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Cambridge IGCSE™
Physics
Third Edition
Heather Kennett
310575 Cambridge IGCSE
9781398310575.indd
1 Physics WB CV.indd 1
27/07/2020
10:35
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PM
Cambridge International copyright material in this publication is reproduced under licence and
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Exam-style questions [and sample answers] have been written by the authors. In examinations, the
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ISBN: 978 1398 310 575
© Heather Kennett 2021
First published in 2012
Second edition published in 2015
This third edition published in 2021 by
Hodder Education
An Hachette UK Company
Carmelite House, 50 Victoria Embankment, London EC4Y 0DZ
www.hoddereducation.com
Impression number
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Year
2025 2024 2023 2022 2021
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Printed in the UK
A catalogue record for this title is available from the British Library
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Contents
Introduction
1A Measurement, motion, mass, weight and density
Student’s Book Topics 1.1–1.4
1B Forces and momentum
Student’s Book Topics 1.5, 1.6
1C Energy, work, power and pressure
Student’s Book Topics 1.7, 1.8
2 Thermal physics
Student’s Book Topics 2.1–2.3
3 Waves
Student’s Book Topics 3.1–3.4
4A Electricity and magnetism
Student’s Book Topics 4.1–4.4
4B Electromagnetic effects
Student’s Book Topic 4.5
5 Nuclear physics
Student’s Book Topics 5.1, 5.2
6 Space physics
Student’s Book Topics 6.1, 6.2
1
2
12
21
29
38
56
70
79
86
Introduction
This new edition of the Cambridge IGCSE Physics Workbook is designed as a ‘write-in’ book for
students to practise and test their knowledge and understanding of the content of the Cambridge
IGCSETM Physics course.
The sections are presented in the same order as those in the Student’s Book, Cambridge IGCSE Physics
Fourth Edition, and as in the Cambridge IGCSETM Physics syllabus for examination from 2023. All
questions have been marked as either Core or Supplement. At the end of every section, there are
longer questions (Exam-style questions) which aim to introduce students to an examination format.
This Workbook should be used as an additional resource throughout the course alongside the Student’s
Book. The ‘write-in’ design is ideal for use in class by students or for homework.
This Workbook is designed to be used throughout the Cambridge IGCSETM Physics course and, as such,
its structure mirrors the Student’s Book which also is part of this series. It should be used as extra
practice for students to apply the theoretical concepts they have studied in the Student’s Book.
This Workbook covers what we feel is a representative selection of the content within the syllabus,
although not every syllabus point has a specific question related to it.
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1A
Measurement, motion,
mass, weight and density
Core
1 State the number of millimetres in each measurement.
a 2 cm = ..............................
d 0.5 m = ..............................
b 0.4 cm = ..............................
e 1.4 m = ..............................
c 12 cm = ..............................
2 Convert each length to metres.
a 1500 cm = ..............................
c 15 cm = ..............................
b 150 cm = ..............................
d 1.5 cm = ..............................
3 Give each number as a power of ten with one figure before the decimal point.
a 1000 = ..............................
c 650 = ..............................
b 225 000 = ..............................
d 15 000 = ..............................
4 Give each number in full.
a 104 = ..............................
c 1.5 × 106 = ..............................
b 2.5 × 102 = ..............................
d 3.5 × 108 = ..............................
5 Give each decimal as a power of ten with one figure before the decimal point.
a 0.001 = ..............................
c 0.0012 = ..............................
b 0.02 = ..............................
d 0.0102 = ..............................
6 Give each fraction as i a power of ten, and ii a decimal.
a
b
c
d
2
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1
100
i .............................. ii ..............................
2
1000
i .............................. ii ..............................
3
10 000
4
5000
i .............................. ii ..............................
i .............................. ii ..............................
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1A Measurement, motion, mass, weight and density
7 State each length in metres as a power of ten.
a 5 mm = ...............................
b 50 cm = ..............................
c 5 km = ................................
8 State the number of significant figures in each of the following measurements.
a 1.53 m
number of significant figures = ..............................
b 2.5 × 104 m number of significant figures = ..............................
c 0.016 m
number of significant figures = ..............................
9 Round 1.263 m to:
a one significant figure ...................................
b two significant figures .................................
c three significant figures. ..............................
10 Calculate the area of a rectangle of length 6.0 cm and width 4.5 cm, giving your answer to an
appropriate number of significant figures.
area = ..............................
11 Calculate the area of a right-angled triangle of sides 30 cm, 40 cm, 50 cm. Show your working.
area = ..............................
12 Calculate how many bricks of size 5 cm × 2 cm × 3 cm a child would need to build a rectangular
block of dimensions 15 cm × 15 cm × 10 cm. Show your working.
number of bricks = ..............................
13 A student records the time taken for 20 complete swings of a pendulum to be 32 seconds.
Calculate the period of the pendulum.
period = ..............................
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1A Measurement, motion, mass, weight and density
14 Four runners competing in a 1 km race finish the race with these times:
A 200 s B 180 s C 230 s D 215 s
a Identify the runner that finished first. ..............................
b Identify the runner that finished last. ..............................
c Calculate the average speed in m/s of runner A. Show your working.
average speed of runner A = ..............................
15 A farmer goes for a drive in his tractor. The graph below shows how his distance from the farm
varies with time. Distance OD = 270 m.
distance/m
D
O
A
B
time/min
C
a State how far the tractor travels in time interval:
i OA ............................................................
ii AB ............................................................
iii BC ............................................................
b If BC = 3 minutes, calculate the speed in m/s of the tractor over time interval BC.
Show your working.
speed over time interval BC = ..............................
16 The Mars Rover Curiosity has a mass of 900 kg. Taking the gravitational field strength to be 9.8 N/kg
on Earth and 3.7 N/kg on Mars, give the value of the weight of the Rover on:
a Earth .................................................................
b Mars ..................................................................
4
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1A Measurement, motion, mass, weight and density
17 Give the weight of the following masses. Take the gravitational field strength to be 9.8 N/kg.
a A mass of 15 g has a weight of ..............................
b A mass of 51 g has a weight of ..............................
c A mass of 0.3 kg has a weight of ..............................
d A mass of 3.1 kg has a weight of ..............................
18 On the Earth the acceleration of free fall is about 9.8 m/s2. On the Moon the acceleration of free
fall is about 1.6 m/s2. A man weighs 784 N on the Earth. Give his:
a mass measured on the Moon
mass = ..............................
b weight measured on the Moon.
weight = ..............................
19 Circle the correct SI unit of density.
A g/cm2
B g/m3
C kg/m3
D kg/cm3
20 A block of ice has dimensions 2.0 cm × 2.0 cm × 2.0 cm and a mass of 7.36 g. Calculate the density
of the ice. Show your working.
density = ..............................
21 A metal spanner has a mass of 200 g. It is lowered into a measuring cylinder of water until it is
completely submerged. The original level of the water was 50 cm3 and the final level is 75 cm3.
Calculate:
a the volume of the metal
volume = ..............................
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1A Measurement, motion, mass, weight and density
b the density of the metal. Show your working.
density = ..............................
22 The density of air is 1.3 kg/m3. Calculate the mass of air in a room of dimensions 3 m × 4 m × 2.5 m.
Show your working.
mass of air = ..............................
Supplement
23 a A bus starts from rest and accelerates smoothly. After 10 s the bus reaches a speed of 8 m/s.
Calculate the acceleration of the bus. Show your working.
acceleration = ..............................
b The bus continues to travel at 8 m/s and then decelerates smoothly as it approaches a bus
stop. If the deceleration is 2 m/s2, calculate the time over which the bus decelerates before it
comes to rest. Show your working.
time = ..............................
24 A lorry is moving with a uniform acceleration of 1.5 m/s2. At a certain time it is travelling at a
speed of 6 m/s. Calculate the speed of the lorry 4 s later. Show your working.
speed = ..............................
25 The speed of a skier increases steadily from 8 m/s to 20 m/s in 60 s. Calculate:
a the average speed of the skier
average speed = ..............................
6
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1A Measurement, motion, mass, weight and density
b the distance travelled by the skier in 60 s. Show your working.
distance = ..............................
c the acceleration of the skier. Show your working.
acceleration = ..............................
26 A girl rides her skateboard in a park. The graph below shows how her speed varies over a
period of time.
speed/m/ s
D
O
A
B
time/s
C
OD = 3 m/s, OA = 20 s, AB = 16 s, BC = 14 s. Calculate:
a the speed of the girl at time A
speed = ..............................
b her acceleration in time interval OA
acceleration = ..............................
c the distance she travels in time interval AB. Show your working.
distance in time interval AB = ..............................
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1A Measurement, motion, mass, weight and density
d the distance she travels in time interval BC. Show your working.
distance in time interval BC = ..............................
27 An object falls from rest from the top of a high building. Ignore air resistance and take g = 9.8 m/s2.
a Calculate:
i the velocity of the object after 2 s
velocity = ..............................
ii the distance the object falls in 2 s. Show your working.
distance = ..............................
b Describe the shape and gradient of a graph of velocity against time for the object.
....................................................................................................................................
....................................................................................................................................
8
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1A Measurement, motion, mass, weight and density
Exam-style questions
Core
1 The volume of a liquid in a measuring cylinder is 500 cm3. The liquid is poured into a square
tank of internal dimensions 10 cm × 10 cm × 10 cm.
a Calculate how full the container will be.
Circle the correct answer.
1
1
1
full
C full
D full
[3]
2
4
3
b A brick of dimensions 4 cm × 3 cm × 5 cm is then lowered into the tank so that it is completely
submerged. Calculate how far the liquid level rises.
A completely full
B
Circle the correct answer.
A 0.6 cm
B 1.0 cm
C 1.5 cm
D 2 cm
[3]
c A book has 120 pages and a thickness of 8.2 mm. The front and back cover of the book are
each 0.5 mm thick. Calculate the thickness of each page.
thickness = ..............................
[3]
[Total: 9]
distance/m
2 A woman goes for a walk to the local park. The graph below shows how her distance from
home varies with time.
O
A
B
time/min
C
Choose the correct answer from the box to the questions a, b and c.
zero
constant
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decreasing
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1A Measurement, motion, mass, weight and density
a During the time interval OA,
i
the distance of the woman from O is ..............................
ii her speed is ..............................
[1]
[1]
b During the time interval AB,
i
the distance of the woman from O is ..............................
ii her speed is ..............................
[1]
[1]
c During the time interval BC,
i
the distance of the woman from O is ..............................
ii her speed is ..............................
[1]
[1]
d Over which time interval is her speed greatest? ..............................
[1]
[Total: 7]
Supplement
3 Oil with a volume of 50 cm3 has a mass of 46 g.
a Calculate the density of the oil.
density of oil = ..............................
[2]
b Vinegar of density 0.98 g/cm3 is poured onto the oil; the two liquids do not mix.
Explain why the vinegar sinks.
...............................................................................................................................
.......................................................................................................................... [2]
[Total: 4]
4 Circle which of the following quantities is a vector.
A density
B velocity
C time
D mass
[Total: 1]
10
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1A Measurement, motion, mass, weight and density
5 A man travels to work by car. He travels on local roads and on the motorway. The graph below
shows how his speed varies with time during the journey.
speed/m/ s
D
O
A
B
time/s
C
Take OD = 30 m/s, OA = 200 s, AB = 450 s and BC = 300 s.
a Calculate the acceleration of the car during OA.
acceleration = ..............................
[2]
b Calculate the deceleration of the car during BC.
deceleration = ..............................
[2]
c Calculate the average speed of the car in time interval BC.
average speed = ..............................
[2]
d Calculate how far the car travels in time interval BC.
distance travelled = ..............................
[2]
e Identify the time interval over which the average speed of the car is the highest.
..............................
[1]
[Total: 9]
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1B Forces and momentum
Core
1 A box is subject to the forces shown in the diagram below.
5N
7.5 N
7.5 N
10 N
a Calculate the size and direction of the resultant force on the box. Show your working.
resultant force = ........................
b State the size and direction of the extra force needed to reduce the resultant to zero.
Show your working.
extra force = ..............................
2 Fill in the gaps in the following paragraph.
If there is no resultant .............................. on a body, it remains at .............................. or
continues to move at a .............................. speed in a .............................. line.
3 A skydiver of mass 80 kg jumps from a plane. Taking g = 9.8 m/s2, determine:
a the weight of the skydiver
weight = ..............................
b the force due to gravity acting on the skydiver ..............................
12
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1B Forces and momentum
c the resultant force on the skydiver when the air resistance is 300 N
resultant force = ..............................
d the value of the air resistance after the skydiver’s parachute has opened and the skydiver has
reached a constant speed. ...............................
4 A uniform metre ruler is balanced at its midpoint.
A weight, W, is hung from one end of the ruler and a load, L, is suspended at a distance X from
the fulcrum, as shown.
X
50 cm
fulcrum
W
L
Calculate the distance X for the ruler to be balanced when:
a L = 2W
X = ..............................
b L = 5W
X = ..............................
c L = 10W
X = ..............................
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1B Forces and momentum
5 Use the following words to fill in the gaps in the paragraph below.
clockwise
equals
forces
no
resultant
direction
equilibrium
moments
point
sum
When a number of parallel .............................. act on a body it will be in ..............................
when (i) the .............................. of the forces in one direction .............................. the sum
of the forces in the opposite .............................. and (ii) the sum of the ..............................
moments about any .............................. equals the sum of the anticlockwise ..............................
about the same point. This means that there is .............................. resultant force and no
.............................. turning effect when a system is in equilibrium.
6 A uniform board of length 90 cm is pivoted at a hinge at one end. It is kept level by an upward
vertical force T applied at the opposite end. The weight of the board is 6 N.
T
90 cm
6N
a Take moments about the hinge to calculate T when the board is level. Show your working.
T = ..............................
b The hinge exerts an upward force, F, on the board. Equate parallel forces to determine F when
the board is level. Show your working.
F = ..............................
7 Explain how you would calculate the centre of gravity of a triangular-shaped piece of card using a
pivot and a plumb line.
.........................................................................................................................................
.........................................................................................................................................
.........................................................................................................................................
.........................................................................................................................................
