork is held above the top of a tube that is filled with water. The water gradually runs out of the tube until a maximum loudness of sound is heard.

Which of the following best shows the standing wave pattern set up in the tube at this position?

A.

B.

C.

D.

P Q

Lv

2 vL2 L

v4v

L4

pattern 1

pattern 2

frequency f1

frequency f2

2

1

ff

31

32

pipe

P Q

x

y

tuning fork

water

tap

A. B. C. D.

143

10. Which of the following is a correct description of the Doppler effect?

A. Change in frequency of light due to motion of the source of light.

B. Change in frequency of light due to relative motion between the source of light and the observer.

C. Change in observed frequency of light due to relative motion between the source of light and the observer.

D. Change in observed frequency of light due to change in velocity of the source of light.

11. Which one of the following diagrams best represents wavefronts produced by a source of sound of constant frequency as it moves at constant speed towards a stationary observer at O?

12. A source of sound moves directly towards a stationary observer. The frequency of the sound detected by the observer is different from the source frequency because

A. the loudness of the sound increases as the source moves towards the observer.

B. the apparent wavelength of the sound is longer.

C. the speed of sound relative to the observer is increased.

D. the apparent wavelength of the sound is shorter.

13. A source of sound emits waves of wavelength Ȝ, period T and speed v when at rest. The source moves away from a stationary observer at speed V, relative to the observer. The wavelength of the sound waves, as measured by the observer is

A. Ȝ + vT. B. Ȝ – vT. C. Ȝ +VT. D. Ȝ – VT.

14. A sound emitting source moves along a straight line with speed v relative to an observer at rest.

The speed of sound relative to the medium is c. The observer measures the speed of sound emitted by the source as

A. c. B. c + v. C. c – v. D. v – c.

O

O

O

O

A.

C.

B.

D.

v

Observer

144

15. A stationary source emits sound of frequency f0. An observer is moving towards the source at constant speed along the path indicated by the dotted line. The observer passes very close to the source at time T.

Which one of the following graphs best shows the variation with time t of the frequency f heard by the observer?

16. The phenomenon of diffraction is associated with

A. sound waves only. B. light waves only. C. water waves only. D. all waves.

17. Two binary stars emit radio waves of wavelength 6.0 × 10í2 m. The waves are received by a radio telescope whose collecting dish has a diameter of 120 m. The two stars are just resolved if their minimum angular separation in radians is of the order of

A. 2 × 104. B. 2 × 102. C. 5 × 10–2. D. 5 × 10–4. 18. Unpolarized light of intensity I0 is incident on a polarizer. The transmitted light is then incident on a

second polarizer. The axis of the second polarizer makes an angle of 60" to the axis of the first polarizer.

The cosine of 60� is The intensity of the light transmitted through the second polarizer is

A. I0. B.

C.

D.

observer

stationary source

A. f

f0

B. f

f0

T t T t

C. f

f0

D. f

f0

T t T t

.21

.20I .

40I .

80I

145

19. Light is diffracted at a single slit. Which of the following graphs best represents how the intensity I of the diffracted light varies with the diffraction angle ș?

A.

B.

C.

D.

20. $�SDUDOOHO�EHDP�RI�PRQRFKURPDWLF�OLJKW�RI�ZDYHOHQJWK�Ȝ�SDVVHV�WKURXJK�D�VOLW�RI�ZLGWK�b. After passing through the slit the light is incident on a distant screen. The angular width of the central maximum is

A. 2 radians. B. radians. C. 2 degrees. D. degrees.

bO

bO

bO

bO

146

21. A beam of coherent light is incident on a single slit of width b. After passing through the slit, the light is incident on a screen at a distance D from the slit.

Which of the following changes, carried out separately, in respect of b and D will result in an increase in width of the first diffraction maximum formed on the screen?

b D

A. decrease increase

B. increase increase

C. decrease decrease

D. increase decrease

22. The images of two sources are just resolved. Which of the following is a correct statement of the Rayleigh criterion for this situation?

A. The central maximum of the diffraction pattern of one source must coincide with the central maximum of the diffraction pattern of the other source.

B. Light from the sources must pass through a circular aperture.

C. Light from the sources must be coherent.

D. The first minimum of the diffraction pattern of one source must coincide with the central maximum of the diffraction pattern of the other source.

23. The diagram below shows two identical filament lamps separated by a small distance. Light from the lamps is incident on a narrow slit behind a green filter. The slit is parallel to the filament of each lamp. A photograph is taken of the lamps through the slit. The images of the filaments on the photograph are just resolved.

The green filter is replaced by a red filter and then by a violet filter. For each filter a photograph is taken of the lamps through the slit. Which of the following correctly describes the resolution of the images using a red and using a violet filter?

Red filter Violet filter

A. resolved resolved

B. resolved not resolved

C. not resolved resolved

D. not resolved not resolved

24. In an electron microscope, high energy electrons are used in order to increase the

A. interference effects. B. diffraction effects.

C. resolving power of the microscope. D. magnifying power of the microscope.

25. Two galaxies with an angular separation at the observer of 5.0 × 10–4 radians are observed with a radio telescope. Both galaxies emit radio waves of wavelength 2.5 × 10–2 m.

The images of the galaxies are just resolved by the telescope. The diameter of the circular collecting dish of the telescope is

A. 61 m. B. 50 m. C. 30 m. D. 25 m.

147

26. The diagram represents a beam of unpolarized light incident on a diamond.

The refractive index of the diamond is n.

At an angle șp, the beam reflected from the diamond is plane polarized normal to the page. The angle șp is

A. tan–1 n. B. tan–1 . C. sin–1 . D. cos–1 .

27. An optically active substance

A. completely absorbs polarized light. B. unpolarizes polarized light.

C. polarizes unpolarized light. D. rotates the plane of polarization.

28. Horizontally polarized light is transmitted through a polarizer whose transmission axis is horizontal. The light enters a container with a sugar solution and is then incident on a second polarizer whose transmission axis is vertical.

When the second polarizer is rotated by a small angle, no light is transmitted through the second polarizer. The explanation for this observation is that the sugar solution

A. causes destructive interference.

B. rotates the plane of polarization of light.

C. can only transmit vertically polarized light.

D. refracts light so no light is incident on the second polarizer.

29. In a monochromatic liquid crystal display (LCD), such as those used in calculators, the purpose of the liquid crystal is to

A. change colour from white to black when a segment is to be displayed.

B. lubricate the small gap between the plates to prevent overheating.

C. rotate the plane of polarization of the light passing through it.

D. act as a conducting pathway between the segment electrodes.

¸¹·

¨©§

n1

¸¹·

¨©§

n1

¸¹·

¨©§

n1

148


1. This question is about some properties of waves associated with the principle of superposition.

Stationary (standing) waves and resonance

(a) State two ways in which a standing wave differs from a continuous wave.

1. .........................................................................................................................

.........................................................................................................................

2. .........................................................................................................................

......................................................................................................................... (2)

(b) State the principle of superposition as applied to waves.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(c) A stretched string is fixed at one end. The other end is vibrated continuously to produce a wave along the string. The wave is reflected at the fixed end and as a result a standing wave is set up in the string.

The diagram below shows the displacement of the string at time t = 0. The dotted line shows the equilibrium position of the string.

(i) The period of oscillation of the string is T. On the diagrams below, draw sketches of the

displacement of the string at time and at time

4Tt .

2Tt

4Tt

free end

fixed end

149

(2)

(ii) Use your sketches in (i) to explain why the wave in the string appears to be stationary.

.........................................................................................................................

......................................................................................................................... (2)

(d) Stationary waves are often associated with the phenomenon of resonance.

(i) Describe what is meant by resonance.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(ii) On 19 September 1985 an earthquake occurred in Mexico City. Many buildings that were about 80 m tall collapsed whereas buildings that were taller or shorter than this remained undamaged. Use the data below to suggest a reason for this.

period oscillation of an 80 m tall building = 2.0 s

speed of earthquake waves = 6.0 × 103 m s–1

average wavelength of the waves = 1.2 × 104 m

.........................................................................................................................

......................................................................................................................... (3)

(Total 13 marks)

2. This question is about standing waves.

(a) State two properties of a standing (stationary) wave.

1. ..................................................................................................................................

......................................................................................................................................

2. ..................................................................................................................................

...................................................................................................................................... (2)

2Tt

150

(b) The diagram shows an organ pipe that is open at one end.

The length of the pipe is l. The frequency of the fundamental (first harmonic) note emitted by the pipe is 16 Hz.

(i) On the diagram, label with the letter P the position along the pipe where the amplitude of oscillation of the air molecules is the largest.

(1)

(ii) The speed of sound in the air in the pipe is 330 m s–1. Calculate the length l.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(c) Use your answer to (b)(ii) to 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.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 8 marks) 3. This question is about the Doppler effect.

A stationary loudspeaker emits sound of frequency of 1000 Hz. Nadine attaches the loudspeaker to a string.

She moves the loudspeaker in a horizontal circle above her head at a speed of 30 m s–1. The speed of sound in

air is 330 m s–1. An observer is standing well away from Nadine. (a) Explain why the sound heard by the observer changes regularly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .[3] (b) Determine the maximum frequency of the sound heard by the observer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .[3]

151

4. This question is about the Doppler effect.

At one point in an artery, blood cells flow along the axis of the artery with speed v, as shown.

ultrasound beam frequency 4.5 MHz

blood cell

v 40�

artery wall

A parallel beam of ultrasound of frequency 4.5 MHz is incident on the artery at an angle of 400.

The speed of ultrasound in the body tissues is c = 1.5 ×103 m sí1. The ultrasound detected after reflection from the blood cells is found to be Doppler-shifted in frequency by 740 Hz. The expression for the Doppler shift ¨f of the ultrasound of frequency f may be assumed to be

¨f = (2 fv cosș )

. c

(a) For this stated expression, explain the inclusion of

(i) the factor of 2.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

(ii) the factor cosș.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

(b) Determine a value for the speed of the blood cells in the artery.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

152

5. This question is about diffraction and resolution.

(a) 3ODQH�ZDYHIURQWV�RI�PRQRFKURPDWLF�OLJKW�RI�ZDYHOHQJWK�Ȝ�DUH�LQFLGHQW�RQ�D�QDUURZ�VOLW� After passing through the slit they are incident on a screen placed a large distance from the slit.

The width of the slit is b and the point X is at the centre of the slit. The point M on the screen is the position of the first minimum of the diffraction pattern formed on the screen. The path difference between light from the top edge of the slit and light from the bottom edge of the slit is l.

Use the diagram to explain why the distance l is equal to Ȝ.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

The wavefronts in (a) are from a monochromatic point source S1. Diagram 1 is a sketch of how the intensity of the diffraction pattern formed by the single slit varies with angle ș. The units on the vertical axis are arbitary.

Diagram 1

153

Another identical point source S2 is placed close to S1 as shown in diagram 2.

Diagram 2

(b) The diffraction patterns formed by each source are just resolved.

On diagram 1 sketch the intensity distribution of the light from source S2. (2)

(c) Outline how the Rayleigh criterion affects the design of radio telescopes.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(d) The dish of the Arecibo radio telescope has a diameter of 300 m. Two distant radio sources are 2.0 × 1012 m apart. The sources are 3.0 × 1016 m from Earth and they emit radio waves of wavelength 21 cm. Determine whether the radio telescope can resolve these sources.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 10 marks)

6. This question is about polarization.

(a) State what is meant by polarized light.