14
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1B Forces and momentum
Supplement
8 A
mass of 0.5 kg extends a spring by 10 cm. When an unknown mass, M, is hung on the spring,
the extension is 15 cm. Calculate the value of M. Show your working.
M = ..............................
9 A
force of 10 N extends a spring by 3.0 cm. Calculate the extension if a mass of 0.3 kg is attached
to the end of the spring. Show your working.
Circle the correct answer.
A 0.9 mm
B 1.0 mm
C 3.0 mm
D 9.0 mm
10 Describe the difference between a scalar and a vector, and give an example of each.
.........................................................................................................................................
.........................................................................................................................................
.........................................................................................................................................
11 Forces of 4 N and 3 N act at 90° to each other. Calculate the magnitude and direction of their
resultant. Show your working.
magnitude of resultant = ..............................
direction of resultant = ..............................
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1B Forces and momentum
12 A mass of 50 kg experiences a force F1 to the right and a force F2 to the left.
a If F1 = 100 N and F2 = 80 N, calculate:
i the resultant force on the mass. Show your working.
force = ..............................
ii the acceleration of the mass. Show your working.
acceleration = ..............................
b If F1 = F2 = 80 N, calculate:
i the resultant force on the mass
force = ..............................
ii the acceleration of the mass.
acceleration = ..............................
13 Calculate the resultant force that produces an acceleration of 4 m/s2 in a mass of 15 kg.
resultant force = ..............................
16
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1B Forces and momentum
14 A girl whirls a ball on the end of a string in a vertical circle at a constant speed.
The velocity of the ball is changing.
a Describe the difference between speed and velocity in terms of vectors and scalars.
.....................................................................................................................................
.....................................................................................................................................
b Explain what causes the velocity of the ball to change.
....................................................................................................................................
....................................................................................................................................
c When the girl whirls the ball faster and faster, the string breaks when the ball is at its lowest
point. In which direction does the ball fly off?
....................................................................................................................................
15 The momentum of a body of mass m and velocity v is equal to m × v. Calculate the momentum of
a 5.0 kg trolley travelling at velocity:
a 3 m/s
momentum = ..............................
b 40 m/s
momentum = ..............................
16 An ice hockey puck moves in a straight line with a velocity of 5 m/s. It strikes a second identical
puck, which is initially at rest, head-on. The second puck moves off in the same straight line as
the first puck with a velocity of 4 m/s. Calculate the velocity of the first puck after the collision.
Show your working.
velocity of first puck after collision = ..............................
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1B Forces and momentum
17 A ball of mass 50 g is at rest before being struck by a bat. The collision between the bat and the
ball lasts for 0.002 s, and the speed of the ball immediately after it leaves the bat is 20 m/s.
a Calculate the momentum of the ball just after it leaves the bat.
momentum of ball = ..............................
b Calculate the impulse acting on the ball during the collision.
impulse on ball = ..............................
c Calculate the steady force which the bat exerts on the ball during the collision.
force = ..............................
Exam-style questions
Core
1 The following measurements are obtained when a spring is stretched.
Stretching force/N
2
4
6
8
10
Extension/mm
1
2
3
4.2
6
a Sketch an extension–force graph for the spring. Plot extension on the y-axis and force on
the x-axis.
[4]
18
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1B Forces and momentum
b Mark on your graph the region over which the plot is linear.
[1]
c Calculate the gradient of your graph.
[2]
gradient = ..............................
[Total: 7]
Supplement
2 a Calculate the spring constant of a spring which is stretched 10 cm by a mass of 2 kg.
[2]
spring constant = ..............................
b The length of an unstretched spring is 20 cm. When a force of 0.5 N is applied to the spring
it stretches to a total length of 30 cm. Assume the limit of proportionality is not exceeded.
Calculate the spring constant.
[2]
spring constant = ..............................
c The spring in part b is now stretched to 40 cm. Assuming again that the limit of
proportionality is not exceeded, calculate the extension and the force applied.
i
[1]
extension of spring = ..............................
ii force applied = .............................
[1]
[Total: 6]
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1B Forces and momentum
3 A trestle consists of a plank resting on two supports which exert upward forces of P and Q, as
shown. The weight of the plank is 80 N (shown acting through its centre).
1m
3m
2m
P
2m
Q
O
plank
80 N
a Take moments about the left support to calculate the value of Q.
Q = ..............................
[2]
b Equate parallel forces to calculate the value of P.
P = ..............................
[2]
[Total: 4]
4 A golfer strikes a stationary golf ball of mass 45 g with a golf club. The golf club is in contact
with the ball for a time of 0.001 s and exerts a force of 1350 N on it.
a Calculate the acceleration of the ball during the time it is in contact with the club.
[2]
acceleration = ..............................
b Calculate the velocity of the ball just after it is struck.
[2]
velocity = ..............................
c Give two ways by which the velocity of the golf ball could be increased.
1 ..............................................................................................................................................
2 ........................................................................................................................................ [2]
[Total: 6]
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1C
Energy, work, power and
pressure
Core
1 State how energy is transferred from:
a a steam turbine
.....................................................................................................................................
b a generator.
.....................................................................................................................................
2 State the stores between which energy is transferred:
a when a stone falls from a cliff
............................................................ → .............................................................
b when coal is burnt to heat water in a boiler.
............................................................ → .............................................................
3 A dog pulls a sledge across a flat snowfield for a distance of 500 m. The dog exerts a steady force
of 120 N on the sledge. Calculate the work done. Show your working.
work done = ..............................
4 When a force of 150 N is applied to a piston X, it moves through a distance of 10 cm in the
direction of the force.
a Calculate the work done by piston X. Show your working.
work done = ..............................
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1C Energy, work, power and pressure
b Another piston, Y, does the same amount of work as piston X in part a. The force on piston Y is
750 N. Calculate how far piston Y moves in the direction of the force. Show your working.
distance = ..............................
5 Explain what is meant by ‘renewable’ and ‘non-renewable’ energy resources. Give two examples of
each type of resource.
a renewable energy resources:
.....................................................................................................................................
example: ................................................................................................................................
example: ................................................................................................................................
b non-renewable energy resources:
.....................................................................................................................................
example: ................................................................................................................................
example: ................................................................................................................................
6 A lift raises a load of 9000 N to a height of 20 m in 15 seconds.
a Calculate the work done. Show your working.
work done = ..............................
b Calculate the power of the lift. Show your working.
power = ..............................
7 Calculate the pressure on a surface when a force of 40 N acts on an area of:
a 4.0 m2
pressure = ..............................
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b 0.5 m2
pressure = ..............................
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1C Energy, work, power and pressure
c 0.1 m2
pressure = ..............................
d 4.0 cm2
pressure = ..............................
8 Calculate the force on each area if a pressure of 20 Pa acts on it.
a area = 2 m2
force = ..............................
c area = 1 cm2
force = ..............................
b area = 1 m2
force = ..............................
d area = 0.1 cm2
force = ..............................
9 A boy decides to go for a walk in some soft snow. Which of the following footwear should he
choose so that he sinks into the snow the least distance?
Circle the correct answer.
A boots of contact area 0.7 m2
B snow shoes of contact area 1.5 m2
C skis of contact area 1.0 m2
D ice skates of contact area 5 × 10–4 m2
10 In a hydraulic jack a force of 100 N is applied to a piston of surface area 4.0 cm2.
a Calculate the pressure applied to the fluid by the piston. Show your working.
pressure = ..............................
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1C Energy, work, power and pressure
b The fluid transmits the pressure to a larger piston of surface area 20 cm2.
i Calculate the force exerted by the larger piston. Show your working.
force = ..............................
ii Calculate the weight that can be lifted by the jack.
weight = ..............................
Supplement
11 Calculate the kinetic energy of a mass of 5 kg travelling at a velocity of:
a 6 m/s
b 12 m/s
Show your working.
Ek = ..............................
Ek = ..............................
12 Taking g = 9.8 N/kg, calculate the gravitational potential energy gained by a mass of 5.1 kg raised to a
height of:
a 10 m above the ground
b 25 m above the ground
Show your working.
ΔEp = ..............................
ΔEp = ..............................
13 Calculate the velocity of a truck with kinetic energy 2.7 kJ and mass 600 kg. Show your working.
velocity = ..............................
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1C Energy, work, power and pressure
14 A box of mass 3 kg is dropped from a height of 5.1 m.
a Neglecting air resistance, calculate and show your working for:
i the gravitational potential energy of the box before it is dropped
Ep = ..............................
ii the kinetic energy of the box just before it reaches the ground
Ek = ..............................
iii the velocity of the box just before it strikes the ground.
velocity = ..............................
b Explain what happens to the kinetic energy of the box when it strikes the ground.
....................................................................................................................................
15 Water flows over a dam wall at a rate of 2000 kg/s. The dam wall is 10 m high. Calculate how much
power can be generated by the falling water if 90% of its potential energy can be harnessed to
produce electricity. Show your working.
power generated = ..............................
16 An electrical appliance has a power input of 500 W.
a The appliance transfers energy at a rate of 350 W. Calculate its efficiency. Show your working.
efficiency = ..............................
b Explain what happens to the ‘lost’ energy’.
....................................................................................................................................
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1C Energy, work, power and pressure
17 A swimming pool contains water at a depth of 3.05 m. Calculate the difference in water pressure
between the top and bottom of the pool. Show your working. Take the density of water to be
1.0 × 103 kg/m3.
pressure difference = ..............................
Exam-style questions
Core
1 Two identical ropes are attached to either end of a beam of weight 600 N.
a Calculate the tension (force), T, in each rope when they support the beam horizontally above
the ground.
T = ..............................
[1]
b Calculate the work done if the beam is raised vertically by 1.5 m.
work done = ..............................
[2]
c Calculate the power needed to raise the beam 1.5 m in 3 seconds.
power = ..............................
[2]
[Total: 5]
2 Give two advantages and two disadvantages of using the following as sources of energy for
electricity generation.
a solar energy
i
advantages: ..........................................................................................................
.......................................................................................................................... [2]
ii disadvantages: ......................................................................................................
.......................................................................................................................... [2]
26
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1C Energy, work, power and pressure
b nuclear energy
i
advantages: ..........................................................................................................
.......................................................................................................................... [2]
ii disadvantages: ......................................................................................................
.......................................................................................................................... [2]
c wind energy
i
advantages: ..........................................................................................................
.......................................................................................................................... [2]
ii disadvantages: ......................................................................................................
.......................................................................................................................... [2]
d gas-fired power stations
i
advantages: ..........................................................................................................
.......................................................................................................................... [2]
ii disadvantages: ......................................................................................................
.......................................................................................................................... [2]
[Total: 16]
Supplement
3 a A cyclist freewheels (without pedalling) from rest down a hill. Explain the energy transfers
which occur during her descent.
..............................................................................................................................
..............................................................................................................................
..............................................................................................................................
.......................................................................................................................... [3]
b On reaching level ground the cyclist pedals along a straight road with a constant speed of
12 m/s. She experiences a resistive force, F, of 5 N, which acts in the opposite direction to that
in which she is travelling. Calculate the work she does against F in 1 second.
work done = ..............................
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1C Energy, work, power and pressure
c F then increases to 7.5 N. Calculate the cyclist’s new speed, if she maintains the same rate
of working as in part b.
i
rate of working = ..............................
[1]
ii speed = ..............................
[2]
[Total: 8]
4 A ball of mass 60 g is projected vertically upwards from ground level with an initial velocity of
30 m/s. Neglect the effect of air resistance on the motion of the ball. Determine:
a the initial kinetic energy of the ball
initial Ek = ..............................
[3]
b the initial potential energy of the ball
initial Ep = ..............................
[1]
c the potential energy of the ball when it reaches its greatest height
Ep at greatest height = ...............................
[1]
d the greatest height reached by the ball.
greatest height = ..............................
[2]
[Total: 7]
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2
Thermal physics
Core
1 Identify the state of matter – solid, liquid or gas – in which the molecules are:
a least densely packed ..............................
b ordered in a regular pattern ..............................
c moving at high speed over large distances ..............................
d moving about over small distances ..............................
e vibrating towards and away from a fixed point. ..............................
2 Identify the state of matter – solid, liquid or gas – which:
a is highly compressible ..............................
b has a definite shape ..............................
c flows easily. ..............................
3 Some smoke particles are allowed to drift into a glass box which contains air. The box is then
sealed and illuminated. The random motion of the smoke particles in the box is viewed through a
microscope.
a Explain the random motion of the smoke particles with reference to the size, number and
motion of air molecules.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
b The box is heated so that the temperature of the air it contains rises. Explain how the rise in
temperature affects the motion of the smoke particles.
.....................................................................................................................................
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2 Thermal physics
.
4 Use the kinetic particle model to explain how a gas exerts a pressure on the walls of its container;
give two key facts.
.........................................................................................................................................
.........................................................................................................................................
5 The air in a closed container is heated.
a State how the air pressure inside the container changes when the temperature rises.
.....................................................................................................................................
b Explain your answer to a in terms of the kinetic particle model. State the effect on the motion
of the molecules, their interaction with the walls and the resulting effect.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
6 The volume of a gas remains constant when it is heated in a closed container.
Circle the statement that is false.
A The pressure of the gas will increase.
B The average kinetic energy of the molecules will decrease.
C The molecules will hit the walls of the container more often.
D The molecules will move in all directions.
7 A fixed mass of gas is heated in a container which maintains the gas at constant pressure.
Circle the statement that is true.
A The volume of the gas will decrease.
B The volume of the gas will increase.
C The number of molecules will decrease.
D The molecules will hit the walls of the container more often.
8 On the Celsius scale of temperature, state the value of:
a the melting temperature of ice ..............................
b the boiling temperature of water at normal pressure. ..............................
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2 Thermal physics
9 A temperature has a different value in degrees Celsius than it has in Kelvin.
a State the relationship between a temperature T (in K) to its value q (in °C).
.....................................................................................................................................
b Convert a temperature of 30°C to a value in Kelvin. .................................................................
c Convert a temperature of 150 K to a value in °C. ......................................................................
10 State the meaning, with reference to states of matter, of:
a melting temperature
.....................................................................................................................................
.....................................................................................................................................
b boiling temperature
.....................................................................................................................................
.....................................................................................................................................
11 Which of these materials would you choose to use for the following applications?
A wood
B glass
C steel
D fibreglass
E cardboard
a a cooking pot ................................................................
b the handle of a saucepan ...............................................
c a container for a takeaway pizza ...................................
d roof insulation for a house .........................................
12 Describe an experiment, using metal and wood rods (of the same dimensions), to show the
difference between a good conductor and a bad conductor of thermal energy.
.........................................................................................................................................
.........................................................................................................................................
.........................................................................................................................................
.........................................................................................................................................
.........................................................................................................................................
.........................................................................................................................................
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2 Thermal physics
13 Explain why a metal object at room temperature feels cold compared to a plastic object at the
same temperature.
.........................................................................................................................................
.........................................................................................................................................
14 Circle the following statement that is incorrect.
A hot air rises
C cold air is less dense
B cold air sinks
D hot air is less dense
15 Circle the correct answer below.
Convection takes place in:
A only solids
C only gases
B only liquids
D gases and liquids
16 These are features of a vacuum flask:
A double-walled glass container
C silvered glass surfaces
B vacuum
D metal container
State which of the above features reduces the transfer of thermal energy by:
a both conduction and convection ..............................
b radiation. ..............................
17 Use the following words to fill in the gaps in the paragraph below.
electromagnetic
fluid
lower
temperature
energy
higher
radiation
thermal
Conduction is the transfer of .............................. energy through matter from places of
.............................. temperature to places of .............................. temperature without
movement of the matter as a whole. Convection is the transfer of thermal ..............................
through a fluid from places of higher .............................. to places of lower temperature by
movement of the ............................... In .............................., thermal energy is transferred from
one place to another by means of .............................. waves; no medium is required.
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2 Thermal physics
Supplement
18 A fixed mass of gas occupies a volume of 200 cm3 at a temperature of 27°C and a pressure of
1 atmosphere. If the temperature is kept constant, calculate and show your working for:
a the volume occupied when the pressure is halved
volume = ..............................
b the volume occupied when the pressure is doubled.
volume = ..............................
19 A fixed mass of gas occupies a volume of 100 cm3 at a pressure of 2 × 105 Pa. The temperature of
the gas is kept constant. Calculate and show your working for:
a the pressure when the volume is doubled
pressure = ..............................
b the pressure when the volume is halved.
pressure = ..............................
20 The following amounts of energy in joules are needed to raise the temperature of 1 kg of different
materials, A, B, C and D, by 1°C.
A 4000
B 960
C 450
D 390
a Which material has the highest, specific heat capacity? ..............................
b Define ‘specific heat capacity’.
....................................................................................................................................
....................................................................................................................................
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2 Thermal physics
21 Passive solar houses are energy-efficient buildings designed to trap and store sunlight in the
winter. They often include an internal feature of a brick or concrete wall close to a window.
Explain the purpose of the wall and why brick or concrete is used.
........................................................................................................................................
........................................................................................................................................
22 A cup of coffee is heated in a microwave oven. The mass of the liquid is 70 g and its specific
heat capacity is 4000 J/kg °C. Calculate the energy needed to raise the temperature of the
coffee by 60°C. Show your working.
energy required = ..............................
23 A 150 W immersion heater is used to heat 500 g of water in an insulated container. It takes
9 minutes and 20 seconds to raise the temperature of the water from 20°C to 60°C.
Calculate the specific heat capacity of the water. Show your working.
specific heat capacity of water = ..............................
24 For a and b, circle one statement that is incorrect.
a During melting:
A the temperature remains constant
B the average kinetic energy of the particles increases
C the distance between particles increases
D thermal energy is absorbed.
b During solidification:
A the temperature of the material increases
B the average kinetic energy of the molecules remains constant
C the distance between particles decreases
D thermal energy is given out.
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2 Thermal physics
25 This question is about evaporation.
a Use the kinetic particle model to explain why a liquid cools when evaporation from its
surface occurs. Compare the speed and kinetic energy of particles escaping from, or remaining
in, the liquid.
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
b Identify two factors that increase the rate of evaporation of a liquid.
1 .................................................
2 .................................................
26 This question is about radiation.
a Two copper blocks are immersed in hot water until they reach the same temperature.
The blocks are identical except that block A is painted black and block B has a shiny surface.
When the two blocks are removed from the hot water and placed well separated on a wooden
board, which block cools faster? Give a reason for your answer.
....................................................................................................................................
....................................................................................................................................
b Explain why:
i shiny aluminium foil is sometimes placed behind central heating radiators
................................................................................................................................
ii it is cooler to wear a white t-shirt than a black one on a hot day.
................................................................................................................................
Exam-style questions
Core
1 There are three states of matter: solid, liquid and gas.
a Explain how the temperature of a liquid changes when it i boils and ii solidifies.
i
...................................................................
ii ...................................................................
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2 Thermal physics
b State how the separation of the particles in a liquid changes when it i boils and ii solidifies.
i
...................................................................
ii ...................................................................
[2]
c Explain what happens to a liquid during evaporation.
..............................................................................................................................
..............................................................................................................................
.......................................................................................................................... [3]
[Total: 7]
2 Air is a poor conductor of thermal energy but a good insulator.
a Give three everyday examples of the use of trapped air to provide insulation.
1 ...................................................................
2 ...................................................................
3 ...................................................................
[3]
b Explain why using trapped air for insulation is more effective than using air alone.
.......................................................................................................................... [1]
[Total: 4]
Supplement
3 Describe an experiment to measure the specific heat capacity of an aluminium block.
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
.......................................................................................................................................................
.......................................................................................................................................................
.......................................................................................................................................................
[Total: 8]
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2 Thermal physics
4 This question is about conduction.
a Use the kinetic particle model to explain how thermal energy is transferred through a
solid object.
..............................................................................................................................
..............................................................................................................................
..............................................................................................................................
.......................................................................................................................... [4]
b Explain why poor electrical conductors are also poor thermal conductors.
..............................................................................................................................
.......................................................................................................................... [1]
[Total: 5]
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3
Waves
Core
1 Explain the difference between a transverse wave and a longitudinal wave.
.........................................................................................................................................
.........................................................................................................................................
displacement/cm
2 The diagram below shows a displacement–distance graph of a wave at a particular instant.
distance/cm
Label a crest, a trough, the amplitude and the wavelength.
1
3 A wave crest passes a particular point every 10 th of a second. Calculate the frequency of the wave.
frequency = ..............................
4 A heart rate is timed at 72 beats a minute. Calculate the frequency of the heart rate. Show your
working.
frequency = ..............................
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3 Waves
5 The lines drawn below represent the crests of water waves in a ripple tank.
wave
crest
wave
generator
36 cm
The distance occupied by six waves is 36 cm. The frequency of the wave generator is 5 Hz.
Calculate:
a the wavelength of the waves
wavelength = ..............................
c the speed of the waves
wave speed = ..............................
b the frequency of the waves
frequency = ..............................
d the time taken to travel 9.6 m.
time taken = ..............................
6 When a water wave enters shallower water, its speed changes from 10 m/s to 5 m/s. State the
changes that occur to:
a the frequency .........................................................................
b the wavelength ......................................................................
c the direction of travel. ...........................................................
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3 Waves
7 Use some of the following words to fill in the gaps in the paragraph below.
after
lines
beam
narrower
before
slower
direction
ray
diverging
wider
faster
Light travels in straight ............................... In diagrams a ray is used to represent the
.............................. in which the light is travelling. A .............................. is drawn as a straight
line with an arrow on it. A .............................. of light consists of many rays which may be
parallel, .............................. or converging. A diverging beam spreads out, while a converging
beam becomes ............................... Light travels much .............................. than sound. We see a
lightning flash .............................. we hear the corresponding sound of the thunder.
8 Sketch light rays in the following types of beam:
a parallel
b converging
c diverging
9 A ray of light is reflected from a plane mirror, as shown.
a Label the plane mirror, the incident ray, the normal to the mirror, the reflected ray, the angle
of incidence, i, and the angle of reflection, r.
b Use a protractor to determine:
i the angle of incidence, i = ..............................
ii the angle of reflection, r = ..............................
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3 Waves
10 In each of the following diagrams:
a sketch the normal to the plane mirror at the point the light ray strikes it
b mark on the angle of incidence, i
c sketch the reflected ray.
i
ii
iii
iv
v
vi
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3 Waves
11 Two plane mirrors, AB and BC, are set up at right angles. ON is a normal to the mirror AB. A ray of
light XO is incident on AB, as shown. It is reflected at mirror AB and then travels on to mirror BC,
where it is again reflected.
A
X
35°
N
O
C
B
a On the diagram, continue the ray XO to show the path it takes after reflection at each mirror.
b Determine the following values:
i angle of incidence at mirror AB = ..............................
ii angle of reflection at mirror AB = ..............................
iii angle of incidence at mirror BC = ..............................
iv angle of reflection at mirror BC = ..............................
c Comment on the path of the reflected ray.
....................................................................................................................................
12 Circle the statement that is false.
The image in a plane mirror is:
A as far behind the mirror as the object is in front
B larger than the object
C virtual
D upright.
13 Explain what is meant by a ‘real’ image. Give two key facts.
.........................................................................................................................................
.........................................................................................................................................
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3 Waves
14 A girl is standing 0.5 m away from a plane mirror.
a State how far away the girl is from her image in the mirror.
distance from image = ..............................
b Determine how far the girl must walk away from the mirror to be 3 m from her image.
distance walked = ..............................
15 Describe what happens to a ray of light when it passes from air into a different material, such as
glass or water.
........................................................................................................................................
........................................................................................................................................
16 Use the following words to fill in the gaps in the paragraph below.
away from
denser
normal
normally
optically
towards
A ray of light is bent .............................. the normal when it enters an optically
.............................. medium and .............................. the .............................. when it enters an
.............................. less dense medium. When a ray strikes a surface .............................., it is
not refracted.
17 Circle the diagram which shows the ray of light refracted correctly.
A
C
water
air
air
glass
B
D
air
glass
water
air
18 When sunlight falls on a triangular glass prism, a band of colours (called a spectrum) is obtained.
a Explain why this happens.
....................................................................................................................................
....................................................................................................................................
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3 Waves
b Give the colours of the spectrum, in order of diminishing wavelength.
....................................................................................................................................
....................................................................................................................................
c Sketch the path of red and blue rays of light through the prism.
prism
19 Explain what is meant by ‘total internal reflection’ in terms of optical density, angle of incidence
and critical angle.
.........................................................................................................................................
.........................................................................................................................................
.........................................................................................................................................
20 Use the following words to fill in the gaps in the paragraph below.
centre
refracted
F
thin
focus
top
parallel
two
principal
undeviated
The image of an object formed by a .............................. converging lens can be found by drawing
.............................. of the following three rays:
• a ray from the top of the object .............................. to the principal axis of the lens which is
refracted through the principal ..............................
• a ray from the top of the object which passes .............................. through the optical
.............................., C, of the lens
• a ray from the .............................. of the object through the principal focus, ..............................,
which is .............................. parallel to the .............................. axis of the lens.
21 An object is placed 15 cm from a converging lens of focal length 12 cm. Circle the correct
description of the image.
A virtual, erect and larger
C real, inverted and the same size
B real, inverted and smaller
D real, inverted and larger
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3 Waves
22 Explain how you could estimate the focal length of a converging lens.
.........................................................................................................................................
.........................................................................................................................................
23 A small lamp is placed at the principal focus of a converging lens. Identify the type of beam that
will be produced by the lens. ..............................
24 This question is about electromagnetic waves.
a Identify four properties that are common to all types of electromagnetic wave.
1 .................................................
3 .................................................
2 .................................................
4 .................................................
b Identify the type of electromagnetic wave used in:
i intruder alarms ...................................................
ii cooking .............................................................
iii detecting broken bones ......................................
iv remote controllers for TVs ...................................
v luggage screening at airports ..............................
vi mobile phones. ..................................................
25 Identify which of the waves in the box below:
infrared light
blue light
X-rays
radio waves
a has the longest wavelength .....................................
b has the highest frequency .......................................
c is the most penetrating. .........................................
26 The speed of light in air is 3 × 108 m/s.
a Calculate the wavelength in air of violet light of frequency 7.5 × 1014 Hz. Show your working.
wavelength of violet light = ..............................
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3 Waves
b Calculate the wavelength in air of red light of frequency 4.3 × 1014 Hz. Show your working.
wavelength of red light = ..............................
27 Identify the risk associated with and a precaution that can be taken when:
a using a mobile phone
risk:..............................................................................................................................
precaution: ...................................................................................................................
b taking a medical X-ray photograph.
risk:..............................................................................................................................
precaution: ...................................................................................................................
Supplement
28 Two light rays, OP and OQ, from a point object, O, are incident on a plane mirror.
P
Q
O
a Sketch the normals to the mirror at the points of contact of the rays, and sketch the reflected
rays. Use dotted lines to extend the reflected rays behind the mirror to locate and mark the
position of the image, I.
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3 Waves
b State the characteristics of the image.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
c Comment on the distance of the image from the mirror.
.....................................................................................................................................
29 Light travels at a speed of 3 × 108 m/s in air. Calculate and show your working for the speed of
light in:
a glass of refractive index 3
b water of refractive index 4
2
3
speed of light in glass = ..............................
speed of light in water = ..............................
30 a An optical fibre is made of glass of refractive index 1.5. Sketch the path of a ray that undergoes
total internal reflection in the optical fibre.
optical fibre
b Are analogue or digital signals preferred for transmitting data in optical fibres?
.....................................................................................................................................
31 Water has a critical angle of 49°.
a Sketch what happens to a ray of light incident on a water/air boundary at the critical angle.
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3 Waves
b Calculate the refractive index of water using the equation n = 1 . Show your working.
sin c
refractive index = ..............................
32 The critical angle for light travelling in a certain liquid is 52°. Calculate the refractive index of
the liquid. Show your working.
refractive index = ..............................
33 a Circle which one of the following does not change when red light enters glass from air.
A speed
B frequency
C wavelength
D angle ray makes
to the normal
b Define the term ‘monochromatic’.
....................................................................................................................................