......................................................................................................................................

...................................................................................................................................... (1)

154

(b) Unpolarized light is incident on the surface of a plastic. The angle of incidence is ș. The reflected light is viewed through an analyser whose transmission axis is vertical.

The variation with ș of the intensity I of the transmitted light is shown in the graph.

(i) Explain why there is an angle of incidence, for which the intensity of the transmitted light is zero.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Calculate the refractive index of the plastic.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(c) Unpolarized light from a source is split, so that there is a path difference of half a wavelength between the two beams.

155

A lens brings the light to focus at point P on a screen. The lens does not introduce any additional path difference.

State and explain whether any light would be observed at P, in the case in which the polarizers have their transmission axes

(i) parallel.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) at right angles to each other.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 9 marks)

7. This question is about polarized light.

(a) Distinguish between polarized and unpolarized light.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) A beam of plane polarized light of intensity I0 is incident on an analyser. The direction of the beam is at right angles to the plane of the analyser.

The angle between the transmission axis of the analyser and the plane of polarization of the light is ș. In the position shown the transmission axis of the analyser is parallel to the plane of polarization of the light (ș�= 0).

On the axes, sketch a graph to show how the intensity I of the transmitted light varies with ș�as the

156

analyser is rotated through 180°.

(2)

(Total 4 marks)

8. (a) State what is meant by unpolarized light.

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

(b) A beam of unpolarized light of intensity 1.0 Wm–2 is incident on an ideal polarizing filter.

State the value of the intensity of the transmitted light. Explain your answer.

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

(c) Outline how polarized light may be used to measure the concentration of a sugar solution.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

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

157

Topic 12: Electromagnetic induction

1. A conductor in the shape of a solid square is moving with constant velocity in a region of magnetic field as shown in the diagram below.

The direction of the field is into the plane of the page.

Which of the following diagrams correctly represents the separation of the induced charges?

2. A uniform magnetic field of strength B completely links a coil of area S. The field makes an angle I to the plane of the coil.

The magnetic flux linking the coil is

A. BS. B. BS cos I.

C. BS sin I. D. BS tan I.

3. Faraday’s law of electromagnetic induction states that the induced emf is

A. proportional to the change in magnetic flux linkage.

B. proportional to the rate of change of magnetic flux linkage.

C. equal to the change in magnetic flux linkage.

D. equal to the change of magnetic flux.

4. The magnetic flux ĭ through a coil having 500 turns varies with time t as shown below.

The magnitude of the emf induced in the coil is

A. 0.25 V.

B. 0.50 V.

C. 250 V.

D. 1 000 V

velocity

conductor

magnetic field into page

+++

+++

+++

+++

–––

–––

–

–

–

–

–

–

A. B. C. D.

area S

B

158

5. The variation with time t of the magnetic flux ĭ through a coil is shown below.

Which of the following diagrams best shows the variation with time t of the emf E induced in the coil?

6. A magnetic field links a closed loop of metal wire. The magnetic field strength B varies with time t as shown.

A current is induced in the loop during the time period

A. t1 only. B. t2 only. C. t2 and t3 only. D. t1 and t3 only.

7. The north pole of a permanent bar magnet is pushed along the axis of a coil as shown below.

The pointer of the sensitive voltmeter connected to the coil moves to the right and gives a maximum reading of 8 units. The experiment is repeated but on this occasion, the south pole of the magnet enters the coil at twice the previous speed.

Which of the following gives the maximum deflection of the pointer of the voltmeter?

A. 8 units to the right B. 8 units to the left

C. 16 units to the right D. 16 units to the left

0 0

0 0

0 0

0 0

t t

t t

A. B.

C. D.

E E

E E

1 2 3t t tB

00 t

V

N Saxis of coil

0 0 t

159

8. The diagram below shows two concentric loops lying in the same plane.

The current in the inner loop is clockwise and increases with time as shown in the graph below.

The induced current in the outer loop is

A. constant in the clockwise direction.

B. constant in the anticlockwise direction.

C. variable in the clockwise direction.

D. variable in the anticlockwise direction.

9. The diagram shows a coil of wire wound on an iron core.

When the switch is closed, the ammeter reading gradually increases from zero to a maximum value. What is the explanation for this gradual growth of current?

A. An e.m.f. is induced in the coil.

B. The e.m.f. of the battery is increasing.

C. The iron core has a very low resistance.

D. The battery has a large internal resistance.

10. A resistor is connected in series with an alternating current supply of negligible internal resistance. The peak value of the supply voltage is Vo and the peak value of the current in the resistor is I0. The average power dissipation in the resistor is

A. B.

C. . D. 2 .

11. A lamp of resistance R is connected in series to a source of alternating voltage. The rms value of the voltage is 20 V. The variation with time t of the power P dissipated in the light bulb is shown below.

The best estimate for the value of the resistance of the filament of the lamp is

A. 4.0 :. B.

C. 8.0 :. D.

200 IV

200 IV

00IV 00IV

.ȍ20.4

.ȍ20.8

inner loop

outer loop

current

0 0 time

A

P / W

100

80

60

40

20

00 t

160

12. The diagram below shows the variation with time t of the emf E generated in a coil rotating in a uniform magnetic field.

What is the root-mean-square value Erms of the emf and also the frequency f of rotation of the coil?

Erms f

A. e

B. e

C.

D.

13. The graph below shows the variation with time t of the current I in a resistor.

Which of the following is the root-mean-square value of the current I?

A. B.I0 C. D.

14. The rms voltages across the primary and secondary coils in an ideal transformer are Vp and Vs respectively. The currents in the primary and secondary coils are Ip and Is respectively.

Which one of the following statements is always true?

A. Vs = Vp B. Is = Ip C. VsIs = VpIp D. .

E

t00

e

ᵴ

T2

T 32T

T2

T1

2e

T2

2e

T1

02I 0I20I

p

s

p

sII

VV

00 t

I

–I

+I

0

0

161

15. The diagram below shows an ideal transformer.

The transformer has n turns on the primary coil and 2n turns on the secondary coil. The waveform produced on the screen of a cathode-ray oscilloscope (cro), when the cro is connected to the primary coil, is shown below.

Which of the following diagrams shows the waveform displayed on the cro when it is connected to the secondary coil? The settings of the cro remain unchanged.

16. The variation with time of the current in the primary coil of an ideal transformer is shown below.

At which time will the magnitude of the induced e.m.f. in the secondary coil be maximum?

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

input output

primary coil secondary coil

A. B.

C. D.

current

0A

time

B C D

162

17. A transformer has a primary coil with Np turns and a secondary coil with Ns turns. An alternating voltage supply of frequency f and r.m.s. value Vp is connected to the primary coil.

Which of the following correctly gives the frequency and r.m.s. voltage in the secondary coil?

Frequency Voltage

A.

B. f

C.

D. f

18. High voltages are used for the transmission of electric power over long distances because

A. high voltages can be stepped down to any required value.

B. larger currents can be used.

C. power losses during transmission are minimized.

D. transformers have a high efficiency.

19. A power station generates electrical energy at a potential difference V and current I. The resistance of the transmission lines between the power station and the consumer is R.

The power lost in the transmission lines is

A. 0. B.

C. RI2. D. VI.


20. Electrical conduction and induced currents

(a) The diagram below shows a copper rod inside which an electric field of strength E is maintained by connecting the copper rod in series with a cell. (Connections to the cell are not shown.)

fNN

p

sp

s

p VNN

ps

p VNN

fNN

s

pp

p

s VNN

pp

s VNN

.2

RV

E

copper rod

163

Describe how the electric field enables the conduction electrons to have a drift velocity in a direction along the copper rod.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (3)

(b) A copper rod is placed on two parallel, horizontal conducting rails PQ and SR as shown below.

The rails and the copper rod are in a region of uniform magnetic field of strength B. The magnetic field is normal to the plane of the conducting rods as shown in the diagram above.

A conducting wire is connected between the ends P and S of the rails. A constant force, parallel to the rails, of magnitude F is applied to the copper rod in the direction shown. The copper rod moves along the rails with a decreasing acceleration.

(i) On the diagram, draw an arrow to show the direction of induced current in the copper rod. Label this arrow with the letter I.

(1)

(ii) Explain, by reference to Lenz’s law, why the induced current is in the direction you have shown in (i).

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(iii) By considering the forces on the conduction electrons in the copper rod, explain why the acceleration of the copper rod decreases as it moves along the rails.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (3)

conducting wire

S

P

B copper rodB

F

B

Q

R

164

(c) The copper rod in (b) eventually moves with constant speed v. The induced emf H in the copper rod is given by the expression

H = Bvl

where l is the length of copper rod in the region of uniform magnetic field.

(i) State Faraday’s law of electromagnetic induction.

.........................................................................................................................

......................................................................................................................... (1)

(ii) Deduce that the expression is consistent with Faraday’s law.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (3)

(iii) The following data are available:

F = 0.32 N

l = 0.40 m

B = 0.26 T

resistance of copper rod = 0.15 :

Determine the induced current and the speed v of the copper rod.

Induced current: ...........................................................................................

...........................................................................................

Speed v: ...........................................................................................

........................................................................................... (4)

(Total 17 marks)

21. Electromagnetic induction

(a) State Lenz’s law.

...................................................................................................................................

................................................................................................................................... (1)

165

(b) A long solenoid is connected in series with a battery and a switch S. Several loops of wire are wrapped around the solenoid close to its midpoint as shown below.

The ends of the wire are connected to a high resistance voltmeter V that has a centre zero scale (as shown in the inset diagram). The switch S is closed and it is observed that the needle on V moves to the right and then drops back to zero.

Describe and explain, the deflection on the voltmeter when the switch S is re-opened.

Description: ...........................................................................................................

...........................................................................................................

...........................................................................................................

...........................................................................................................

Explanation: ...........................................................................................................

...........................................................................................................

...........................................................................................................

........................................................................................................... (4)

(Total 5 marks)

22. This question is about an ideal transformer.

(a) State Faraday’s law of electromagnetic induction.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(b) The diagram below shows an ideal transformer.

laminated core

primary coil secondary coil

166

(i) Use Faraday’s law to explain why, for normal operation of the transformer, the current in the primary coil must vary continuously.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Outline why the core is laminated.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) The primary coil of an ideal transformer is connected to an alternating supply rated at 230V. The transformer is designed to provide power for a lamp rated as 12V, 42W and has 450 turns of wire on its secondary coil. Determine the number of turns of wire on the primary coil and the current from the supply for the lamp to operate at normal brightness.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 9 marks) 23. This question is about electromagnetic induction.

A small coil is placed with its plane parallel to a long straight current-carrying wire, as shown below.

(a) (i) State Faraday’s law of electromagnetic induction.

.............................................................................................

.............................................................................................

........................................................................................................................... (2)

(ii) Use the law to explain why, when the current in the wire changes, an emf is induced in the coil.

...........................................................................................................................

........................................................................................................................... (1)

small coilcurrent-carrying wire

167

The diagram below shows the variation with time t of the current in the wire.

(b) (i) Draw, on the axes provided, a sketch-graph to show the variation with time t of the magnetic flux in the coil.