34 A sound wave has a wavelength of 20 cm and a speed of 330 m/s.
a Calculate the frequency of the sound wave. Show your working.
frequency of wave = ..............................
b State a typical value for a sound wave of:
i audible frequency ..................................
ii ultrasonic frequency ..............................
35 Calculate how far away the storm is when 8 seconds elapse between a lightning flash and the clap
of thunder. Show your working. (Sound travels at 330 m/s.)
distance of storm = ..............................
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3 Waves
Exam-style questions
Core
1 Circle the statement that is true.
The image in a plane mirror is:
A as far behind the mirror as the object is in front
B smaller than the object
C real
D inverted.
[Total: 1]
2 Right-angled glass prisms A and B are made of glass that has a critical angle of 42°.
45°
A
45°
B
a Sketch the path of the rays through prisms A and B.
[5]
b Identify an instrument for each that would use prisms in orientation:
i
A ..............................
[1]
ii B ..............................
[1]
[Total: 7]
3 a Sketch a half-size ray diagram to locate the image of an object placed on the principal
axis, 10 cm from the optical centre of a thin converging lens of focal length 5 cm. Mark the
position of the principal foci, optical centre, object and image on your diagram.
[4]
b Determine how far from the lens the image is formed. ..............................
[1]
c Determine the size of the image compared to that of the object. ..............................
[1]
[Total: 6]
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3 Waves
4 Sailors on a ship hear the echo of their foghorn from a cliff, 3 s after it sounded.
a Calculate the distance of the ship from the cliff. Assume that the sound travels at 330 m/s.
distance of ship from cliff = ..............................
[3]
b The ship moves 165 m towards the cliff. Calculate the time interval between the sounding of
the foghorn and its echo reaching the ship.
time interval = ..............................
[3]
[Total: 6]
5 The speed of sound in air is 330 m/s.
a Calculate how far a sound travels in air in a time interval of 3 ms.
distance = ..............................
[2]
b Sound takes 0.15 ms to travel down an iron bar of length 0.9 m. Calculate the speed of sound in iron.
speed = ..............................
[2]
c Describe an experiment to determine the speed of sound in air.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
..................................................................................................................... [4]
[Total: 8]
6 Identify the following waves as transverse or longitudinal:
a sound
..............................
[1]
d water
..............................
[1]
b red light ..............................
[1]
e radio
..............................
[1]
c X-rays
[1]
f
ultrasonic ..............................
[1]
..............................
[Total: 6]
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3 Waves
Supplement
7 In a ripple tank experiment, straight waves are incident on a barrier with a gap.
a
b
On the diagram, sketch the wave pattern after the waves pass through:
a a gap that is narrow compared with the wavelength
[3]
b a gap that is wide compared with the wavelength.
[3]
[Total: 6]
8 A ray of light is incident at 45° on mirror M1. It is reflected and strikes a second mirror M2.
M2 lies parallel to M1.
45°
M1
M2
a Sketch the path of the ray on the diagram to show how it is reflected from M2.
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3 Waves
b For your diagram in part a, determine:
i
the angle of reflection at M2 = ..............................
[1]
ii the type of instrument in which this arrangement of mirrors could be used.
....................................................................................................................................... [1]
iii Give an advantage the instrument would have if the separation of M1 and M2 was
increased.
....................................................................................................................................... [1]
[Total: 7]
9 A ray of light is incident as shown on a parallel-sided glass block.
a Sketch the normal to the block at the point X. Sketch the path of the ray through the block
and out the other side. Mark the angle of incidence, i, and the angle of refraction, r, on the
diagram.
[4]
air
X
glass
b Comment on the direction of the ray when it leaves the block.
..................................................................................................................................................
............................................................................................................................................ [2]
c The angle of incidence is 30° and the refractive index of the glass block is 1.5. Calculate the
angle of refraction at X.
angle of refraction = ..............................
[4]
[Total: 10]
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3 Waves
10 A small insect is viewed with a magnifying glass of focal length 4 cm. The insect is 2 cm from
the lens.
a Sketch a ray diagram to locate the image of the insect.
[5]
b Determine the distance, v, of the image from the lens.
v = ..............................
[1]
c State the characteristics of the image.
............................................................................................................................................. [3]
............................................................................................................................................. [3]
............................................................................................................................................ [3]
[Total: 9]
11 A laser directs a narrow beam of light along a radius of a semicircular glass block of refractive
index 1.5, as shown.
P
Q
a Explain why the light is not refracted when it enters the glass at P.
............................................................................................................................................ [1]
b Sketch the normal at Q and determine the angle of incidence, i, at Q.
i = ..............................
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3 Waves
c Calculate the critical angle for the glass, using the equation sin c = sin 90°
n
where n is the refractive index of the glass.
[3]
critical angle = ..............................
d Sketch the path of the ray after it reaches Q.
[2]
[Total: 8]
12 Two musical notes X and Y are represented by the following waveforms.
distance/cm
displacement/cm
X
distance/cm
Y
a Identify which of X and Y has:
i
the higher frequency ...................................
[1]
ii the longer wavelength .................................
[1]
iii the louder sound. .......................................
[1]
b Explain what is meant by ‘compression’ and ‘rarefaction’ in a sound wave.
........................................................................................................................................................
........................................................................................................................................................
........................................................................................................................................................
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3 Waves
........................................................................................................................................................
................................................................................................................................................. [3]
c The distance between two consecutive compressions of a sound a wave is 0.85 m and the
speed of sound in the medium is 340 m/s. Calculate the:
i
wavelength = ..............................
[1]
ii frequency = ..............................
[Total: 9]
[2]
13 In a medical ultrasound imaging system, ultrasonic pulses from a transducer placed on the
patient’s skin are reflected from an internal organ. The pulses travel at 1400 m/s through the
body. There is a 40 µs time delay between the transmitted and reflected pulse arriving back at
the transducer.
a Calculate the depth inside the body of the reflecting organ.
[4]
depth = ..............................
b State the relationship between the speed, frequency and wavelength of a wave.
............................................................................................................................................ [1]
c Calculate the wavelength of ultrasonic waves of frequency 106 Hz travelling at 1400 m/s.
[2]
wavelength = ..............................
[Total: 7]
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4A Electricity and magnetism
Core
1 Fill in the gaps in the sentences below using the following words.
attract permanent pole repel soft south steel
A bar magnet has a north .............................. and a .............................. pole. Like poles
.............................. and unlike poles ............................... Magnetic materials, such as iron, which
are easily magnetised and easily lose their magnetism, are termed ...............................
Hard magnetic materials, such as .............................., are used in ............................ magnets.
2 The magnetic field around a bar magnet can be visualised as magnetic field lines.
a Describe an experiment which can be used to determine the pattern of field lines around a bar
magnet using a plotting compass, paper and pencil.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
b Sketch the pattern of magnetic field lines around a bar magnet, marking on the N and S poles.
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4A Electricity and magnetism
3 Circle two of the following materials that a magnet would not attract.
A iron
C steel
B aluminium
D copper
4 Give two ways a magnet can be made from a steel bar.
1 .....................................................................................................................................
2 .....................................................................................................................................
5 When the following charges are brought close together, do they attract or repel each other?
a +
+
..............................
b –
–
..............................
c +
–
..............................
6 Explain, in terms of electron movement, what happens when a Perspex rod is charged positively by
being rubbed with a cloth.
.........................................................................................................................................
.........................................................................................................................................
7 Sketch a circuit diagram containing a battery, an ammeter and two lamps which are connected
a in series
b in parallel.
On each diagram place the ammeter so that it measures the total current from the battery.
a series circuit
b parallel circuit
8 Explain the difference between alternating current (a.c.) and direct current (d.c.).
.........................................................................................................................................
.........................................................................................................................................
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4A Electricity and magnetism
9 A certain type of lamp reaches its full brightness when a 12 V battery is connected across it.
Comment on the brightness of such lamps when:
a a 12 V battery is connected across two of the lamps connected in series
.....................................................................................................................................
b a 12 V battery is connected across two of the lamps connected in parallel
.....................................................................................................................................
c a 6 V battery is connected across two of the lamps connected in parallel.
.....................................................................................................................................
10 This question is about electrical resistance.
a Give the relationship between potential difference, current and resistance.
....................................................................................................................................
b Explain how the circuit is connected, what measurements are taken and what calculations
are made in an experiment to determine the resistance of a wire using a variable resistor, a
voltmeter and an ammeter.
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
11 Calculate the p.d. across a 4 Ω resistor when there is a current of 0.3 A in it. Show your working.
p.d. across resistor = ..............................
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4A Electricity and magnetism
12 There is a current of 2 A in a lamp when a p.d. of 12 V is applied across it. Calculate the resistance
of the lamp. Show your working.
resistance of lamp = ..............................
13 A p.d. of 1.5 V is applied across a resistor of 5 Ω. Calculate the current in the resistor. Show your
working.
current in resistor = ..............................
14 A p.d. of 1.5 V is applied across two resistors of value 6 Ω and 9 Ω connected in series.
Calculate and show your working for:
a the total resistance
b the current
total resistance = ..............................
current = ..............................
c the p.d. across the 6 Ω resistor
d the p.d. across the 9 Ω resistor.
p.d. across 6 Ω resistor = ....................
p.d. across 9 Ω resistor = .....................
15 Circle the statement that is false for a series circuit.
A The current at every point is the same.
B The sum of the p.d.s across each component equals the total p.d. across the supply.
C The combined resistance of the resistors is less than the sum of the individual resistors.
D A complete circuit is needed for there to be a current.
16 Circle the statement that is incorrect for an electrical appliance.
A A fuse protects the appliance.
C A fuse should be placed in the neutral wire.
B A fuse should be placed in the live wire.
D The metal case should be earthed.
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4A Electricity and magnetism
17 A washing machine is rated at 10 A, 240 V. Calculate and show your working for:
a the power of the washing machine
power = ..............................
b the energy supplied to the washing machine in 40 minutes.
energy supplied = ..............................
c The cost of electricity is 10 cents per kWh. Calculate the cost of using the washing machine
for 40 minutes.
cost = ..............................
18 Calculate the size of fuse to be used for a 600 W electric motor connected to a 240 V supply.
Show your working.
size of fuse = ..............................
19 Four appliances are plugged into a power board which is protected by a 13 A fuse and connected
to a 240 V supply. The appliances are rated at 1.5 kW, 1.0 kW, 500 W and 300 W.
Circle the correct number of appliances that can be turned on together without the fuse blowing.
Calculate the current in each appliance and the total current drawn by all four appliances before
selecting your answer. Show your working.
A 1
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B 2
C 3
D 4
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4A Electricity and magnetism
Supplement
20 Explain, with reference to the motion of electrons, why:
a metals are good electrical conductors
....................................................................................................................................
....................................................................................................................................
b plastics are good electrical insulators.
....................................................................................................................................
....................................................................................................................................
21 A positively charged rod is brought near to a negatively charged electroscope and is then
removed without touching it. Identify what happens to the leaf of the electroscope.
Circle the correct answer.
The leaf of the electroscope:
A rises more and stays at that deflection
B rises more and then returns to its previous deflection
C falls and stays at that deflection
D falls and returns to its previous deflection.
22 Make a sketch showing the electric field lines:
a between two oppositely charged parallel metal plates
b around a small isolated positive point charge.
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4A Electricity and magnetism
23 The current in a circuit is 5 A. Calculate and show your working for how much charge passes any
point in the circuit in:
a 4 seconds
charge = ..............................
b 2 minutes.
charge = ..............................
24 Calculate and show your working for the current in a circuit when:
a 30 C of charge flows past a point in a circuit in 15 s
current = .............................
b 60 C of charge flows in 1 minute.
current = .............................
25 Circle the statement that is false for an electric circuit.
A Conventional current flows in a circuit from the positive terminal of a supply to the
negative terminal.
B A complete circuit is needed for current to flow.
C Electrons flow in the same direction as the conventional current.
D Electrons flow in the opposite direction to the conventional current.
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4A Electricity and magnetism
26 A potential divider circuit is shown below.
I
R1
V1
R2
V2
V
I
a Circle the correct answer.
The ratio
V1
V2
of the p.d.s across the two resistors R1 and R2 is given by:
A R1 + R2 B
R1
R2
C
R2
R1
D
1
R1
b If R1 = 5 Ω, R2 = 15 Ω and V1 + V2 = 10 V, calculate i V2 and ii V2. Show your working.
i V1 = ..............................
ii V2 = ..............................
27 The p.d. across a device is 6 V. Calculate and show your working for the energy transferred when:
a a charge of 0.5 C passes through it
b the current is 3 A for 20 s.
energy = ..............................
energy = ..............................
28 A battery supplies 48 J of energy to a device in 10 seconds. If the p.d. across the device is 12 V,
calculate and show your working for:
a the charge flowing through the
device in the 10 seconds
b the current in the device.
charge = ..............................
current = ..............................
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4A Electricity and magnetism
29 A number of 1.5 V cells are available.
a State the number of cells needed and how they should be connected to produce a 6 V battery.
....................................................................................................................................
b Calculate how much energy the 6 V battery transfers when it drives 2 C around a complete
circuit. Show your working.
energy = ..............................
30 Give the name and symbol of the unit used to measure the following:
a charge ..................................................
b current .................................................
c e.m.f. ...................................................
d potential difference ..............................
e resistance .............................................
31 A p.d. of 6 V is applied across two resistors of value 4 Ω and 12 Ω connected in parallel.
Calculate and show your working for:
a the total resistance
total resistance = ..............................
b the current from the battery
current from battery = ..............................
c the current in the 4 Ω resistor
current in 4 Ω resistor = ..............................
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4A Electricity and magnetism
d the current in the 12 Ω resistor.
current in 12 Ω resistor = ..............................
32 Sketch how the current varies with the p.d. across:
a a resistor of constant resistance
b a filament lamp.
33 State how the resistance varies with current direction in:
a a semiconductor diode ..........................................................................................................
....................................................................................................................................
b a filament lamp. ...................................................................................................................
34 State how the resistance of a wire changes when:
a its length is doubled ............................................................................................................
b its length is halved ..............................................................................................................
c its cross-sectional area is halved ...........................................................................................
d its cross-sectional area is doubled. ........................................................................................