(1)

(ii) Construct, on the axes provided, a sketch-graph to show the variation with time t of the emf induced in the coil.

(2)

(iii) State and explain the effect on the maximum emf induced in the coil when the coil is further away from the wire.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(c) Such a coil may be used to measure large alternating currents in a high-voltage cable. Identify one advantage and one disadvantage of this method.

Advantage: …..……………………………..........................................................

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

Disadvantage: …..……………………………..........................................................

…..…………………………….......................................................... (2)

(Total 10 marks)

current

e.m.f

magneticflux

t

t

t

0

0

0

0

0

0

168

Topic 13: Quantum physics and nuclear physics

1. The photoelectric effect involves the emission of electrons from

A. the surface of a metal when the metal is heated.

B. the surface of a metal when it is illuminated with electromagnetic radiation.

C. an atom of a material when the material is negatively charged.

D. an atom of a material when the material is heated.

2. The work function of a metal may be defined as

A. the minimum frequency of the incident electromagnetic radiation required to cause photoelectric emission.

B. the minimum wavelength of the incident electromagnetic radiation required to cause photoelectric emission.

C. the minimum energy of photons incident on a surface required to cause photoelectric emission.

D. the minimum energy required to take an electron from the interior to the surface to cause photoelectric emission.

3. When light is incident on a metal surface, electrons may be ejected. The following graph shows the variation with frequency f of the maximum kinetic energy Ek max of the ejected electrons.

Which one of the following graphs best shows the variation with frequency f of the maximum kinetic energy Ek max of the ejected electrons if another metal

surface with a lower threshold frequency is used?

4. Light incident on a clean metal surface produces photoelectrons. The threshold frequency of the light is determined by

A. the intensity of the incident light.

B. the wavelength of the incident light.

C. the nature of the metal surface.

D. the maximum kinetic energy of the photoelectrons.

E max

E max

E max

E max

k

k

k

k

0

0

0

0

0

0

0

0

f

f

f

f

A.

C.

B.

D.

E maxk

0 0 f

169

5. In an experiment to investigate the photoelectric effect, monochromatic light is incident on a metal surface. The photoelectric current and the maximum kinetic energy of the photoelectrons are measured.

Which one of the following correctly shows the change, if any, in the photoelectric current and in the maximum kinetic energy of the photoelectrons when light of the same intensity but higher frequency is incident on the same metal surface?

Photoelectric current Maximum kinetic energy

A. decreases no change

B. decreases increases

C. no change decreases

D. no change increases

6. According to the de Broglie hypothesis, matter waves are associated with

A. electrons only. B. charged particles only. C. neutral particles only. D. all particles.

7. Which of the following phenomena provides evidence for de Broglie’s hypothesis?

A. Electron diffraction B. X-ray production C. Line spectra D. Nuclear energy levels

8. The de Broglie wavelength of a particle that has kinetic energy Ek is Ȝ. The wavelength Ȝ is proportional to

A. Ek. B. . C.

D. Ek2.

9. Which one of the following best shows the variation with kinetic energy E of the de Broglie wavelength Ȝ associated with a particle?

10. An electron of mass me and a proton of mass mp are moving with the same speed. The de Broglie wavelengths associated with the electron and with the proton are Oe and Op respectively.

The ratio is equal to

A. B.

C.

D.

kE1

kE1

E

E

E

E

A.

C.

B.

D.

ep

ȜȜ

.e

p

mm

.p

e

mm .

e

p

mm

.p

e

mm

170

11. Which one of the following provides evidence for the existence of atomic energy levels?

A. The photoelectric effect B. Characteristic X-ray spectra

C. Matter waves D. Alpha particle scattering

12. Some of the energy levels of the hydrogen atom are shown below.

–––––––––––––– – 0.54 eV –––––––––––––– – 0.85 eV

–––––––––––––– – 1.51 eV

–––––––––––––– – 3.39 eV

–––––––––––––– – 13.6 eV

Electrons are excited to the 0.85 eV level. How many different photon frequencies will be observed in the emission spectrum of hydrogen?

A. 3 B. 4 C. 5 D. 6

13. The diagram below shows some possible electron transitions between three principal energy levels in the hydrogen atom. Which electron transition is associated with the absorption of a photon of the longest wavelength?

14. The diagram below shows the three lowest energy levels of an atom of an element.

Which of the following diagrams best represents the emission spectrum that results from electron transitions between these energy levels?

A. B.

increasing wavelength increasing wavelength

C. D.

increasing wavelength increasing wavelength

B D

A C

0 eV –1.2 eV

–13.6 eV n = 3n = 2

n = 1

energy

171

15. A free electron is confined within a one dimensional region of fixed length. Which of the diagrams below shows the four lowest energy levels of the electron?

16. A beam of electrons of uniquely defined wavelength O is incident on an aperture of height d. The beam is traveling along the x direction. The height d is of the same order as O.

After passing through the aperture, the component of momentum in the x direction is px and the component in z the direction is pz. Which of the following shows the uncertainty in px and the uncertainty in pz?

'px 'pz

A. 0 0

B. 0

C. 0

D.

dhS4

dhS4

dhS4 d

hS4

172

17. The diameter of a nucleus may be estimated from

A. determinations of half-life. B. gamma-ray spectra.

C. charged particle scattering experiments. D. fusion and fission reactions.

18. The ratio of mass-to-charge was measured for a sample of a pure element in a mass spectrometer. The values obtained were

17.5 18.5 35.0 37.0

where is the mass-to-charge ratio for a hydrogen ( ) nucleus. The data suggest that two isotopes

are present with masses

A. 17.5u and 18.5u. B. 17.5u and 37.0u. C. 18.5u and 5.0u. D. 35.0u and 37.0u.

19. The masses of nuclei in a sample of uranium are determined using a mass spectrometer. Measurements suggest that some nuclei in the sample have double the mass of others.

Which of the following is the most likely explanation for this observation?

A. Uranium nuclei are decaying radioactively.

B. Several uranium isotopes are present.

C. The uranium ions have different speeds.

D. The uranium ions have different charges.

20. Which one of the following gives evidence for the existence of nuclear energy levels?

A. Alpha particle scattering B. Gamma ray spectra C. Photoelectric effect D. Matter waves

21. Which of the following correctly describes the nature of the energy spectra of alpha (Į), beta (ȕ) and gamma (Ȗ) radiation?

Į ȕ Ȗ

A. discrete continuous discrete

B. continuous discrete discrete

C. discrete discrete continuous

D. continuous continuous discrete

22. The spectrum of energy of ȕ–-particles emitted in radioactive decay is explained on the basis of

A. the emission of neutrinos during the decay process.

B. the emission of antineutrinos during the decay process.

C. the absorption of neutrinos during the decay process.

D. the absorption of antineutrinos during the decay process.

qm

qm

qm

qm

qm

H11

173

23. A nucleus of potassium-40 undergoes E+ decay to an excited state of a nucleus of argon-39. The argon-39 then reaches its ground state by the emission of a J-ray photon. The diagram represents the E+ and J energy level diagram for this decay process.

The particle represented by the letter X is

A. an antineutrino. B. a neutrino. C. an electron. D. a photon.

24. Which one of the following is a correct definition of the decay constant of a radio-isotope?

A. The constant of proportionality linking half-life to rate of decay of nuclei.

B. The constant of proportionality linking decay rate to number of undecayed nuclei.

C. The reciprocal of the half-life of the radio-isotope.

D. The rate of decay of nuclei in a fresh sample of the radio-isotope.

25. The decay constant of two nuclei is O. One nucleus decays within a time interval of one second. The probability of decay of the other nucleus in the same time interval is

A. 0. B.

C. O. D. 2O.

26. The half-life of a radioactive nuclide is 1×103 s.

What is the probability of decay per second of a nucleus of the nuclide, quoted to one significant digit?

A. 7×10–4 B. 1×10–3 C. 1×103 D. 7×103

27. The decay constant O of a nuclide with a long half-life may be determined using the equation

activity = O × number of nuclei present.

Which of the following is the best explanation as to why this equation may be used?

A. The decay constant O is very large.

B. The number of nuclei in a sample decreases rapidly.

C. The activity of the sample decreases slowly.

D. The sample contains a large number of nuclei.

.2Ȝ

ground state energy level of potassium–40

excited energy level of argon–39

ground state energy level of argon–39

X

ȕ +

174


28. This question is about the photoelectric effect.

(a) State three pieces of evidence provided by the photoelectric effect that support the particle nature of electromagnetic radiation.

1. ................................................................................................................................

................................................................................................................................

2. ................................................................................................................................

................................................................................................................................

3. ................................................................................................................................

................................................................................................................................ (3)

The graph below shows the variation with frequency f of the stopping potential VS for photoelectrons emitted from a metal surface.

The photoelectric equation may be written in the form of the word equation

photon energy = work function + maximum kinetic energy of electron.

(b) (i) State this equation in terms of f and VS, explaining all other symbols you use.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

V / V

f /×10 Hz 15

s 2.0

1.5

1.0

0.5

0.0 0.9 1.0 1.1 1.2 1.3 1.4 1.5

175

(ii) Use your equation to deduce that the gradient of the graph is .

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) Given that the Planck constant is 6.6 × 10–34 J s, calculate a value for the work function of the surface.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 10 marks)

29. This question is about the wave nature of matter.

(a) Describe the concept of matter waves and state the de Broglie hypothesis

.....................................................................................................................................

..................................................................................................................................... (3)

(b) An electron is accelerated from rest through a potential difference of 850 V. For this electron

(i) calculate the gain in kinetic energy.

...........................................................................................................................

........................................................................................................................... (1)

(ii) deduce that the final momentum is 1.6 × 10–23 Ns.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) determine the associated de Broglie wavelength. (Electron charge e = 1.6 × 10–19 C, Planck constant h = 6.6 × 10–34 J s)

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 8 marks)

eh

176

30. This question is about models of the hydrogen atom.

In 1913 Niels Bohr developed a model of the hydrogen atom which successfully explained many aspects of the spectrum of atomic hydrogen.

(a) State one aspect of the spectrum of atomic hydrogen that Bohr’s model did not explain.

.....................................................................................................................................

..................................................................................................................................... (1)

Bohr proposed that the electron could have only certain stable orbits. These orbits are specified by the relation

mvr = with n = 1, 2, 3..........

where m is the mass of the electron, v its speed, r the radius of the orbit and h the Planck constant. This is sometimes known as Bohr’s first postulate.

(b) State the other postulate proposed by Bohr.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

By using Newton’s second law and the Coulomb law in combination with the first postulate, it can be shown that

r =

where k = .

It can also be shown that the total energy En of the electron in a stable orbit is given by

En = – .

(c) Using these two expressions, deduce that the total energy En may be given as

En = –

where K is a constant.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

S2nh

22

22

ʌ4 mkehn

0ʌ41İ

rke2

2

2nK

177

(3)

(d) State and explain what physical quantity is represented by the constant K.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(e) Outline how the Schrödinger model of the hydrogen atom leads to the concept of energy levels.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

(Total 10 marks)

31. This question is about the Heisenberg uncertainty principle.

A beam of electrons is incident normally to the plane of a narrow slit as shown below.

The slit has width 'x equal to 0.01 mm.

As an electron passes through the slit, there is an uncertainty 'x in its position.

(a) Calculate the minimum uncertainty 'p in the momentum of the electron.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(b) Suggest, by reference to the original direction of the electron beam, the direction of the component of the momentum that has the uncertainty 'p.

................................................................................................................................... (1)

(Total 3 marks)

slit

beam of electrons Dx

178

32. This question is about calculating the distance of closest aSSURDFK�RI�DQ�Į-particle to a nucleus.

An D-particle approaches a nucleus of palladium. The initial kinetic energy of the D-particle is 3.8 MeV. The particle is brought to rest at point P, a distance d from the centre of the palladium nucleus. It then moves back along the path from which it came as shown in the diagram below.

(a) &DOFXODWH�WKH�YDOXH��LQ�MRXOHV��RI�WKH�HOHFWULF�SRWHQWLDO�HQHUJ\�RI�WKH�Į-particle at point P. Explain your working.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(b) The atomic (proton) number of palladium is 46. Calculate the distance d.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (3)

(c) Gold has an atomic (proton) number of 79.

Explain whether the distance of closest approach of this D-particle to a gold nucleus would be greater or smaller than your answer in (b).

...................................................................................................................................

................................................................................................................................... (1)

(d) The radius R of a nucleus of mass (nucleon) number A is given by

(i) State in terms of the unified atomic mass unit u, the approximate mass of a nucleus of mass number A.

......................................................................................................................... (1)

palladium nucleus

P

d

-particle

.m102.1 31

15 AR �u

179

(ii) The volume of a sphere of radius R is given by Deduce that the density of all

nuclei is approximately 2 ×1017 kg m–3.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (1)

(Total 8 marks) 33. This question is in about radioactivity and nuclear energy levels.

(a) Define the following terms.

(i) Radioactive half-life ( )

...........................................................................................................................

........................................................................................................................... (1)

(ii) Decay constant (Ȝ)

...........................................................................................................................

........................................................................................................................... (1)

(b) Deduce that the relationship between and Ȝ is

Ȝ = ln2.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

Thorium-227 (Th-227) undergoes D-decay with a half-life of 18 days to form radium-223 (Ra-223). A sample of Th-227 has an initial activity of 3.2 × 105 Bq.

(c) Determine the activity of the remaining thorium after 50 days.

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... (2)

.3

4 3RV S

21T

21T

21T

180

In the decay of a Th-227 nucleus, a J-ray photon is also emitted.

(d) (i) Use the following data to deduce that the energy of the Ȗ-ray photon is 0.667 MeV.

mass of Th-227 nucleus = 227.0278 u mass of Ra-223 nucleus = 223.0186 u mass of helium nucleus = 4.0026 u energy of Į-particle emitted = 5.481 MeV unified atomic mass unit (u) = 931.5 MeVc–2

You may assume that the Th-227 nucleus is stationary before decay and that the Ra-223 nucleus has negligible kinetic energy.

(3)

........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(ii) Calculate the frequency of the Ȗ-ray photon.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

Although in the decay of a Th-227 nucleus, an Į-particle and a Ȗ-ray photon are emitted, they may have different energies to those in (d)(i). However, all the Į-particles emitted in the decay of Th-227 have discrete energies as do the associated J-ray photons. This provides evidence for the existence of nuclear energy levels. The diagram below represents some of the energy levels of a nucleus of Ra-223 relative to Th-227.

(e) On the diagram above label (i) the arrows associated with Į-particles (with the letter A).

(1) (ii) the arrows associated with Ȗ-ray photons (with the letter G).

(1) (iii) the ground state energy level of Ra-223 (with the letter R).

(1)

(f) Use data from (d), to suggest a value for the energy difference between the ground states of a nucleus of Th-227 and the ground state of a nucleus of Ra-223.

..................................................................................................................................... (1)

(Total 16 marks)

energy

energy levels of Ra–223

Th–227

181

Topic 14: Digital technology

1. The binary equivalent of the number 12 is

A. 1010.

B. 1100.

C. 0011.

D. 0101.

2. The depth of a “pit” on a CD is 150 nm. The wavelength of the laser used to read the information on the CD must be

A. 600 nm.

B. 450 nm.

C. 300 nm.

D. 150 nm.

3. The amount of charge that builds on a pixel in a charged coupled device (CCD) is proportional to which property of the incident light?

A. Intensity B. Wavelength

C. Frequency D. Amplitude


4. In a computer code, text (letters, spaces and punctuation marks) is represented by binary numbers. The letter “E” is represented by the two four bit binary numbers below.

0100 and 0101

(a) Define least significant bit.

...................................................................................................................................

................................................................................................................................... (1)

(b) Calculate the decimal equivalent for the two four bit binary numbers.

0100 .........................................................................................................................

0101 ......................................................................................................................... (1)

(c) Using this computer code state how many separate bits would be needed to represent the following phrase.

IBO Physics is easy!

................................................................................................................................... (1)

182

(d) Discuss, in terms of reproducibility and portability, the disadvantages of storing text in analogue rather than digital form.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (5)

(e) State one environmental implication of storing text in analogue form.

...................................................................................................................................

................................................................................................................................... (1)

(Total 9 marks)

5. Charge coupled device (CCD)

(a) A digital camera is used to take a photograph of a plant. The CCD in the camera has 1.6 × 107 square pixels. Each pixel has an area of 2.3 × 10–10 m2. A particular leaf of the plant has an area of 2.5 × 10–2 m2. The image of the leaf formed on the CCD is 1.0 × 10–3 m2. Two indentations on the leaf are separated by 0.50 mm. Deduce that it is unlikely that the images of the two indentations will be resolved.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (4)

(b) Light is incident on the image collection area for a time of 100 ms. The number of photons incident on one pixel is 5.5 × 104. Each pixel has a quantum efficiency of 80� and a capacitance 40 pF.

(i) State what is meant by quantum efficiency.

.........................................................................................................................

......................................................................................................................... (1)

183

(ii) Estimate the change in potential difference across each pixel.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (4)

(c) Outline how the variation in potential difference across individual pixels enables a black and white image to be produced by a digital camera.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(Total 11 marks) 6. A digital camera is used to photograph an object. Two points on the object are separated by 0.0020 cm.

The charged coupled device (CCD) in the camera has a collecting area of 16 cm2 and contains 4.0 megapixels. The magnification of the camera is 1.5.

(a) Define magnification.

...................................................................................................................................

................................................................................................................................... (1)

(b) Deduce that the images of the points can be resolved.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (4)

(Total 5 marks)

184

Option E: Astrophysics 1. This question is about some of the planets in the solar system.

Four of the planets in the solar system are Mars, Venus, Jupiter and Neptune.

(a) List these planets in order of increasing distance from the Sun.

(2)

(b) List these planets in order of decreasing diameter.

(2)

(Total 4 marks)

2. This question is about the relative population density of stars and galaxies.

The number of stars around the Sun, within a distance of 17 ly, is 75. The number of galaxies in the local group, within a distance of 4.0 × 106 ly from the Sun, is 26.

(a) Calculate the average population density, per ly3, of stars and galaxies.

Stars: ...........................................................................................................................

......................................................................................................................................

......................................................................................................................................

Galaxies: ......................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) Use your answer to (a) to determine the ratio

......................................................................................................................................

...................................................................................................................................... (1)

(Total 3 marks)

galaxies ofdensity population averagestars ofdensity population average

185

3. This question is about the star Antares.

The star Antares is a red supergiant star in the constellation Scorpius.

(a) Describe three characteristics of a red supergiant star and state what is meant by a constellation.

Red supergiant star:

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

Constellation:

......................................................................................................................................

...................................................................................................................................... (4)

(b) The apparent magnitude of Antares is + 1.1 and its absolute magnitude is –5.3.

(i) Distinguish between apparent magnitude and absolute magnitude.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Show that the distance of Antares from Earth is 3.9 × 107 AU.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(iii) State the name of the method that is used to measure the distance of Antares from Earth.

........................................................................................................................... (1)

(c) The apparent brightness of Antares is 4.3 × 10–11 times the apparent brightness of the Sun.

(i) Define apparent brightness.

...........................................................................................................................

........................................................................................................................... (1)

186

(ii) Using the answer to (b)(ii), show that Antares is 6.5 × 104 times more luminous than the Sun.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(d) Alnitak is a main sequence star with a luminosity similar to that of Antares. Use the value quoted in (c)(ii) to deduce that the mass of Alnitak is in the range 16 MS to 40 MS, where MS is the mass of the Sun.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(e) Explain, in terms of the Chandrasekhar limit, why it unlikely that Alnitak will develop into a white dwarf.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(f) State the probable final evolutionary state of Alnitak

...................................................................................................................................... (1)

(Total 20 marks)

4. This question is about the star Becrux and Cepheid variables.

(a) Describe what is meant by

(i) the apparent magnitude scale.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

187

(ii) absolute magnitude.

...........................................................................................................................

........................................................................................................................... (1)

(b) Becrux is a main sequence star and is one of the stars that make up the Southern Cross. The following data are available for Becrux.

Apparent magnitude = 1.25 Absolute magnitude = –3.92 Apparent brightness = 7.00 × 10–12 bSun

bSun is the apparent brightness of the Sun. Use the data to deduce that the

(i) distance of Becrux from Earth is 108 pc.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(ii) luminosity of Becrux is 3.43 × 103 LSun where LSun is the luminosity of the Sun. (1 pc = 2.05 ×105 AU)

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(c) Given that the power in the mass–luminosity relationship is 3.5, show that the mass of Becruz is about 10MSun where MSun is the mass of the Sun.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(d) State the differences between the eventual fate of the Sun and Becrux after they leave the main sequence.

Sun: .............................................................................................................................

......................................................................................................................................

188

Becrux: ........................................................................................................................

...................................................................................................................................... (2)

(e) Becrux is a spectral class B star. On the axes of the Hertzsprung–Russell diagram

(i) label, with the letter B, the approximate position of Becrux. (1)

(ii) draw the evolutionary path of Becrux after it leaves the main sequence.

(1)

(f) On the axes of the Hertzsprung–Russell diagram above, draw the approximate region in which Cepheid variable stars are located.

(1)

(g) State the reason for the periodic variation in luminosity of a Cepheid variable.

......................................................................................................................................

...................................................................................................................................... (1)

(h) State the two quantities that need to be measured in order to use a Cepheid variable as a “standard candle” to determine the distance to the galaxy in which the Cepheid is located.

1. ..................................................................................................................................

2. .................................................................................................................................. (2)

(Total 19 marks)

189

5. This question is about stars.

Betelgeuse and Rigel are two super giants in the constellation of Orion.

(a) Distinguish between a constellation and a stellar cluster.

Constellation: ..........................................................................................................

..........................................................................................................

Stellar cluster: ..........................................................................................................

.......................................................................................................... (2)

(b) The star Betelgeuse has a parallax of 0.0077 arc second. Deduce that its distance from Earth is approximately 130 pc.

...................................................................................................................................

................................................................................................................................... (1)

(c) State why the Hipparcos satellite which orbits Earth is able to measure stellar parallaxes for stars at considerably greater distances than 130 pc.

................................................................................................................................... (1)

(d) The table below gives some information about the types and magnitudes of Betelgeuse and Rigel.