35 Circle the statement that is false for a parallel circuit.
A The current from the source equals the sum of the currents in each branch.
B The p.d. across each component is less than the total p.d. across the supply.
C The combined resistance of resistors is less than that of the resistors individually.
D A complete circuit is needed for there to be a current.
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4A Electricity and magnetism
36 Sketch the I–V curve for a semiconductor diode.
37 Explain the difference between analogue and digital voltages.
........................................................................................................................................
........................................................................................................................................
38 Give two examples of:
a input devices that transfer energy from the surroundings to an electrical circuit
1 ...............................................................................................................................
2 ...............................................................................................................................
b output devices that transfer energy from an electrical circuit to the surroundings.
1 ...............................................................................................................................
2 ...............................................................................................................................
39 A light-dependent resistor (LDR) in series with a resistor is used in a potential divider across a
d.c. supply to operate a relay and a lamp, as shown.
R
relay
6V
d.c.
lamp
LDR
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4A Electricity and magnetism
When light falls on the LDR, its resistance and the p.d. across it fall.
a State what happens to the following:
i the p.d. across R, when light falls on the LDR
...............................................................................................................................
ii the relay, when the p.d. across it reaches its operating p.d.
...............................................................................................................................
iii the lamp, when the relay reaches its operating p.d. when light falls on the LDR.
...............................................................................................................................
b Suggest a use for the circuit.
....................................................................................................................................
Exam-style questions
Core
1 This question is about the hazards of electricity.
a Suggest two checks you could make to reduce the risk of receiving an electric shock from
an old electrical appliance.
1 ....................................................................................................................................................
2 .............................................................................................................................................. [2]
b Explain why the severity of an electric shock is increased by damp conditions.
..................................................................................................................................................
............................................................................................................................................ [2]
c Explain what causes a wire to overheat.
............................................................................................................................................ [2]
d Explain the purpose of a fuse in a circuit.
..................................................................................................................................................
............................................................................................................................................ [2]
[Total: 8]
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4A Electricity and magnetism
Supplement
2 Twenty party lights are connected in parallel and operated by a 24 V power supply.
a Explain why it is preferable to connect party lights in parallel rather than in series.
..................................................................................................................................................
............................................................................................................................................ [2]
b If each light has a resistance of 80 Ω, calculate:
i
the current in each lamp
[2]
current = ..............................
ii the total current drawn from the power supply
[2]
total current from supply = ..............................
iii the total current drawn from the power supply if one lamp fails.
[2]
total current if one lamp fails = ..............................
[Total: 8]
3 A p.d. of 9 V is applied across a potential divider circuit containing a thermistor, R1, and a
fixed resistor, R2 .
9V
R1
R2
thermistor
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4A Electricity and magnetism
a Calculate the current in the circuit and the values of the p.d.s across R1 and R2 when
R1 = 18 Ω and R2 = 12 Ω.
i
current = .............................................
[2]
ii p.d. across R1 = ...................................
[3]
iii p.d. across R2 = ...................................
[1]
b Calculate the current in the circuit and the values of the p.d.s across R1 and R2 when
R1 = 33 Ω and R2 = 12 Ω.
i
current = .............................................
[2]
ii p.d. across R1 = ...................................
[3]
iii p.d. across R2 = ...................................
[1]
c Explain how the p.d. across the thermistor changes as its resistance increases.
............................................................................................................................................ [1]
[Total: 13]
4 A p.d. of 6 V is connected across a potential divider consisting of a light-dependent resistor
(LDR) and a resistor R.
a If the resistance of the LDR decreases, state what happens to:
i
the current in the circuit ...................................
[1]
ii the p.d. across R ................................................
[1]
iii the p.d. across the LDR. ....................................
[1]
b If R = 10 Ω, calculate the resistance of the LDR when the p.d. across it is 3.5 V.
[4]
resistance of LDR = ..............................
[Total: 7]
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4B Electromagnetic effects
Core
1 Circle the correct answer.
An e.m.f. is induced in a conductor when it:
A moves parallel to magnetic field lines
B moves across magnetic field lines
C is at rest in a magnetic field
D is heated in the absence of a magnetic field.
2 An electromagnet is constructed by winding a solenoid on a soft iron core. Give two ways by which
the strength of the electromagnet could be increased.
1 ...............................................................................................................................
2 ...............................................................................................................................
3 When a coil is rotated in a magnetic field, an e.m.f. is generated. Give the three factors on which
the size of the induced e.m.f. depends.
1 ...............................................................................................................................
...............................................................................................................................
2 3 ...............................................................................................................................
4 Sketch the field around a current-carrying straight wire, showing the direction of the current and
of the field lines.
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4B Electromagnetic effects
5 A current-carrying straight wire is placed between the poles of a magnet, as shown.
current
N
S
The wire moves downwards when current flows.
State the direction in which the wire moves when:
a the current direction is reversed ..........................................
b the magnetic field direction is reversed. ..............................
6 Explain why electricity is distributed around the country using a.c. rather than d.c.
.........................................................................................................................................
.........................................................................................................................................
7 Circle the correct answer.
The main function of a step-up transformer is to:
A increase power
B increase current
C increase voltage
D decrease resistance of a circuit.
8 240 V a.c. is applied to the primary coil of a transformer which has 600 turns. The secondary coil
has 30 turns.
a Calculate the p.d. across the secondary coil. Show your working.
p.d. across secondary coil = ..............................
b State the type of transformer. ..............................
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4B Electromagnetic effects
Supplement
9 A bar magnet is moved in and out of a coil that is connected to a sensitive centre-zero meter,
as shown.
sensitive
centre-zero
meter
coil
bar magnet
The meter needle swings to the left when the magnet is moving towards the coil. State how the
needle behaves when the bar magnet:
a is at rest inside the coil ...................................................................................................
b is moving back out of the coil ...........................................................................................
c moves more quickly towards the coil ..................................................................................
d is at rest and the coil is moved away from the magnet. .........................................................
10 A straight wire is moved upwards through a horizontal magnetic field. Mark on the diagram the
direction in which current will flow in the wire if it is connected to a complete circuit.
wire
N
S
11 A bar magnet is moved towards a coil of wire connected to a meter, as shown.
N
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4B Electromagnetic effects
An e.m.f. is induced in the coil and current flows in the circuit making the coil act like a magnet.
State the polarity of the end of the coil nearest the magnet when the N pole of the magnet:
a approaches the coil ..............................................................................
b is pulled back from the coil ...................................................................
c is at rest and the coil is moved towards the magnet. ..............................
12 Electricity transmission lines deliver 80 kW of power to the consumer at a voltage of 400 000 V.
The resistance of the transmission lines is 15 Ω.
a Calculate the current in the transmission lines. Show your working.
current = ..............................
b Calculate the rate of loss of energy from the transmission lines. Show your working.
rate of energy loss = ..............................
13 The pattern of magnetic field lines in and around a solenoid is shown below.
solenoid
field line
A
B
current direction
a A solenoid, like a bar magnet, has a N and a S pole.
i Is position A or B nearest to the S pole of the solenoid? ..............................
ii Explain how the polarity of the solenoid could be reversed. ....................................
iii In which direction would the N pole of a plotting compass point if placed at A?
....................................................................
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4B Electromagnetic effects
b State where the magnetic field is:
i strong ......................................................................................................................
ii weak. .......................................................................................................................
14 The current in the primary coil of a step-down transformer is 0.15 A. The input to the primary coil
is 240 V and the output from the secondary coil is 12 V.
Calculate and show your working for the current that can be drawn from the secondary coil if the
transformer is:
a 100% efficient in transferring power
secondary coil current = ..............................
b 90% efficient in transferring power.
secondary coil current = ..............................
15 A high-speed electron beam enters a region of uniform electric field, produced by a p.d. applied
to two parallel metal plates, as shown.
+
electrons
–
In which direction are the electrons deflected? ..............................
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4B Electromagnetic effects
16 A high-speed electron beam enters a region of uniform magnetic field, as shown.
magnetic field
acting into page
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
electrons
In which direction are the electrons deflected? ..............................
Exam-style questions
Core
1 The diagram below represents a relay when it is switched off.
insulator
springy metal
P
X
pivot
Q
iron armature
R
S
coil
soft iron core
a Explain what will cause the relay to switch on. �����������������������������������������������������������������������
............................................................................................................................................ [1]
b Explain why there is a soft iron core in the relay. ��������������������������������������������������������������������
........................................................................................................................................... [2]
c State what happens at X when the relay is switched on. ����������������������������������������������������������
........................................................................................................................................... [2]
d Give a reason for using a relay. �����������������������������������������������������������������������������������������������
........................................................................................................................................... [2]
[Total: 7]
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4B Electromagnetic effects
2 An electromagnet, P, is used to lift some scrap iron. The table shows the maximum load that
can be lifted when there are different currents in the electromagnet.
Current/A
0.5
1.0
1.5
2.0
2.5
Load/N
20
40
60
80
100
a Sketch a load–current graph with current along the x-axis and load along the y-axis.
[4]
b Describe the shape of your graph. ..............................
[1]
c Determine the current needed to lift a load of 30 N. ..............................
[1]
d State the maximum load that could be lifted by a current of 1.25 A. ..............................
[1]
e A second electromagnet, Q, has the same design as electromagnet P but has twice the
number of turns on the coil. State the advantages that electromagnet Q would have over
electromagnet P.
............................................................................................................................................ [1]
..................................................................................................................................................
[Total: 8]
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4B Electromagnetic effects
Supplement
3 The diagram below shows a simple generator.
coil
N
slip rings
(rotate
with coil)
rotation
S
brushes (fixed)
a Explain the function of the slip rings.
............................................................................................................................................ [1]
b Sketch the voltage output of the generator against time for one revolution of the coil.
[3]
c State the position of the coil when the induced voltage is a maximum.
............................................................................................................................................ [1]
d State the type of current there would be in a circuit connected to the brushes.
............................................................................................................................................ [1]
[Total: 6]
4 In a d.c. electric motor, a current-carrying coil attached to a split-ring commutator is mounted
between the poles of a magnet. The coil experiences a turning effect.
coil
N
brush
(fixed)
S
brush
(fixed)
split-ring
commutator
(rotates with coil)
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4B Electromagnetic effects
a State the result of the turning effect on the coil.
............................................................................................................................................ [1]
b State how the size of the turning effect on the coil can be increased.
..................................................................................................................................................
........................................................................................................................................... [3]
c Describe the effect on the coil of increasing the turning effect.
............................................................................................................................................ [1]
d Explain the function of the split-ring commutator.
..................................................................................................................................................
........................................................................................................................................... [2]
[Total: 7]
5 When 250 V a.c. is applied to the primary coil of a step-up transformer, the output from the
secondary coil is 1000 V. The current in the primary coil is 0.8 A and there are 100 turns on the
primary coil.
a Calculate the number of turns on the secondary coil.
[3]
number of turns on secondary coil = ..............................
b Calculate the power input to the transformer.
[2]
power input = ..............................
c Calculate the current in the secondary coil if no energy were lost in the transformer.
current in secondary coil = ..............................
[3]
d Explain the effect the resistance of the coil windings has on the efficiency of a transformer.
............................................................................................................................................ [1]
[Total: 9]
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5
Nuclear physics
Core
1 Circle the incorrect statement.
A All the positive charge of an atom is concentrated in the nucleus.
B Most of the mass of an atom is concentrated in the nucleus.
C Negatively charged electrons orbit the nucleus.
D The nucleus has a very small size compared with the whole atom.
E The nucleus consists of protons and neutrons which have a similar mass.
F Electrons and protons have equal and opposite charge.
G Electrons and neutrons have the same charge.
H The mass of an electron is very small compared with the mass of a proton or neutron.
2 The nucleon number of an atom is written as A, the proton number as Z and the neutron number as N.
a Give the relationship between A, Z and N.
.....................................................................................................................................
b In terms of A, Z and N, how many electrons are there in a neutral atom?
.....................................................................................................................................
c An atom X may be represented in nuclide notation as ZA X . In this format, explain how you would
represent the following:
i a helium atom with two neutrons and two protons in its nucleus ..............................
ii an electron ..............................
iii a neutron. ................................
3 Explain the term ‘isotopes of an element’.
..........................................................................................................................................
..........................................................................................................................................
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5 Nuclear physics
4 Carbon exists as different isotopes.
a A neutral atom of one isotope of carbon has six protons, six electrons and eight neutrons.
Calculate the nucleon number for this isotope.
nucleon number = ..............................
b A second isotope of carbon has a nucleon number of 12. For a neutral atom of this isotope,
state the number of:
i protons ..........................................................................................
ii neutrons ........................................................................................
iii electrons. ......................................................................................
c Will the two isotopes have the same chemical properties? ..............................
5 State which of the following radiations:
α-particles
β-particles
γ-rays
a causes most ionisation ......................................................................................................
b causes least ionisation ......................................................................................................
c is most penetrating ...........................................................................................................
d is least penetrating ...........................................................................................................
e requires a few millimetres of aluminium to stop it ...............................................................
f travels only a few centimetres in air ...................................................................................
6 If the charge on an electron is denoted as being –1 unit, state the charge on:
a a proton .....................................
d a β-particle ..................................
b a neutron ...................................
e a γ-ray .........................................
c an α-particle ..............................
f a helium nucleus. .........................
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5 Nuclear physics
7 State which of the following radiations:
α-particles
β-particles
γ-rays
a are electrons ..........................................................................................................................
b are helium nuclei ....................................................................................................................
c are electromagnetic waves ......................................................................................................
d are easily deflected by an electric field ...................................................................................
e are not deflected by a magnetic field ......................................................................................
f have a positive charge ............................................................................................................
g have a negative charge. ..........................................................................................................
8 α, β and γ are ionising radiations.
a Explain what happens when ionisation of a gas occurs.
.....................................................................................................................................
.....................................................................................................................................
b State how ionisation can be detected.
.....................................................................................................................................
9 Circle the incorrect statement.
Radioactive decays:
A occur randomly over space and time
C result from unstable nuclei
B are affected by chemical interactions
D produce α-particles, β-particles and γ-rays.
10 Explain the meaning of the terms:
a half-life
....................................................................................................................................
....................................................................................................................................
b background radiation.
....................................................................................................................................