Star Type Apparent magnitude Colour Apparent

brightness

Betelgeuse M í0.04 2.0 × 10í7 W mí2

Rigel B 0.12 3.4 × 10í8 W mí2

(i) Complete the above table for the colours of the stars. (2)

(ii) State why Betelgeuse has a lower apparent magnitude than Rigel.

.........................................................................................................................

......................................................................................................................... (1)

(iii) Given that the distance of Betelgeuse from Earth is 130 pc, calculate the luminosity of Betelgeuse.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (4)

190

(iv) The luminosity of Rigel is 2.3 × 1031 W. Without any further calculation, explain whether Rigel is closer or further than Betelgeuse from Earth.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (3)

(Total 14 marks)

6. This question is about the properties of a star.

(a) Describe what is meant by a

(i) constellation.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) stellar cluster.

...........................................................................................................................

........................................................................................................................... (1)

(b) Some data for the variable star Betelgeuse are given below.

Average absolute magnitude = –5.1 Average apparent magnitude = + 0.60 Average apparent brightness = 1.6 × 10–7 W m–2 Radius = 790 solar radii

The luminosity of the Sun is 3.8 × 1026 W and it has a surface temperature of 5700 K.

(i) Show that the distance from Earth to Betelgeuse is about 4.0 × 1018 m.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(ii) Determine, in terms of the luminosity of the Sun, the luminosity of Betelgeuse.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

191

(iii) Calculate the surface temperature of Betelgeuse.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(c) On the Hertzsprung–Russell diagram above,

(i) label the position of Betelgeuse with the letter B. (1)

(ii) sketch Betelgeuse’s likely evolutionary path. (1)

(d) Some stars, such as Betelgeuse, are in combination with a companion star forming a spectroscopic binary system. Describe and explain the characteristics of a spectroscopic binary system.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 15 marks)

192

7. This question is about the luminosity, size and distance of stars.

The Hertzsprung–Russell (HR) diagram shows the variation with spectral class of the absolute magnitude of stars.

The star Capella and the Sun are in the same spectral class (G). Using the HR diagram,

(a) (i) suggest why Capella has a greater surface area than the Sun.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) estimate the luminosity of Capella in terms of that of the Sun.

...........................................................................................................................

........................................................................................................................... (1)

(iii) calculate the radius of Capella in terms of that of the Sun.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

193

(b) The spectroscopic parallax method can be used to measure the distance of star Vega.

(i) Using the HR diagram, state the absolute magnitude of Vega.

........................................................................................................................... (1)

(ii) The apparent magnitude of Vega is 0.0. Determine (in parsec) the distance of Vega from Earth.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(iii) Light from Vega is absorbed by a dust cloud between Vega and Earth. Suggest the effect, if any, this will have on determining the distance of Vega from Earth.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(c) Vega is a very massive star. State why Vega does not undergo gravitational collapse.

......................................................................................................................................

...................................................................................................................................... (1)

(Total 12 marks)

8. This question is about the characteristics of the stars Procyon A and Procyon B.

(a) The stars Procyon A and Procyon B are both located in the same stellar cluster in the constellation Canis Minor. Distinguish between a constellation and a stellar cluster.

Constellation: ..............................................................................................................

......................................................................................................................................

Stellar cluster: ..............................................................................................................

...................................................................................................................................... (2)

(b) The table shows some data for Procyon A and Procyon B.

Apparent magnitude

Absolute magnitude

Apparent brightness / W m–2

Procyon A (PA) +0.400 +2.68 2.06 × 10–8

Procyon B (PB) +10.7 +13.0 1.46 × 10–12

194

Explain, using data from the table, why

(i) as viewed from Earth, PA is much brighter than PB.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) the luminosity of PA is much greater than that of PB.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(c) Deduce, using data from the table in (b), that PA and PB are approximately the same distance from Earth.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(d) State, using your answers to (a) and (c), why PA and PB might be binary stars.

......................................................................................................................................

...................................................................................................................................... (1)

(e) Calculate, using data from the table in (b), the ratio where LA is the luminosity of PA and LB

is the luminosity of PB.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

B

A

LL

195

(f) The surface temperature of both PA and PB is of the order of 104 K. The luminosity of PA is of the order of 10LS, where LS is the luminosity of the Sun. The diagram shows the grid of a Hertzsprung–Russell diagram.

Label, on the grid above, the approximate position of

(i) star PA with the letter A. (1)

(ii) star PB with the letter B. (1)

(g) Identify the nature of star PB.

...................................................................................................................................... (1)

(h) On the grid provided in (f), draw the evolutionary path of the star PA. (2)

(i) The luminosity of the main sequence star Regulus is 150 LS. Assuming that, in the mass–luminosity relationship, n = 3.5 show that the mass of Regulus is 4.2 MS where MS is the mass of the Sun.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(j) The star Betelgeuse is about five times the mass of Regulus. One possible outcome of the final stage of the evolution of Betelgeuse is for it to become a black hole. State the

(i) other possible outcome of the final stage of the evolution of Betelgeuse.

........................................................................................................................... (1)

196

(ii) reason why the final stage in (j)(i) is stable.

...........................................................................................................................

........................................................................................................................... (1)

(Total 21 marks)


(a) Distinguish between apparent magnitude and absolute magnitude.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) The table gives information on three stars, Achernar, EG 129 and Mira.

Absolute magnitude Apparent magnitude Spectral class

Achernar –3.0 +0.50 B

EG 129 +13.0 +14.0 B

Mira –3.0 +5.0 M

(i) State which one of the three stars appears brightest from Earth.

........................................................................................................................... (1)

(ii) Estimate the ratio where LA is the luminosity of Achernar and LE is the luminosity of

EG 129.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(iii) Show that the distance of the star Achernar from Earth is approximately 50 pc.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

E

A

LL

197

(c) The surface temperature of Mira is 5 times lower than that of Achernar. Estimate the ratio

where RM is the radius of Mira and RA is the radius of Achernar.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(d) State and explain which of the stars in the table in (b) is a white dwarf.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 14 marks)

10. This question is about determining some properties of the star Wolf 359.

(a) The star Wolf 359 has a parallax angle of 0.419 arcseconds.

(i) Describe how this parallax angle is measured.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(ii) Calculate the distance in light-years from Earth to Wolf 359.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

A

M

RR

198

(iii) State why the method of parallax can only be used for stars at a distance of less than a few hundred parsecs from Earth.

...........................................................................................................................

........................................................................................................................... (1)

(b) The ratio

is 3.7 × 10–15.

Show that the ratio

is 8.9 × 10–4. (1ly = 6.3 × 104 AU)

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (4)

(c) The surface temperature of Wolf 359 is 2800 K and its luminosity is 3.5 × 1023 W. Calculate the radius of Wolf 359.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(d) By reference to the data in (c), suggest why Wolf 359 is neither a white dwarf nor a red giant.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 15 marks)

Sun theof brightnessapparent 359 Wolfof brightnessapparent

Sun theof luminosity359 Wolfof luminosity

199

11. This question is about the Hertzsprung–Russell (HR) diagram and using it to determine some properties of stars.

The diagram below shows the grid of an HR diagram, on which the positions of selected stars are shown. (LS = luminosity of the Sun.)

(a) (i) Draw a circle around the stars that are red giants. Label this circle R. (1)

(ii) Draw a circle around the stars that are white dwarfs. Label this circle W. (1)

(iii) Draw a line through the stars that are main sequence stars. (1)

(b) Explain, without doing any calculation, how astronomers can deduce that star B has a larger diameter than star A.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

200

(c) Using the following data and information from the HR diagram, show that star A is at a distance of about 800 pc from Earth.

Apparent brightness of the Sun = 1.4 × 103 W m–2 Apparent brightness of star A = 4.9 × 10–9 W m–2 Mean distance of Sun from Earth = 1.0 AU 1 pc = 2.1 × 105 AU

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (4)

(d) Explain why the distance of star A from Earth cannot be determined by the method of stellar parallax.

......................................................................................................................................

...................................................................................................................................... (1)

(Total 11 marks)

12. This question is about the mass–luminosity relation and also the evolution of stars.

The mass–luminosity relation for main sequence stars is assumed to be L M3.5, where L is the luminosity and M is the mass. Star X is 8 × 104 times more luminous than the Sun and 25 times more massive than the Sun.

(a) Deduce that star X is a main sequence star.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) Outline with reference to the Oppenheimer–Volkoff limit, the evolutionary steps and the fate of star X after it leaves the main sequence.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 5 marks)

v

201

13. This question is about cosmic microwave background radiation.

The graph shows the spectrum of the cosmic microwave background radiation.

The shape of the graph suggests a black body spectrum i.e. a spectrum to which the Wien displacement law applies.

(a) Use the graph to estimate the black body temperature.

......................................................................................................................................

...................................................................................................................................... (2)

(b) Explain how your answer to (a) is evidence in support of the Big Bang model.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(c) State and explain another piece of experimental evidence in support of the Big Bang model.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 6 marks)

14. This question is about stellar evolution.

(a) Outline what is meant by the Oppenheimer-Volkoff limit.

......................................................................................................................................

...................................................................................................................................... (1)

202

(b) Eta Carinae is a main sequence star whose mass is about 100 times larger than that of the Sun. The star will evolve to become a neutron star.

(i) By reference to the Oppenheimer-Volkoff limit, outline the evolution of Eta Carinae from when it leaves the main sequence until the neutron star stage.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) State the reason why Eta Carinae will not undergo further collapse when it becomes a neutron star.

........................................................................................................................... (1)

(c) The mass-luminosity relationship for stars such as Eta Carinae and the Sun is given by the expression L = kM3.5 where k is a constant and M is the mass of the star. The mass of Eta Carinae is 100 times larger than that of the Sun.

(i) Calculate the ratio , where l = is the luminosity per unit mass.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) A star will leave the main sequence after it has converted 12 % of its mass into energy. By reference to your answer to (i) suggest why Eta Carinae will spend less time on the main sequence than the Sun.

...........................................................................................................................

........................................................................................................................... (1)

(Total 7 marks)

15. This question is about Olbers’ paradox.

(a) Newton assumed that the universe is static and that the stars are uniformly distributed. State one further assumption of the Newtonian universe.

...................................................................................................................................

................................................................................................................................... (1)

(b) Explain how Newton’s assumptions led to Olbers’ paradox.

...................................................................................................................................

...................................................................................................................................

Sun

Carinae Eta

ll

ML

203

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (5)

(Total 6 marks)

16. This question is about cosmology.

(a) The diagram below represents a spherical region of space based on Newton’s model of the universe. Earth is at the centre of the region. The dark line represents a very thin spherical shell of space distance R from Earth.

With reference to the diagram and Newton’s model of the universe explain quantitatively Olbers’ paradox.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (4)

(b) The Big Bang theory provides a resolution to Olbers’ paradox. Two pieces of evidence to support the theory are the existence of cosmic microwave background radiation (CMB) and the red-shifted light from distant galaxies.

(i) Outline how CMB is consistent with the Big Bang theory.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

204

(ii) The following data are available for the red-shift of light from a distant galaxy.

Wavelength of light from galaxy = 130 nm Wavelength measured in laboratory = 120 nm Hubble constant = 74 km s–1 Mpc–1

Use the data to determine the distance of the galaxy from Earth.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(Total 11 marks)

17. This question is about models of the universe.

Observations of the night sky indicate that there are many regions of the universe that do not contain any stars.

(a) Explain why this observation contradicts Newton’s model of the universe.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(b) Outline how the Big Bang model of the universe is consistent with this observation.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 6 marks)

205

18. This question is about cosmic microwave background radiation (CMB) and the density of the universe.

The graph shows the relative intensity of the CMB as a function of wavelength.

(a) Explain how this graph is consistent with the Big Bang model of the universe.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(b) The density of the universe will determine its ultimate fate. Outline the problems associated with determining the density of the universe.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(c) Outline how the expansion of the universe ultimately made it possible for stable nuclei and atoms to exist.

......................................................................................................................................

...................................................................................................................................... (1)

(Total 6 marks)

19. This question is about the Big Bang model and red-shift.

(a) Describe what is meant by the Big Bang model.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (1)

206

(b) In the 1960s, Penzias and Wilson discovered a uniform cosmic background radiation (CMB) in the microwave region of the electromagnetic spectrum.

(i) Explain how the CMB is consistent with the Big Bang model.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(ii) State why the red-shift of light from galaxies supports the Big Bang model.

...........................................................................................................................

........................................................................................................................... (1)

(c) Many galaxies are a great distance from Earth. Explain, with reference to Hubble’s law, how the measurement of the red-shift of light from such galaxies enables their distance from Earth to be determined.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(d) State one problem associated with using Hubble’s law to determine the distance of a galaxy a great distance from Earth.

......................................................................................................................................

...................................................................................................................................... (1)

(Total 9 marks)

20. This question is about stellar evolution.

(a) Describe how a large cloud of hydrogen gas can lead to conditions that initiate a fusion reaction.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

207

(b) State the property of a main sequence star that determines for how long hydrogen in its core fuses into helium.

...................................................................................................................................... (1)

(c) State the end product of nuclear fusion processes in the core of

(i) a red giant.

........................................................................................................................... (1)

(ii) the largest red super giants.

........................................................................................................................... (1)

(Total 6 marks)

21. This question is about galactic motion.

(a) The wavelength of the Lyman-alpha line in the hydrogen spectrum is measured in the laboratory to be 122 nm. In the hydrogen spectrum of a galaxy, the Lyman-alpha line is measured to be 147 nm. Determine the distance of this galaxy from the Earth. Assume that the Hubble constant H0 is 75km s–1 M pc–1.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(b) Suggest one reason why there is uncertainty in the value of the Hubble constant.

......................................................................................................................................

...................................................................................................................................... (1)

(Total 4 marks)

22. This question is about Hubble’s law and the expansion of the universe.

(a) The spectrum of the cluster of galaxies Pegasus I shows a shift of 5.04 nm in the wavelength of the K-line. The wavelength of this line from a laboratory source is measured as 396.8 nm. Calculate the velocity of recession of the cluster.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

208

(b) The graph shows the recession velocities of a number of clusters of galaxies as a function of their approximate distances.

(i) State one method by which the distances shown on the graph could have been determined.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Use the graph to show that the age of the universe is about 1017 s.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 5 marks)

23. This question is about the density of the universe.

(a) Explain, with reference to the possible fate of the universe, the significance of the critical density of matter in the universe.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

209

(b) Suggest one reason why it is difficult to estimate the density of matter in the universe.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 5 marks)

24. This question is about the evolution of stars.

(a) State what is meant by the

(i) Chandrasekhar limit.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Oppenheimer–Volkoff limit.

...........................................................................................................................

........................................................................................................................... (1)

(b) Suggest how your answers in (a) can be used to predict the fate of a main sequence star.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 5 marks)

25. This question is about the Hubble constant.

(a) Outline the measurements that must be taken in order to determine a value for the Hubble constant.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

210

(b) One estimate of the Hubble constant is 60 km s–1 Mpc–1. Cygnus A is a radio galaxy at a distance of 6.0 × 108 ly from Earth. Calculate, in km s–1, the recessional speed of Cygnus A relative to the Earth.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 5 marks)

26. This question is about the Big Bang model and red-shift.

(a) Describe what is meant by the Big Bang model.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (1)

(b) In the 1960s, Penzias and Wilson discovered a uniform cosmic background radiation (CMB) in the microwave region of the electromagnetic spectrum.

(i) Explain how the CMB is consistent with the Big Bang model.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(ii) State why the red-shift of light from galaxies supports the Big Bang model.

...........................................................................................................................

........................................................................................................................... (1)

(Total 5 marks)

27. This question is about cosmology.

(a) State how the observed red-shift of many galaxies is explained.

...................................................................................................................................... (1)

211

(b) Explain how the cosmic microwave background (CMB) radiation is consistent with the Big Bang model.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(c) Calculate the temperature of the universe when the peak wavelength of the CMB was equal to the wavelength of red light (7.0 × 10–7 m).

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 5 marks)

28. This question is about the main sequence star Khad (Phi Orionis).

The luminosity of Khad is 2.0 × 104 LS, where LS is the luminosity of the Sun.

(a) Assuming that the exponent n in the mass–luminosity relation is 3.5, show that the mass of Khad is about 17 solar masses.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) Outline the likely evolution of the star Khad after it leaves the main sequence.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 5 marks)

212

29. This question is about Hubble’s law and the age of the universe.

(a) (i) State Hubble’s law.

...........................................................................................................................

........................................................................................................................... (1)

(ii) State why Hubble’s law cannot be used to determine the distance from Earth to nearby galaxies, such as Andromeda.

...........................................................................................................................

........................................................................................................................... (1)

(b) (i) Show that is an estimate of the age of the universe, where H0 is the Hubble constant.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Assuming H0 = 80 km s–1 M pc–1, estimate the age of the universe in seconds.

...........................................................................................................................

........................................................................................................................... (1)

(Total 5 marks)

30. This question is about Hubble’s law.

Hubble’s law states that

v =H0d

where v is the relative recessional speed between galaxies, d is their separation and H0 is the Hubble constant. Recent measurements place the value of H0 in the range 60 to 90 km s–1 Mpc–1.

(a) Suggest why a precise value of H0 is not known.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

0

1H

213

(b) Estimate, in seconds, the maximum known age of the universe.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 4 marks)

31. This question is about Hubble’s law.

(a) State Hubble’s law.

......................................................................................................................................

...................................................................................................................................... (2)

(b) Suggest why, in verifying Hubble’s law, data from nearby galaxies cannot be used.

......................................................................................................................................

...................................................................................................................................... (1)

(Total 3 marks)


Describe the final nuclear reaction in the core, and the final evolutionary state, of

(a) a low-mass star (of the order of 1 solar mass).

nuclear reaction: ....................................................................................................

....................................................................................................

evolutionary state: ....................................................................................................

.................................................................................................... (2)

(b) a high-mass star (of approximately 15 solar masses).

nuclear reaction: ....................................................................................................

....................................................................................................

evolutionary state: ....................................................................................................

.................................................................................................... (2)

(Total 4 marks)

214

33. This question is about extragalactic astrophysics.

(a) In an observation of a distant galaxy, spectral lines are recorded. Spectral lines at these wavelengths cannot be produced in the laboratory. Explain this phenomenon.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(b) Describe how Hubble’s law is used to determine the distance from the Earth to distant galaxies.

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(c) Explain why Hubble’s law is not used to measure distances to nearby stars or nearby galaxies (such as Andromeda).

...................................................................................................................................

...................................................................................................................................

................................................................................................................................... (2)

(Total 6 marks)

215

Option F: Communications

1. This question is about modulation.

In order to test a temporary radio communication link, an audio signal is broadcast using amplitude modulation (AM). The power spectrum of the resulting carrier wave is shown below.

(a) Use the information in the power spectrum to determine the

(i) frequency of the carrier wave.

........................................................................................................................... (1)

(ii) frequency of the audio signal.

........................................................................................................................... (1)

(iii) bandwidth of this signal.

........................................................................................................................... (1)

(b) (i) Distinguish between AM and frequency modulation (FM).

AM: ...................................................................................................................

...........................................................................................................................

FM: ...................................................................................................................

........................................................................................................................... (2)

(ii) Outline one advantage and one disadvantage of using FM as opposed to AM for the transmission.

Advantage: ........................................................................................................

...........................................................................................................................

Disadvantage: ...................................................................................................

........................................................................................................................... (2)

(Total 7 marks)

216

2. This question is about amplitude modulation (AM).

The graph shows the power spectrum of an AM carrier wave.

(a) Use the graph to determine the


........................................................................................................................... (1)

(ii) frequency of the signal wave.

........................................................................................................................... (1)

(iii) bandwidth of the transmitted signal.

........................................................................................................................... (1)

(b) A broadcasting company has been given permission to broadcast in a frequency range of 320 kHz. The transmissions have the bandwidth found in (a)(iii).

Determine how many radio stations the company can operate in this frequency range.

...................................................................................................................................... (1)

(Total 4 marks)


(a) Outline what is meant by the modulation of a wave.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) The frequency spectrum of the signal from a radio transmitter is shown below.

217

(i) State the name of this form of radio transmission.

........................................................................................................................... (1)

(ii) State the frequency of the carrier wave.

........................................................................................................................... (1)

(iii) Determine the bandwidth of this signal.

........................................................................................................................... (1)

(Total 5 marks)


(a) A carrier wave may be amplitude modulated or frequency modulated.

State

(i) what is meant by modulation.

...........................................................................................................................

........................................................................................................................... (1)

(ii) why carrier waves are modulated.

...........................................................................................................................

........................................................................................................................... (1)

(b) A sinusoidal carrier wave has a frequency of 500 kHz and an amplitude of 8.0 V. The carrier wave is frequency modulated by a sinusoidal information signal of frequency 2.5 kHz and amplitude 1.2 V. The frequency deviation of the carrier wave is 15 kHz V–1. Describe quantitatively the variation with time of the carrier wave.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (4)

(Total 6 marks)

218


(a) The diagram shows how the voltage signal of a frequency modulated (FM) carrier wave varies with time.

The carrier wave is modulated by a single frequency signal.

On the above axes sketch the information signal. (1)

(b) State and explain one advantage of using FM modulation rather than amplitude modulation (AM).

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 3 marks)


(a) State what is meant by the modulation of a carrier wave.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (1)

(b) The graph shows how the voltage signal strength V of an amplitude modulated (AM) carrier wave varies with time t.

Use the

219

graph to determine the


...........................................................................................................................

........................................................................................................................... (1)

(ii) frequency of the signal wave.

...........................................................................................................................

........................................................................................................................... (1)

(iii) amplitude of the signal wave.

...........................................................................................................................

........................................................................................................................... (2)

(iv) bandwidth.

........................................................................................................................... (1)

(c) A carrier wave may also be frequency modulated (FM). State and explain one advantage of FM compared to AM.

......................................................................................................................................

...................................................................................................................................... (2)

(Total 8 marks)

7. This question is about amplitude-modulated radio waves.

The diagram below shows a sketch graph of signal voltage against time for an amplitude-modulated radio wave.

(a) The information signal consists of a continuous single frequency sine wave. The frequency of the carrier wave is 18 kHz.

(i) Determine the frequency of the information signal.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (3)

220

(ii) On the axes below, draw the power spectrum for the amplitude-modulated wave. (Numerical values are not required on the power axis.)

(3)

(b) The block diagram below shows the principal systems in a radio that receives an amplitude-modulated signal. The unlabelled boxes represent amplifiers.