....................................................................................................................................
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5 Nuclear physics
11 Radioactive carbon-14 has a half-life of 5700 years. A 10 g piece of wood found in an
archaeological excavation gives a count rate of 80 counts/minute. A 10 g sample of a piece of
wood cut recently from a living tree has a count rate of 160 counts/minute.
Estimate the age of the wood taken from the excavation. Show your working.
estimated age of wood = ..............................
Supplement
12 A beam of α-particles enters a region of uniform magnetic field, as shown.
+
+
+
+
+
+
magnetic field
α -particles
acting into page
+
+
+
+
+
+
In which direction would the α-particles initially experience a force? ..............................
13 In order to monitor paper quality in a factory, a radiation source is placed close to one side of a
moving sheet of paper and a Geiger counter is placed on the opposite side.
a Explain what happens to the count-rate on the Geiger counter when the paper passing it:
i becomes thicker ..............................
ii becomes thinner. ............................
b Identify the type of radiation source that should be used for this application. Give a reason for
your answer.
....................................................................................................................................
....................................................................................................................................
14 In a famous experiment α-particles were fired at a thin metal foil. Explain how the behaviour of
the α-particles provided evidence for the nuclear model of the atom.
........................................................................................................................................
........................................................................................................................................
........................................................................................................................................
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5 Nuclear physics
15 The radioactive nuclide iodine-131 decays through β-particle emission as indicated in the
equation below.
131
A
0
53 I → Z Xe + −1 e
a Calculate the values of A and Z.
i A = ..............................
ii Z = ..............................
b Calculate the number of neutrons in the nucleus of an atom of iodine-131.
.....................................................................................................................................
c Determine the number of neutrons in the nucleus of an iodine-131 atom when it decays to xenon.
.....................................................................................................................................
Exam-style questions
Core
1 Give two examples of:
a dangers of ionising radiation
1 .......................................................................................................................................
2 .................................................................................................................................. [2]
b sources of background radiation
1 .......................................................................................................................................
2 .................................................................................................................................. [2]
c safety precautions that should be taken when handling radioactive materials.
1 .......................................................................................................................................
2 .................................................................................................................................. [2]
[Total: 6]
Supplement
2 Some large unstable nuclei undergo nuclear fission.
a Explain the term ‘nuclear fission’.
..........................................................................................................................................
..................................................................................................................................... [2]
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5 Nuclear physics
b The equation below represents what may happen when a nucleus of U-235 is struck by and
absorbs a neutron.
235
1
A
90
1
1
92 U+ 0 n → 56Ba + Z Kr + 0 n + 0 n
Calculate the values of A and Z.
i
A = ..............................
[2]
ii Z = ..............................
[2]
c Energy is released in nuclear fission.
i
Identify the energy store to which nuclear energy is transferred.
....................................................................................................................................... [1]
ii Describe how this energy is used in a nuclear power station.
....................................................................................................................................... [1]
[Total: 8]
3 In certain conditions some nuclei can undergo nuclear fusion.
a Explain the term ‘nuclear fusion’.
..................................................................................................................................................
............................................................................................................................................ [2]
b One of the fusion reactions that occurs in the Sun is given by the following equation.
3
3
A
1
1
2He + 2He → 2 X + 1H+ Z Y
Calculate the values of A and Z.
i
A = ..............................
[2]
ii Z = ..............................
[2]
[1]
ii Y ..............................
[1]
c Identify the nuclides:
i
X ..............................
d Energy is released in the fusion reactions that take place in the Sun. State how this energy
is transferred to us.
............................................................................................................................................. [1]
[Total: 9]
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5 Nuclear physics
4 A very small amount of radioactive americium dioxide is used in a smoke detector.
The nuclide americium-241 decays to neptunium-237, as shown in the equation below.
241
237
A
95 Am → 93Np + Z X
a Calculate the values of A and Z.
i
A = ..............................
[2]
ii Z = ..............................
b Identify the particle ZA X emitted in the decay process. ..............................
[2]
[1]
c State the function that X performs in the smoke detector.
............................................................................................................................................ [1]
[Total: 6]
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6
Space physics
Core
1 Circle the statement which is not true.
A The Earth goes around the Sun once each year.
B The Earth has seasons because its axis is tilted.
C When the Earth’s northern hemisphere is tilted away from the Sun, the night there is shorter
than the day.
D Day and night are due to the Earth spinning on its axis.
2 Circle the statement which is not true.
A The Earth spins on its axis once every 24 hours.
B The Moon spins on its axis once every 24 hours.
C The Moon spins on its axis approximately once a month.
D The Moon orbits the Earth approximately once a month.
3 a Identify two factors which cause the Earth to have seasons.
1 .................................................................................................................................
2 .................................................................................................................................
b Explain why it is winter in the northern hemisphere when it is summer in the southern
hemisphere.
.....................................................................................................................................
.....................................................................................................................................
4 Circle the statement which is incorrect.
A There are billions of galaxies in the Universe.
B A galaxy is a large collection of stars.
C A light-year is the time it takes for light from the Sun to reach the Earth.
D The Solar System lies in the Milky Way.
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6 Space physics
5 Circle the statement which is incorrect.
A The Sun is a star.
B The Solar System lies in the Andromeda galaxy.
C There are billions of stars in the Milky Way.
D A light-year is the distance travelled by light in one year.
6 Choose the distance which matches each of the following statements.
A 2 million light-years
C 4 light-years
B 100 thousand light-years
D 150 million km
a the distance of the second nearest star to the Earth is more than ..............................
b the distance of the nearest galaxy to the Earth is more than .....................................
c the distance of the Earth from the Sun is approximately ......................................
d the diameter of the Milky Way is approximately ...................................................
Supplement
7 Identify which of the following values is approximately equal to one light-year.
A 3 × 108 m/s
B 9.5 × 1015 m
C 1016 km
D 2.2 × 10–18 s–1
8 Explain the following facts.
a A year on Mercury is less than one year on Earth.
.....................................................................................................................................
.....................................................................................................................................
b The nights on Mars are very cold.
.....................................................................................................................................
.....................................................................................................................................
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6 Space physics
c The four giant outer planets have atmospheres containing hydrogen gas but the Earth does not.
.....................................................................................................................................
.....................................................................................................................................
9
The average distance of Venus from the Sun is 108 × 106 km. Calculate the number of Earth days it
takes Venus to complete one orbit if its orbital speed is 35 km/s. Show your working.
number of days = ..............................
10 Explain how stars are formed. Describe the chemical composition, the influence of gravitational
forces, temperature, nuclear reactions and the balancing of forces in the development of a stable
star from interstellar clouds of dust and gas.
........................................................................................................................................
........................................................................................................................................
........................................................................................................................................
........................................................................................................................................
........................................................................................................................................
........................................................................................................................................
........................................................................................................................................
11 Use the following words to fill in the gaps in the paragraph below.
carbon collapse dwarf energy expand fusion planetary temperature
The Sun is powered by the release of .............................. in the nuclear .............................. of
hydrogen into helium. It will run out of hydrogen in about 5000 million years when its core will
.............................. into a red giant and its outer layers will .............................. and cool. In the
core of the red giant, the .............................. will become high enough for helium to be converted
into .............................. but eventually all the helium will be used up, the core will collapse again
and a .............................. nebula with a white .............................. at its centre will be formed.
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6 Space physics
12 Give the stages in the life cycle of a star with a mass more than 8 times the mass of the Sun.
.........................
.........................
.........................
..........................
13 In the schematic diagram below, showing the life cycle of low mass and high mass stars, fill in
the empty boxes A to E by choosing from the following list.
black hole supernova neutron star planetary nebula white dwarf
stable
star
red giant
low mass
stars
high mass
stars
A
C
B
D
E
14 Identify which of the following provides evidence in support of the Big Bang theory.
A supernova explosions
B cosmic microwave background radiation
C nuclear fusion of helium into carbon
D black holes
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6 Space physics
15 State two discoveries that support the Big Bang theory of the origin of the Universe.
1 ....................................................................................................................................
....................................................................................................................................
2 ....................................................................................................................................
....................................................................................................................................
16 Redshift measurements from a distant galaxy show that it is moving away from the Earth at a
speed of 350 km/s.
Calculate how far away the galaxy is from the Earth. Show your working.
(Assume H0 = 2.2 × 10–18 s–1.)
distance of the galaxy from Earth = ..............................
17 Calculate the Hubble constant if a galaxy 1100 million light years from the Earth is receding at
24 000 km/s. Show your working.
Hubble constant = ..............................
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6 Space physics
Exam-style questions
Core
1 Daily and seasonal occurrences can be explained by the motion and tilt of the Earth.
a Explain why the Sun rises in the east and sets in the west each day.
..................................................................................................................................................
........................................................................................................................................... [2]
b State when the Sun is at its greatest height above the horizon in the northern hemisphere.
..................................................................................................................................................
........................................................................................................................................... [2]
[Total: 4]
2 Astronomers study the spectrum of light from distant stars.
a State what causes a star to emit radiation in the ultraviolet, visible and infrared parts of the
electromagnetic spectrum.
..................................................................................................................................................
........................................................................................................................................... [2]
b Explain how this light appears if a distant star is moving away from the Earth.
..................................................................................................................................................
........................................................................................................................................... [2]
c Explain how light from distant stars provides evidence that the Universe is expanding.
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
........................................................................................................................................... [4]
[Total: 8]
Supplement
3 Stars have several stages in their evolution.
a Explain how a protostar is formed.
..................................................................................................................................................
............................................................................................................................................ [1]
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6 Space physics
b Describe how a star is powered.
..................................................................................................................................................
........................................................................................................................................... [2]
c Explain when a stable star becomes unstable.
..................................................................................................................................................
............................................................................................................................................ [1]
d Explain how a red giant is formed.
..................................................................................................................................................
..................................................................................................................................................
........................................................................................................................................... [3]
[Total: 7]
4 The orbital time of Neptune around the Sun is 165 Earth years and its orbital path is 30 times
longer than that of the Earth.
a Calculate the orbital speed of Neptune relative to the Earth.
[4]
orbital speed = ..............................
b State how the speed of travel of Neptune compares with that of the Earth.
............................................................................................................................................ [1]
[Total: 5]
5 a Explain what is meant by ‘redshift’.
..................................................................................................................................................
..................................................................................................................................................
........................................................................................................................................... [3]
b State Hubble’s law.
..................................................................................................................................................
........................................................................................................................................... [2]
[Total: 5]
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6 Space physics
6 Redshift measurements show that a galaxy is moving away from the Earth at the speed of
60 000 km/s.
Taking the Hubble constant H0 as 2.2 × 10 –18 s–1 and 1 light-year as 1013 km, calculate and show
your working for:
a how far the galaxy is from the Earth
[3]
distance = ..............................
b how long it has taken light from the galaxy to reach the Earth
[2]
time taken = .......................................
c the time the galaxy and the Milky Way have been travelling apart.
[5]
time = ...................................................
d Explain the significance of the time you calculated in c.
..................................................................................................................................................
............................................................................................................................................ [1]
[Total: 11]
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Reinforce learning and deepen understanding
of the key concepts in this Workbook,
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» Develop understanding and build confidence
ahead of assessment: the Workbook is in
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questions to test knowledge, and sections
providing exam-style questions.
» Differentiated content: both Core and
Supplement content is clearly flagged with
differentiated questions.
» Provide extra practice and self-assessment:
each Workbook is intended to be used by
students for practice and homework. Once
completed, it can be kept and used for
revision.
Ca
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WITH
on
al E
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For over 25 years we have
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Physics Student’s Book
Fourth Edition
9781398310544
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✓ Provides learner support for the Cambridge
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Cambridge IGCSE™ Physics
Answers to Workbook
Cambridge Assessment International Education bears no responsibility for the example answers to questions taken from
its past question papers which are contained in this publication. Exam-style questions and sample answers have been
written by the authors. In examinations, the way marks are awarded may be different. References to assessment and/or
assessment preparation are the publisher’s interpretation of the syllabus requirements and may not fully reflect the
approach of Cambridge Assessment International Education.