(i) Label the blank boxes with the type of amplifier used. (1)

(ii) State the function of the demodulator.

.........................................................................................................................

......................................................................................................................... (1)

(Total 8 marks)

8. This question is about radio communication.

(a) State the difference between

(i) a signal wave and a carrier wave.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) amplitude modulation and frequency modulation.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(b) Graph A shows a sketch of how the signal strength of a certain radio carrier wave varies with time

221

at a particular point in space.

Graph B shows how the signal strength of the wave is amplitude modulated by a signal wave.

The time scale for both graphs is the same.

The frequency of the carrier wave is fc and that of the signal wave fs. Use both graphs to estimate

the ratio and explain how you arrived at your answer.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(c) On graph B sketch the wave form of the signal wave. (1)

(d) Describe one advantage and state one disadvantage of using amplitude modulation in radio transmission as compared to the use of frequency modulation.

Advantage: ..................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

Disadvantage: ..............................................................................................................

...................................................................................................................................... (3)

(Total 10 marks)

s

c

ff

222

9. This question is about sampling.

A telephone call is sampled with a sampling frequency of 8.0 kHz. Each sample is stored as a four bit binary number. The duration of each bit in the sample is 4.0 µs.

(a) Calculate the time interval between the end of one sample and the beginning of the next.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(b) Outline, with reference to your answer in (a), what is meant by time-division multiplexing.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 5 marks)

10. The graph below shows the variation with time t of the voltage V of an analogue signal.

The signal is sampled at a frequency of 200 Hz and digitized using a three-bit analogue to digital converter (ADC). The first sample is taken at t = 0.

The possible outputs of the ADC are given below.

223

(a) Calculate the time at which the fourth sample is taken.

...................................................................................................................................

................................................................................................................................... (2)

(b) Determine the binary output of the fourth sample.

...................................................................................................................................

................................................................................................................................... (2)

(c) The ADC output is fed into a three-bit digital to analogue converter (DAC). State, and explain, whether the output of the DAC will be a faithful reproduction of the original analogue signal.

...................................................................................................................................

................................................................................................................................... (2)

(Total 6 marks)

11. This question is about data transmission systems.

The block diagram below represents an electronic system, S1, which converts an analogue input signal into a serial digital output signal ready for transmission. It involves three separate system blocks labelled A, B and C.

(a) State whether the signal between block A and block B is analogue, digital or multiplexed.

...................................................................................................................................... (1)

(b) State the function of system block A.

......................................................................................................................................

...................................................................................................................................... (1)

224

(c) A similar system, S2, is based on the same system blocks as S1, but has fewer signal lines between block B and block C, as shown below.

Explain what differences, if any, there are between S1 and S2 with respect to the maximum quality of the reproduction of the analogue signal after transmission.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(d) The serial digital output signal is transmitted using an optical fibre link. The attenuation per unit length of the optical fibre is –4 dB km–1.

(i) Define attenuation.

...........................................................................................................................

........................................................................................................................... (1)

(ii) The input power to the fibre optic cable is 100 mW and the output power at the end of the cable is 1 mW. Determine the length of the cable.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(iii) State two processes that must take place in order for this digital signal to be transmitted over a very long distance.

1. .......................................................................................................................

2. ....................................................................................................................... (2)

(Total 9 marks)

225

12. This question is about transmission and sampling of signals.

(a) The block diagram illustrates the principles of the transmission and reception of digital signals.

Describe the function of each of the blocks labelled P, Q, R and S.

P: .................................................................................................................................

......................................................................................................................................

Q: .................................................................................................................................

......................................................................................................................................

R: .................................................................................................................................

......................................................................................................................................

S: .................................................................................................................................

...................................................................................................................................... (4)

(b) The graph shows thirteen sampled values of an analogue signal as a function of the time at which the sampling took place.

226

Each sample is converted into a 4-bit binary number, according to the encoding scheme:

Signal / mV Sample / mV 4-bit binary number

2.000–2.999 2 0010

3.000–3.999 3 0011

4.000–4.999 4 0100

Determine the

(i) 4-bit binary number corresponding to the sample at t = 0.07 ms.

........................................................................................................................... (1)

(ii) bit-rate of the digital transmission.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(c) State one advantage and one disadvantage of increasing the sampling frequency used to sample an analogue signal.

Advantage: ..................................................................................................................

......................................................................................................................................

Disadvantage: ..............................................................................................................

...................................................................................................................................... (2)

(Total 9 marks)

13. This question is about transmission of signals.

In a particular transmission system a single piece of analogue information is converted into a 4-bit binary “word” represented by the letters ABCD. The word is transmitted along an optic fibre to the receiver. The block diagram shows the principle components for the transmission and reception of this word.

� � �

� � �

227

(a) On the diagram label the components X and Y and outline the function of each component.

X: .................................................................................................................................

......................................................................................................................................

Y: .................................................................................................................................

...................................................................................................................................... (3)

(b) The diagram is a representation of a two-input time division multiplexer.

Outline, with reference to the diagram, how this device enables two sets of digital data to be transmitted apparently simultaneously along the same optic fibre.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(c) As a signal is transmitted along an optic fibre its signal strength is attenuated. For this reason amplifiers have to be placed at points along the fibre.

(i) Explain what is meant by attenuation.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) In a particular fibre, the signal needs to be amplified when the signal power is 8.2 × 10–19 W. The fibre has an attenuation loss of 2.0 dB km–1. Determine, for an input signal of power 5.0 mW, the separation of the amplifiers along the fibre.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 10 marks)

228

14. This question is about the transmission of signals.

The signal from a microphone is amplified and then transmitted to a distant receiver. The variation with time t of the amplified signal before transmission is shown below.

(a) The amplified signal is transmitted using a coaxial cable as illustrated.

On the axes below, sketch the waveform of the signal at point X after transmission along the coaxial cable.

(3)

(b) A second transmission system, as shown below, uses a cable containing many separate fibres (multi-core optic cable).

229

(i) Suggest why a multi-core optic cable is required rather than a single-core optic fibre.

........................................................................................................................... (1)

(ii) State what circuits should be included in the transmission system so that a single-core optic fibre may be used.

...........................................................................................................................

........................................................................................................................... (1)

(c) The received signal of the second transmission system is shown below.

Calculate the

(i) minimum number of output bits of the ADC.

...........................................................................................................................

........................................................................................................................... (2)

(ii) sampling frequency of the ADC.

...........................................................................................................................

........................................................................................................................... (2)

(d) State one advantage and one disadvantage of the coaxial cable transmission as compared with the fibre optic cable.

Advantage: ..................................................................................................................

......................................................................................................................................

Disadvantage: ..............................................................................................................

...................................................................................................................................... (2)

(Total 11 marks)

230

15. This question is about digital signals.

(a) The graph shows the variation with time of an analogue signal.

In order to convert the analogue signal into a 3-bit digital signal it is sampled every 100 µs. The possible output voltages of the analogue to digital converter that is used are shown below.

Analogue signal / V Binary output

0 – < 0.5 000

0.5 – < 1.0 001

1.0 – < 1.5 010

1.5 – < 2.0 011

2.0 – < 2.5 100

2.5 – < 3.0 101

3.0 – < 3.5 110

3.5 – < 4.0 111

Determine, explaining your answer, the

(i) bit-rate (data transfer rate).

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) digital output of the signal for the sixth sample starting from t = 0 s.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

231

(b) Explain the effects that increasing the sampling frequency and number of bits will have on the quality of the representation of the analogue signal.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(c)The digital signal in (a) is to be transmitted along an optic fibre that has a power loss of 2.0 dB km–1.

(i) State, in watts, how power loss is defined on the decibel scale.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Calculate the distance travelled by the signal that will result in a power loss of 75 %.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(d) As a result of noise in electric circuits, digital pulses can often lose their shape and hence distort the information that they carry. The pulses can be re-shaped using a circuit called a Schmitt trigger. The diagram shows a Schmitt trigger that incorporates an operational amplifier.

(i) State two essential properties of an operational amplifier.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) In the situation shown the output voltage V0 of the amplifier is at its minimum value of – 6.0 V. The voltage at the non-inverting input to the amplifier is equal to 1.0 V and at the inverting input it is VX. The output voltage will switch to its maximum value + 6.0 V if the voltage VX just exceeds +1.0 V. Determine the minimum voltage Vin that will result in an output voltage of + 6.0 V.

232

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (4)

(Total 16 marks)

16. This question is about the transmission of signals along an optic fibre.

(a) A ray of light enters an optic fibre from air. The ray makes an angle ș�with the normal. The ray undergoes total internal reflection at point P.

The refractive index of the core is 1.56 and that of the cladding is 1.38.

(i) Calculate the critical angle of the cladding-core boundary.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Show that the largest angle of incidence ș�in air, at which total internal reflection at the cladding-core boundary takes place, is 46.7°.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

233

(b) Distinguish between modal dispersion and material dispersion in an optic fibre.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(c) The signal shown is fed into a monomode optic fibre.

(i) State what the shaded area represents.

........................................................................................................................... (1)

(ii) Use the axes above to draw the shape of the signal after it has travelled a large distance in the fibre.

(2)

(iii) The input signal power in a monomode fibre is 15.0 mW. The attenuation per unit length for this fibre is 1.24 dB km–1. Determine the power of the output signal after the signal has travelled a distance of 3.40 km in the fibre.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 12 marks)

17. This question is about optical fibres.

(a) Outline what is meant by material dispersion.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

234

(b) Suggest why material dispersion sets a limit on the bit-rate of transmission.

......................................................................................................................................

...................................................................................................................................... (1)

(c) (i) The signal shown below is fed into a monomode optical fibre.

On the diagram above, show the effects of material dispersion on the input signal by drawing the shape of the signal after it has travelled a long distance in the optical fibre.

(1)

(ii) State and explain how the effects on the signal drawn in (c)(i) may be reduced.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(d) Digital data are transmitted in an optical fibre with a glass core which has a refractive index of 1.5. The duration of one bit in the transmission is 0.50 ns and each sample in the signal consists of 32 bits.

(i) Calculate the time required for the signal to travel a distance of 500 km.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Determine the sampling frequency.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(e) The data in (d) are confidential and must be protected. Without taking financial costs into account, outline whether a direct optical fibre connection or a transmission through a geosynchronous satellite would be more suitable for the transfer of these data.

......................................................................................................................................

235

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 12 marks)

18. This question is about optical fibres.

(a) State one cause of attenuation and one cause of dispersion in an optical fibre.

Attenuation: .................................................................................................................

......................................................................................................................................

Dispersion: ..................................................................................................................

...................................................................................................................................... (2)

(b) An optical fibre of length 5.4 km has an attenuation per unit length of 2.8 dB km–1. The signal power input is 80 mW.

(i) Calculate the output power of the signal.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) In order for the power of the output signal to be equal to the input power an amplifier is installed at the end of the fibre.

State the gain, in decibels (dB), of the amplifier at the end of the fibre.

........................................................................................................................... (1)

(c) The signal to noise ratio (SNR), in dB, is defined as SNR = 10log where Psignal and Pnoise

are the powers of the signal and noise respectively.