1A Measurement, motion, mass, weight and density
Core
1
2
3
4
5
6
a
20
b
4
c
120
d
500
e
1400
a
15.00 m
b
1.50 m
c
0.15 m
d
0.015 m
a
1 × 103
b
2.25 × 105
c
6.5 × 102
d
1.5 × 104
a
10 000
b
250
c
1 500 000
d
350 000 000
a
1 × 10−3
b
2 × 10−2
c
1.2 × 10−3
d
1.02 × 10−2
a
i
1 × 10−2
ii
0.01
i
2 × 10−3
ii
0.002
i
3 × 10−4
ii
0.0003
i
8 × 10−4
ii
0.0008
b
c
d
7
a
5 × 10−3 m
Cambridge IGCSE Physics
© Hodder & Stoughton Limited 2021
1
Cambridge IGCSE Physics Workbook answers
8
9
b
5 × 10−1 m
c
5 × 103 m
a
3
b
2
c
3
a
1m
b
1.3 m
c
1.26 m
10 27 cm2 (do not accept 27.0 cm2)
11 Area of triangle =
× base × height =
× 30 cm × 40 cm = 600 cm2
12 Number of bricks = (15 cm × 15 cm × 10 cm) / (5 cm × 2 cm × 3 cm) = 75
13 32 s / 20 = 1.6 s
14 a
B
b
C
c
Average speed = 1000 m / 200 s = 5 m/s
15 a
i
270 m
ii
No distance
iii 270 m
b
270 m / (3 × 60 s) = 1.5 m/s
16 a
mgEarth = 918 kg × 9.8 N/kg = 9.0 × 103 N
b
mgMars = 918 kg × 3.9 N/kg = 3.6 × 103 N
17 a
mg = 0.015 kg × 9.8 N/kg = 0.15 N
b
mg = 0.051 kg × 9.8 N/kg = 0.50 N
c
mg = 0.3 kg × 9.8 N/kg = 3 N
d
mg = 3.1 kg × 9.8 N/kg = 30 N
18 a
b
m = weight/g = 784 N / 9.8 N/kg = 80 kg
Weight on Moon = mgMoon = 80 kg × 1.6 m/s2 = 128 N
19 C
20 ρ = m/V = 7.36 g / (2.0 cm × 2.0 cm × 2.0 cm) = 0.92 g/cm3 or 920 kg/m3
21 a
b
V = (75 − 50) cm3 = 25 cm3
ρ = m/V = 200 g / 25 cm3 = 8 g/cm3 = 8 × 103 kg/m3
22 m = ρV = 1.3 kg/m3 × (3 m × 4 m × 2.5 m) = 39 kg
Supplement
23 a
a = Δv/Δt = (8 − 0) m/s / 10 s = 0.8 m/s2
b
Δt = Δv/a = (0 − 8) m/s / (−2 m/s2) = 4 s
24 Δv = a Δt = 1.5 m/s2 × 4 s = 6 m/s
v2 = v1 + a Δt = 6 m/s + 6 m/s = 12 m/s
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25 a
b
Average speed = (v1 + v2) / 2 = (8 m/s + 20 m/s) / 2 = 14 m/s
Average speed = total distance travelled/total time taken,
so distance travelled = average speed × total time taken = 14 m/s × 60 s = 840 m
c
26 a
a = Δv/Δt = (20 m/s − 8 m/s) / 60 s = 0.2 m/s2
3.0 m/s
b
a = Δv/Δt = 3.0 m/s / 20 s = 0.15 m/s2
c
Distance = average speed × total time taken (or area under graph in time interval AB)
= 3 m/s × 16 s = 48 m
d
Distance = average speed × total time taken (or area under graph in time interval BC)
= (base × height of triangle)/2) = (3/2) m/s × 14 s = 21 m
27 a
b
i
Δv = a Δt = 9.8 m/s2 × 2 s = 20 m/s downwards
ii
Distance = average speed × total time taken = (20/2) m/s × 2 s = 20 m
Linear with gradient = 9.8 m/s2
Exam-style questions
Core
1
a
B: volume of liquid = 500 cm3
[1]
Volume of tank = 10 cm × 10 cm × 10 cm = 1000 cm3 [1]
Fraction of tank filled = 500 cm3/1000 cm3 =
b
1
2
[1]
A: volume of brick = 4 cm × 3 cm × 5 cm = 60 cm3 [1]
= volume of liquid displaced = 10 cm × 10 cm × Δh [1]
Δh = rise in liquid level = 60 cm3 / 10 cm × 10 cm = 0.6 cm [1]
c
Thickness of 120 pages = thickness of book − thickness of each cover [1]
= (8.2 mm − 2 × 0.5) mm = 7.2 mm [1]
Thickness of 1 page = 7.2 mm / 120 = 0.06 mm [1]
2
a
b
c
d
i
Increasing [1]
ii
Constant [1]
i
Constant [1]
ii
Zero [1]
i
Increasing [1]
ii
Constant [1]
OA (graph has greatest gradient) [1]
Supplement
3
a
ρ = m/V [1] = 46 g / 50 cm3 = 0.92 g/cm3 [1]
b
Sink; [1] vinegar has a higher density than the oil [1]
4
B [1]
5
a
a = ΔvOA/ΔtOA [1]
= 30 m/s / 200 s = 0.15 m/s2 [1]
b
a = ΔvBC/ΔtBC [1]
= −30 m/s / 300 s = −0.1 m/s2 [1]
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c
Average speed = (v1 + v2) / 2 [1] = (30 m/s + 0 m/s) / 2 = 15 m/s [1]
d
Distance = average speed × total time taken (or area under slope)
= (base × height of triangle)/2) [1] = 30/2 m/s × 5 × 60 s = 4500 m = 4.5 km [1]
e
AB [1]
1B Forces and momentum
Core
1
a
Horizontal forces are equal; resultant force = 10 N − 5 N = 5 N downwards
b
5 N upwards
2
Force, rest, constant, straight
3
a
mg = 80 kg × 9.8 m/s2 = 784 N
b
784 N
c
784 N − 300 N = 484 N
d
784 N
a
When ruler is balanced, L × X = 50 cm × W so X = 50 cm × W/L
4
X = 50 cm × W/2W = 25 cm
b
X = 50 cm ×W/L = 50 cm × W/5W = 10 cm
c
X = 50 cm ×W/L = 50 cm × W/10W = 5 cm
5
Forces, equilibrium, sum, equals, direction, clockwise, point, moments, no, resultant
6
a
(weight of board acts at its centre, i.e. 45 cm from hinge)
When board is level, anticlockwise moment = clockwise moment
so T × 90 cm = 6 N × 45 cm
and T = 6 N × 45 cm / 90 cm = 3 N
b
When board is level, upward force = downward force so F + T = 6 N
and F = 6 N − T = 6 N − 3 N = 3 N
7
Suspend card from one corner and use a plumb line to draw the vertical line on the card from
the point of suspension; repeat with a different point of suspension.
The centre of gravity is located where the two lines intersect.
Supplement
8
Spring constant, k = F/x = m1g/x1 = m2g/x2 so m2 = m1x2/x1
so M = m1x2/x1 = 0.5 kg × 15 cm / 10 cm = 0.75 kg
9
D; spring constant, k = F/x = m1g/x1 = m2g/x2 so x2 = m2x1/m1
extension = 0.3 kg × 3 cm/1.0 kg = 0.90 cm = 9.0 mm
10 Scalars have magnitude only, e.g. mass; vectors have magnitude and direction, e.g. force.
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11
Magnitude of resultant
=
× )
( 3 × 3) + ( 4 4
=
9 + 16 =
25 = 5 N
tan θ = FY/FX = 4/3 = 1.3; direction of resultant 𝜃𝜃 = 53º to 3 N force
12 a
b
i
F = F1 − F2 = 100 N − 80 N = 20 N to the right
ii
F = ma, so a =F/m = 20 N/ 50 kg = 0.4 m/s2
i
Forces are equal and opposite so resultant force F = 0 N
ii
and acceleration = F/m = 0 m/s2
13 F = ma = 15 kg × 4 m/s2 = 60 N
14 a
Speed is a scalar and has magnitude only; velocity is a vector and has magnitude and
direction.
b
Tension in the string acts towards the centre of the circle, continuously changing the ball’s
direction and so its velocity.
c
Along the tangent to the circle at its lowest point
15 a
Momentum p = mv = 5 kg × 3 m/s = 15 (kg m/s)
b
mv = 5 kg × 40 m/s = 200 (kg m/s)
16 Total momentum before collision is (m × 5 m/s) + (m × 0 m/s) = 5m
Total momentum after collision is (m × 4 m/s) + (m × v) = 4m + mv
If momentum is conserved: 5m = 4m +mv, so v = (5m − 4m) / m = 1 m/s
17 a
p = mv = 50 ×10−3 kg × 20 m/s = 1 kg m/s
b
Impulse = Δ(mv) = 1 kg m/s
c
F = Δp/Δt = 1 kg m/s / 0.002 s = 500 N
Exam-style questions
Core
1
a
Graph: axes labelled correctly [1]; easy-to-read scales chosen and at least half of graph
paper used [1]; points clearly and correctly plotted to half a small square [1]; well judged
best-fit curve, thin continuous line joining all points. [1]
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b
Linear region of graph correctly marked [1]
c
Gradient calculated by triangle method using at least half of linear portion of graph [1];
gradient = rise/run = 2 × 103 N/m [1]
Supplement
2
a
Spring constant, k = F/x = mg/x [1] = (2 kg × 10 N/kg) / (10 × 10−2) m = 200 N/m [1]
b
Extension of spring, x = 30 cm − 20 cm = 10 cm [1]
Spring constant, k = F/x = 0.5 N / (10 × 10−2) m = 5 N/m [1]
c
3
a
i
extension, x = 40 cm − 20 cm = 20 cm [1]
ii
F = kx = 5 N/m × 20 × 10−2 m = 1 N [1]
Taking moments about left hand support: 80 N × 3 m = Q × 5 m [1]
Q = 240 N m / 5 m = 48 N [1]
4
b
P + Q = 80 N [1] so P = 80 N − 48 N = 32 N [1]
a
F = ma, so a =F/m [1] = 1350 N / (45 × 10−3) kg = 30 000 m/s2 [1]
b
a = Δv/Δt so Δv = a Δt [1] = 30000 m/s2 × 0.001s = 30 m/s [1]
c
1
Follow through longer to extend collision time [1] 2 strike harder [1]
1C Energy, work, power and pressure
Core
1
2
a
Mechanical work
b
Electrical work
a
Gravitational potential energy → kinetic energy
b
Electrical energy → thermal energy
3
W = Fd = 120 N × 500 m = 60 kJ
4
a
W = Fd = 150 N × (10 × 10−2 m) = 15 J
b
W = Fd, so d = W/F = 15 J / 750 N = 0.02 m (= 2 cm)
a
It cannot be used up; two from: solar, wind, hydroelectric, tidal, geothermal
b
It cannot be replaced once used; two from: coal, oil, gas, nuclear
a
W = Fd = 9000 N × 20 m = 1.8 × 105 J
b
Power = W/t = 1.8 × 105 J / 15 s = 12 kW
a
p = F/A= 40 N / 4.0 m2 = 10 Pa
b
p = F/A= 40 N / 0.5 m2 = 80 Pa
5
6
7
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8
9
c
p = F/A= 40 N / 0.1 m2 = 400 Pa
d
p = F/A= 40 N / 4.0 cm2 = 40 N / (4.0 × 10−4) m2 = 1.0 × 105 Pa
a
F = pA = 20 N/m2 × 2 m2 = 40 N
b
F = pA = 20 N/m2 × 1 m2 = 20 N
c
F = pA = 20 N/m2 × 1 × 10−4 m2 = 2 × 10−3 N
d
F = pA = 20 N/m2 × 0.1 × 10−4 m2 = 2 × 10−4 N
B; p = F/A so larger contact area less pressure
10 a
p = F/A = 100 N / (4.0 × 10−4) m2 = 2.5 × 105 Pa
F = pA = 2.5 × 105 N/m2 × 20 × 10−4 m2 = 500 N
b
i
ii
500 N
Supplement
11 a
Ek =
1
b
Ek =
1
2
2
mv2 = 5 kg ×
1
mv2 = 5 kg ×
1
2
2
(6 m/s)2 = 90 J
(12 m/s)2 = 360 J
12 a
ΔEP = mgΔh = 5 kg × 10 N/kg × 10 m = 500 J
b
ΔEP = mgΔh = 5 kg × 10 N/kg × 25 m = 1250 J
13 Rearranging Ek =
14 a
1
2
mv2, gives v =
2 × 2.7 × 103 J / 600 kg = 3 m/s
i
EP = mgh = 3 kg × 9.8 N/kg × 5.1 m = 150 J
ii
150 J
iii Rearranging Ek =
b
2 Ek / m =
1
2
mv2, gives v =
2 Ek / m =
2 × 150 J/3 kg = 10 m/s
Transferred to thermal energy and sound
15 P = ΔE/t = mgΔh/t = 2000 kg/s × 9.8 N/kg × 10 m = 2.0 × 105 W
90% efficient, so power generated = 2.0 × 105 × 90/100 = 1.8 × 105 W
16 a
b
efficiency =
useful power output
× 100% = (350 W/500 W) × 100% = 70%
total power output
It is transferred to thermal energy
17 Δp = ρgΔh = 1.0 ×103 kg/m3 × 10 m/s2 × 3.05 m = 3.0 × 104 Pa
Exam-style questions
Core
1
2
a
T = 600 N/2 = 300 N [1]
b
W = Fd = 600 N × 1.5 m [1] = 900 J [1]
c
P = W/t = 900 J / 3 s [1] = 300 W [1]
a
i
Renewable [1] clean [1]
ii
The Sun does not always shine [1] expensive to manufacture [1]
i
High energy density [1] readily available [1]
ii
Radiation risks [1] safe disposal of radioactive waste required [1]
i
Renewable [1] clean [1]
b
c
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d
ii
Wind not always available [1] environmental objections [1]
i
High energy density[1] readily available [1]
ii
Non-renewable[1] release carbon dioxide and sulfur dioxide into atmosphere [1]
Supplement
3
a
Gravitational potential energy [1] transferred to kinetic energy [1] and thermal energy
(resulting from resistive forces) [1]
b
Distance travelled/s = 12 m [1]
E = W = Fd = 5 N × 12 m = 60 J [1]
c
i
60 J/s = 60 W [1]
ii
d = E/F = 60 J / 7.5 N = 8 m [1]
v = d/t = 8 m/s [1]
4
1
mv2 [1] = 60 × 10−3 kg × (30 m/s)2 / 2 [1] = 27 J [1]
a
Ek =
b
0 J [1]
c
27 J [1]
d
Rearrange ΔEP = mgΔh to give Δh = ΔEP/mg [1] = 27 J/((60 × 10−3) kg × 9.8 N/kg) = 46 m
[1]
2
2 Thermal physics
Core
1
2
3
a
Gas
b
Solid
c
Gas
d
liquid
e
Solid
a
Gas
b
Solid
c
Liquid
a
Fast-moving air molecules collide with the smoke particles. A smoke particle is much
more massive than an air molecule, but when there are more high-speed molecules striking
one side of it than the other at a particular instant, a net force results and the smoke particle
will move in the direction of the force. The imbalance and the resulting force cause the
smoke particles to change direction rapidly in a random manner.
b
4
They will move faster.
Very large numbers of fast-moving molecules rebounding from the walls of the container
produce a force and hence a pressure on the walls.
5
a
It increases.
b
The air molecules move faster and so have more frequent and more violent collisions
with the walls: the average force on the walls increases.
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6
B
7
B
8
a
0°C
b
100°C
a
T = θ + 273
b
T = (30 + 273) = 303 K
c
θ = (T – 273) = (150 − 273) = −123℃
9
10 a
b
The temperature at which the substance changes from a solid to a liquid.
The temperature at which the substance changes from a liquid to a vapour.
11 a
C
b
A
c
E
d
D
12 For example: melt the same amount of wax onto one end of each rod; place the rods on a tripod
with the waxed ends separated and the other ends close together. Heat the unwaxed ends with a
flame. The wax will begin to drip first from the metal rod because it is a good conductor and
transfers thermal energy quickly.