The SNR of the signal in (b) before amplification was 20 dB. Calculate the SNR after amplification.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 7 marks)

noise

signal

P

P

236

19. This question is about optic fibre transmission.

The variation with time t of the input power to an optic fibre is shown in Diagram 1. The variation with time t of the output power from the optic fibre is shown in Diagram 2.

The scales are the same on both diagrams.

(a) State and explain the feature of the graphs that shows that there is

(i) attenuation of the signal.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) signal noise.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(b) The duration (time width) of the signal increases as it travels along the optic fibre.

(i) State two reasons for this increased time duration.

1:........................................................................................................................

2:........................................................................................................................ (2)

(ii) Suggest why this increase in the width of the pulse sets a limit on the frequency of pulses that can be transmitted along an uninterrupted length of optic fibre.

...........................................................................................................................

........................................................................................................................... (1)

(Total 7 marks)

237

20. This question is about satellites.

A geostationary satellite is used by one country to broadcast information to a different country.

(a) State which part of the electromagnetic spectrum is used for this type of communication.

...................................................................................................................................... (1)

(b) Explain two disadvantages of using a polar satellite for this type of communication, when compared with using a geostationary satellite.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(c) Outline one possible ethical issue associated with this broadcast.

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (1)

(Total 4 marks)

21. This question is about signal power and attenuation.

An optic fibre in a telephone system has length 48 km. The noise power in the optic fibre is 2.5 × 10–18 W.

(a) The signal-to-noise ratio is not to fall below 25 dB. Show that the minimum signal power in the fibre is 7.9 × 10–16 W.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) The attenuation per unit length of the signal in the fibre is 2.7 dB km–1. Use the data in (a) to determine the power of the input signal to the fibre so that the signal-to-noise ratio does not fall below 25 dB.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(Total 4 marks)

238

22. This question is about communication channels.

(a) State the order of magnitude of the frequencies used for communication with geostationary satellites.

................................................................................................................................... (1)

(b) A voice communication channel is to be established between a scientific base in the northern hemisphere and its headquarters in the southern hemisphere.

For this communication channel, state and explain one advantage of using

(i) a geostationary satellite.

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(ii) a polar orbiting satellite.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

......................................................................................................................... (2)

(c) State one reason why the up-link frequency and the down-link frequency for communication satellites are different.

...................................................................................................................................

................................................................................................................................... (1)

(Total 6 marks)

23. This question is about the use of satellites for communication.

(a) (i) State what is meant by a geostationary satellite.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) Explain the advantages of the use of geostationary satellites for communication.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

239

(b) Explain the advantages of the use of polar-orbiting satellites for communication.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

(Total 7 marks)

24. This question is about an amplifier circuit.

The diagram below shows an amplifier circuit incorporating an ideal operational amplifier (op-amp).

The operational amplifier uses a +9 V / 0 / –9 V supply.

(a) Calculate the gain of the amplifier circuit.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (2)

(b) Determine the output potential Vout for values of input potential Vin equal to

(i) –0.9 V.

...........................................................................................................................

........................................................................................................................... (2)

(ii) +2.0 V.

........................................................................................................................... (1)

240

(Total 5 marks)

25. This question is about the operational amplifier.

(a) On the axes below draw a sketch graph to show the variation with input voltage Vin of the output voltage Vout of a non-inverting operational amplifier.

(2)

(b) A temperature warning device makes use of a buzzer that sounds when the potential difference across it is 24 V. The circuit in the warning device is shown.

It is required that the buzzer should sound when the temperature of the thermistor rises above 50 °C.

(i) State the voltage at point Q.

........................................................................................................................... (1)

(ii) At a temperature of 50 °C the resistance of the thermistor is R. Explain why the buzzer will sound when the temperature rises above 50 °C.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (3)

(Total 6 marks)

241

26. This question is about operational amplifiers.

(a) The diagram shows a circuit that uses an operational amplifier as an inverting amplifier.

The point P is a virtual earth, that is at the same potential (0 V) as the earth line.

(i) State the two properties of the operational amplifier which make P a virtual earth.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(ii) In the circuit Rf ��Nȍ�DQG�Rin ��Nȍ��&DOFXODWH�WKH�JDLQ�RI�WKH�DPSOLILHU�

...........................................................................................................................

........................................................................................................................... (1)

(b) The diagram shows a circuit that uses an operational amplifier as a non-inverting Schmitt trigger.

In the situation shown, the potential at point X is 2.0 V and the output potential Vout is at its minimum value of –10 V. Show that for the output potential to switch to its maximum value of +10 V

(i) the current in the resistors R1 and R2 is 0.08 mA.

...........................................................................................................................

........................................................................................................................... (1)

(ii) Vin must rise to 5.8 V.

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

242

(Total 6 marks)

27. This question is about the operational amplifier.

Diagram 1 shows a non-inverting amplifier circuit.

Diagram 1

(a) Suggest why the amplifier is referred to as non-inverting.

......................................................................................................................................

...................................................................................................................................... (1)

(b) The input voltage for the amplifier in (a) is Vin = 2.0 mV.

Calculate the

(i) gain G of the amplifier.

........................................................................................................................... (1)

(ii) output voltage Vout.

........................................................................................................................... (1)

(c) Diagram 2 shows a particular non-inverting amplifier.

Diagram 2

Explain, in terms of the properties of an op-amp, why the gain of this non-inverting amplifier is equal to 1.

......................................................................................................................................

......................................................................................................................................

......................................................................................................................................

...................................................................................................................................... (3)

243

(d) Diagram 3 shows a circuit in which the battery has an emf of 6.0 V and negligible internal UHVLVWDQFH��7ZR��0��UHVLVWRUV�DUH�FRQQHFWHG�LQ�VHULHV�WR�WKH�EDWWHU\�

Diagram 3

(i) State the value of the potential difference between points A and B.

........................................................................................................................... (1)

(ii) $�YROWPHWHU�RI�UHVLVWDQFH��N��is used to measure the potential difference across points A and B.

State why the reading on the voltmeter is not equal to the value stated in (d)(i).

...........................................................................................................................

........................................................................................................................... (1)

(iii) The circuit in diagram 3 is modified to include the circuit shown in diagram 2.

Diagram 4

Explain why the voltmeter reads the value of the potential difference as stated in (d)(i).

...........................................................................................................................

...........................................................................................................................

........................................................................................................................... (2)

(Total 10 marks)

244

28. The diagram below shows an inverting amplifier circuit.

(a) State what is meant by an inverting amplifier circuit.

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(b) The input voltage is 12 mV. Calculate

(i) the current in the 150 k: resistor.

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(ii) the potential difference between A and B.

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(c) Outline any assumptions that you have made in (b).

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(Total 6 marks)

29. This question is about a Schmitt trigger.

The diagram below shows a Schmitt trigger circuit based on an operational amplifier (op-amp).

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The output of this Schmitt trigger is positive saturation (+13 V) or negative saturation (–13 V).

(a) State two properties of an ideal op-amp.

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(b) Determine the input value that will cause the output to switch from –13 V to +13 V.

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(c) Explain how a Schmitt trigger can be used to reshape a digital pulse.

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(Total 8 marks)

30. This question is about digital signals.

(a) The graph shows the variation with time of an analogue signal.

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In order to convert the analogue signal into a 3-bit digital signal it is sampled every 100 µs. The possible output voltages of the analogue to digital converter that is used are shown below.

Analogue signal / V Binary output

0 – < 0.5 000

0.5 – < 1.0 001

1.0 – < 1.5 010

1.5 – < 2.0 011

2.0 – < 2.5 100

2.5 – < 3.0 101

3.0 – < 3.5 110

3.5 – < 4.0 111

Determine, explaining your answer, the

(i) bit-rate (data transfer rate).

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........................................................................................................................... (2)

(ii) digital output of the signal for the sixth sample starting from t = 0 s.

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(b) Explain the effects that increasing the sampling frequency and number of bits will have on the quality of the representation of the analogue signal.

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(c)The digital signal in (a) is to be transmitted along an optic fibre that has a power loss of 2.0 dB km–1.

(i) State, in watts, how power loss is defined on the decibel scale.

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(ii) Calculate the distance travelled by the signal that will result in a power loss of 75 %.

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(d) As a result of noise in electric circuits, digital pulses can often lose their shape and hence distort the information that they carry. The pulses can be re-shaped using a circuit called a Schmitt trigger. The diagram shows a Schmitt trigger that incorporates an operational amplifier.

(i) State two essential properties of an operational amplifier.

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........................................................................................................................... (2)

(ii) In the situation shown the output voltage V0 of the amplifier is at its minimum value of – 6.0 V. The voltage at the non-inverting input to the amplifier is equal to 1.0 V and at the inverting input it is VX. The output voltage will switch to its maximum value + 6.0 V if the voltage VX just exceeds +1.0 V. Determine the minimum voltage Vin that will result in an output voltage of + 6.0 V.

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(Total 16 marks)

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31. This question is about an operational amplifier used in a Schmitt trigger circuit.

(a) An operational amplifier uses a ±6.0 V supply. The operational amplifier operates in the non-inverting mode.

(i) On the axes below, sketch a graph to show how the output voltage VOUT of the amplifier varies with the potential difference V between the two inputs of the amplifier.

(2)

(ii) With reference to the graph sketched in (a)(i), explain why the operational amplifier is said to act as a comparator.

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(b) The diagram shows an operational amplifier connected as a Schmitt trigger. The output of the amplifier is ±6.0 V.

(i) Show that the upper switching voltage of the trigger, i.e. the input voltage VIN for which the output voltage VOUT switches from –6.0 V to +6.0 V, is 2.0 V.

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(ii) The input signal VIN to the trigger is shown in the graph.

The switching voltages of the trigger are ±2.0 V.

On the axes above, sketch a graph to show how the output voltage VOUT varies with time t. (2)

(c) Explain the use of a Schmitt trigger in the transmission of digital signals.

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(Total 10 marks)

32. This question is about a mobile phone network.

Erin is a passenger on a train making a call to a standard fixed telephone line (“landline”) from her mobile phone. The train moves Erin between adjacent communication cells. Outline the changes, if any, that take place in the

(a) cellular exchange.

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(b) public switched telephone network (PSTN).

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(Total 2 marks)

250

33. This question is about a mobile phone network.

A passenger in a car is using a mobile phone. State and explain the role of the base stations and the cellular exchange as the car moves from one cell to another.

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34. This question is about the mobile phone system.

In the mobile phone system, a particular geographic area is divided into a number of cells with a base station in each cell, each connected to a cellular exchange.

Describe the function of the base stations and the cellular exchange.

Base stations: .........................................................................................................................

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Cellular exchange: .................................................................................................................

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35. This question is about the mobile phone system.

(a) Suggest why mobile phones are sometimes referred to as cell phones.

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(b) Explain, based on your answer to (a), why mobile phones can be made small in size.

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(c) State a moral or ethical issue that you consider to arise from the use of mobile phones.

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(Total 4 marks)

36. In a mobile phone system an area is divided into a large number of cells.

(a) State what is meant by a cell.

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(b) Suggest two advantages of organizing the mobile phone system in this way.

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(Total 4 marks) 37. Outline one moral or ethical issue and one environmental issue that arise from the use of mobile phones.

Moral or ethical issue: ..........................................................................................................

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Environmental issue: .............................................................................................................

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................................................................................................................................................ (Total 4 marks)

physics core ahl and option

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