13 Metal transfers thermal energy faster than plastic away from the hand, because it is a better
conductor, so the metal feels colder.
14 C
15 D
16 a
B
b
C
17 Thermal, higher, lower, energy, temperature, fluid, radiation, electromagnetic
Supplement
18 a
p1V1 = p2V2 so V2 = p1V1/p2 = p1 × 200 cm3 / (p1/2) = 400 cm3
b
p1V1 = p2V2 so V2 = p1V1/p2 = p1 × 200 cm3 / (2p1) = 100 cm3
19 a
b
20 a
b
p1V1 = p2V2 so p2 = p1V1/V2 = 2 × 105 Pa × V1/2V1 = 1 × 105 Pa
p1V1 = p2V2 so p2 = p1V1/V2 = 2 × 105 Pa × V1/(V1/2) = 4 × 105 Pa
A
Energy required per unit mass per unit temperature increase
21 The wall is used to store energy; brick and concrete have high specific heat capacities.
22 Rearrange equation c =
∆E
to give the equation
m∆θ
ΔE = m c Δθ = (70 × 10−3) kg × 4000 J/kg ºC × 60ºC = 16 800 J
23 c =
∆E
m∆θ
t = (9 × 60 + 20) s = 560 s
ΔE = P t = 150 W × 560 s so c = 150 J/s × 560 s / (0.5 kg × (60 − 20)ºC) = 4200 J/(kg °C)
24 a
B
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b
25 a
A
Faster-moving particles escape from the surface of the liquid. This results in the
average speed, and therefore the average kinetic energy of the remaining particles being
lowered, so that the temperature of the liquid falls.
b
26 a
b
Two from: large surface area, high temperature, draught/vacuum above liquid
Block A; a black surface is a better emitter of radiation than a shiny one.
i
The shiny foil reflects the radiation back into the room.
ii
The white colour reflects radiation.
Exam-style questions
Core
1
a
b
c
i
Temperature remains constant [1]
ii
Temperature remains constant [1]
i
Increases [1]
ii
Decreases [1]
More energetic particles escape from the liquid surface. [1] This leads to the average
kinetic energy of the liquid falling [1] and so the temperature of the liquid decreases. [1]
2
a
Three from: double-glazed windows, cavity walls, fur or fleece jackets, string vests,
fibreglass roof insulation [3]
b
Transfer of thermal energy by convection is restricted. [1]
Supplement
3
Insert an immersion heater of power P into the centre of a cylinder of metal and place a
thermometer into another hole in the cylinder. Switch on the heater for a measured time, t. [1]
Work out the energy supplied by heater, P × t. [1] Record the temperature of the metal before
the heater is switched on and the highest temperature reached by the metal just after the heater
is switched off. [1] Work out the temperature rise of the metal, ΔT. [1] Measure the mass of the
metal, m. [1] Equate energy supplied by heater to energy gained by metal, Pt = mcΔT. [1]
Hence evaluate specific heat capacity, c. [1] Error in value obtained is due to loss of heat to
the environment. [1]
4
a
Atoms in hot regions pass on their vigorous vibrations [1] to neighbouring atoms in colder
regions. [1] Also, in metals, ‘free’ electrons move faster and further in the hot regions [1]
and can transfer that energy to atoms in cooler regions very quickly[1].
b
There are no ‘free’ electrons available to move rapidly through the material, transferring
energy. [1]
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3 Waves
Core
1
Vibrations are perpendicular to direction of travel for transverse wave, parallel to/in line
with direction of travel for longitudinal wave.
2
Crest, trough, amplitude, and wavelength correctly labelled
3
f = number of wave crests passing a point per second = 1/T = 1/0.1 s = 10 Hz
4
T = 60 s / 72
f = 1/T = 72 / 60 s−1 = 1.2 Hz
5
6
a
36 cm / 6 = 6 cm
b
5 Hz
c
v = f λ = 5 Hz × 6 cm = 30 cm/s
d
Rearrange v = s/t to give t = s/v then t = 960 cm / 30 cm/s = 32 s
a
No change
b
Halved
c
The direction of travel bends towards normal to boundary.
7
Lines, direction, ray, beam, diverging, narrower, faster, before
8
a
b
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c
9
a
The plane mirror, the incident ray, the normal to the mirror, the reflected ray, the
angle of incidence, i, and the angle of reflection, r, correctly labelled
b
i
40°
ii
40°
10 a, b, c
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a
Normal drawn correctly in: (i) and (ii), (iii) and (iv), (v) and (vi)
b
Angle of incidence, i, drawn correctly in: (i) and (ii), (iii) and (iv), (v) and (vi)
c
Reflected ray drawn correctly in: (i) and (ii), (iii) and (iv), (v) and (vi)
11 a
Ray reflected from AB and BC correctly drawn
b
i
55°
ii
55°
iii 35°
iv 35°
c
It is turned through 180° from the incident ray
12 B
13 A real image can be formed on a screen and the light rays pass through the image.
14 a
1m
b
1m
15 The ray is refracted towards the normal.
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16 Towards, denser, away from, normal, optically, normally
17 B
18 a
Dispersion occurs because the prism has different refractive indices for different
colours of light.
b
Red, orange, yellow, green, blue, indigo, violet
c
Dispersion in prism, red ray and blue ray correctly drawn
19 When light is incident on a boundary of lesser optical density at an angle of incidence
greater than a critical angle, c, all of the light is reflected inside the denser medium.
20 Thin, two, parallel, focus, undeviated, centre, top, F, refracted, principal
21 D
22 Use the lens to focus an image of a distant object onto a piece of paper; the lens–image
distance is equal to the focal length.
23 Parallel beam
24 a
Four from: obey wave equation v = fλ; transverse; undergo reflection, refraction,
diffraction; travel at 3 × 108 m/s in a vacuum
b
i
Infrared
ii
Microwaves or infrared
iii X-rays
iv Infrared
v
X-rays
vi Microwaves
25 a
Radio
b
X-rays
c
X-rays
26 a
Rearrange v = f λ to give λ = v/f = 3 ×108 m/s / 7.5 × 1014 Hz = 0.4 µm
b
Rearrange v = f λ to give λ = v/f = 3 ×108 m/s / 4.3 × 1014 Hz = 0.7 µm
27 a
b
Risk: microwaves may harm living cells; precaution: use hands-free devices.
Risk: X-rays can kill or damage living cells and cause cancer; precaution: protect by use of
lead shielding
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Supplement
28 a
Normals to mirror at P and Q, reflected rays at P and Q, extrapolated rays at P and Q
correctly drawn, image position correctly located
b
Virtual, upright, same size as object
c
The same distance behind mirror as the object is in front
29 a
n = speed of light in air/speed of light in medium = c/v; rearrange to give
v = c/n = 3 × 108 m/s / (3/2) = 2 × 108 m/s
b
v = c/n = 3 × 108 m/s / (4/3) = 2.25 × 108 m/s
30 a
Path of ray shown for at least 3 reflections shown in fibre; ray shown exiting fibre
b
Digital
31 a
Normal, incident and reflected rays drawn correctly at boundary
critical angle (49º) marked
b
sin 49º = 0.7547
n = 1/sin c = 1/0.7547 = 1.33
32 sin 52º = 0.7880
n = 1/sin c = 1/0.7880 = 1.27
33 a
b
B
Light of one colour (or frequency)
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34 a
b
Rearrange v = f λ to give f = v/ λ = 330 m/s / 20 × 10−2 m = 1650 Hz
i
20–20 000 Hz
ii
Greater than 20 kHz
35 Rearrange v = s/t to give s = vt then s = 330 m/s × 8 s = 2640 m = 2.64 km
Exam-style questions
Core
1
A [1]
2
a
Prism A: reflection of ray at sloping surface [1] transmission of ray at exit [1]
correctly drawn
Prism B: reflection of ray at vertical surface [1] reflection of ray at horizontal surface [1]
transmission of ray at exit [1] correctly drawn.
b
3
i
A Periscope [1]
ii
B Binoculars [1]
a
Principal foci (F) and optical centre (C) marked [1] construction rays [1] object [1] and
image [1] correctly drawn
4
b
10 cm [1]
c
The same [1]
a
v = s/t = 2d/t where d is the distance of ship from cliff [1]
Rearranging equation gives d = vt/2 [1] = 330 m/s × 3 s /2 = 495 m [1]
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b
Rearranging v = 2d/t gives t = 2d/v [1]
d = (495 − 165) m = 330 m [1] so t = 2d/v = 2 × 330 m / 330 m/s = 2 s [1]
5
a
Rearranging v = s/t gives s = vt [1] = 330 m/s × 3 × 10−3s = 0.99 m [1]
b
v = s/t [1] = 0.9 m / (0.15 × 10−3s) = 6000 m/s [1]
c
Use a digital timer to measure the time, t, that a sharp sound (e.g. a hammer blow on a
metal plate) takes to travel between a ‘start’ and a ‘stop’ microphone. [1] Measure the
distance between the microphones, d. [1] Repeat measurements of t several times and work
out an average value. [1] Speed of sound = d/t. [1]
6
a
Longitudinal [1]
b
Transverse [1]
c
Transverse [1]
d
Transverse [1]
e
Transverse [1]
f
Longitudinal [1]
Supplement
1
a
Curved waves [1] extending into region behind barrier [1] with same spacing as incident
waves [1]
b
Straight waves passing through gap [1] curving into region behind barrier [1] same spacing
as incident waves [1]
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8
a
Reflected ray at M1 [1] normal at M2 [1] and reflected ray at M2 [1] drawn with incident
and exit rays parallel [1]
b
i
45° [1]
ii
Periscope [1]
iii It could be used to see over higher obstacles [1]
9
a
Normal at X, [1] ray through block, [1] i, [1] and r [1] marked correctly
b
Exit ray is parallel to the ray entering the block [1] but is displaced sideways. [1]
c
n = sin i/sin r [1] so sin r = sin i /n [1] = sin 30°/1.5 = 0.3333 [1]; r = sin−1(0.3333) = 19.5°
[1]
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10 a
F and C marked [1] construction rays [1] back extrapolation [1] object [1] and image [1]
correctly drawn
b
4 cm [1]
c
Upright, enlarged, virtual [3]
11 a
The beam strikes the glass normally. [1]
b
Normal drawn correctly [1] i = 55° [1]
c
sin c = sin 90º/n = 1/n [1] = 1/1.5 = 0.6666 [1]; c = sin−1(0.6666) = 42° [1]
d
Ray reflected from Q [1] and exiting glass normally [1] correctly drawn
12 a
i
Y [1]
ii
X [1]
iii Y [1]
b
Molecules in the air vibrate back and forth in the direction of travel of the sound wave; [1]
when the molecules are moving towards each other a compression (region of higher
pressure) results; [1] when they are moving apart a rarefaction (region of lower pressure)
occurs. [1]
c
13 a
i
0.85 m [1]
ii
Rearrange v = f λ to give f = v/λ [1] = 340 m/s / 0.85 m = 400 Hz [1]
v = s/t =2d/t where d is the depth of reflecting organ [1]
Rearranging equation gives d = vt/2 [1] = 1400 m/s × (40 × 10−6)s / 2 [1]
= 2.8 × 10−2 m (= 28 mm) [1]
b
speed = frequency × wavelength [1]
c
Rearrange v = f λ to give λ = v/f [1] = 1400 m/s / 106 Hz = 1.4 × 10−3 m (= 1.4 mm) [1]
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4A Electricity and magnetism
Core
1
Pole, south, repel, attract, soft, steel, permanent
2
a
Using a plotting compass: lay bar magnet on a piece of paper and place plotting compass
near the N pole. Mark the position of the N and S poles of the compass on the paper; then
move the compass so that the S pole is at the point where the N pole was previously and
mark the new position of the N pole. Continue until compass is near S pole then join up the
points to give a field line. Plot other field lines by repeating the process with the compass
at different starting points.
b
Field lines correctly shaped, N and S poles marked, arrows showing direction of field
correctly
3
B, D
4
Two from: stroking with another magnet, hammering in a magnetic field, inserting in a
solenoid and increasing d.c. current through the solenoid
5
6
a
Repel
b
Repel
c
Attract
Electrons are transferred from the Perspex to the cloth, leaving the Perspex positively
charged .
7
a
Correct symbols used for: battery, ammeter and two lamps
lamps connected in series, current direction marked correctly with arrow
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b
Correct symbols used for: battery, ammeter and two lamps
lamps connected in parallel, current direction marked correctly with arrow
8
With a.c. the direction in which current flows reverses regularly;
with d.c. the current flows in one direction only.
9
a
It is dimmer.
b
It has the same (full) brightness.
c
It is dimmer.
10 a
b
potential difference = current × resistance
Connect a battery, ammeter, variable resistor and the wire whose resistance is to be
measured, in series. Connect a voltmeter across the wire. Measure V and I with
different settings of the variable resistor. Evaluate the resistance of the wire R = V/I
for each setting.
11 Rearrange R = V/I to give V = IR = 0.3 A × 4 Ω = 1.2 V
12 R = V/I = 12 V/2 A = 6 Ω
13 Rearrange R = V/I to give I = V/R = 1.5 V / 5 Ω = 0.3 A
14 a
R = R1 + R2 = 6 Ω + 9 Ω = 15 Ω
b
Rearrange R = V/I to give I = V/R = 1.5 V / 15 Ω = 0.1 A
c
Rearrange R1 = V1/I to give V1 = IR1 = 0.1 A × 6 Ω = 0.6 V
d
V2 = IR2 = 0.1 A × 9 Ω = 0.9 V
15 C
16 C
17 a
P = IV = 10 A × 240 V = 2400 W (= 2.4 kW)
b
E = IVt = Pt = 2400 W × 40 × 60 s = 5.76 ×106 J (5760 kJ or 1.6 kWh)
c
16 cents
18 P = IV so I = P/V = 600 W / 240 V = 2.5 A
Use a 3 A fuse
19 C; P = IV so I = P/V;
I1 = 1500 W/240 V = 6.25A, I2 = 1000 W / 240 V = 4.17 A,
I3 = 500 W/240 V = 2.08 A and I4 = 300 W / 240 V = 1.25A
I1 + I2 + I3 + I4 = 6.25 + 4.17 + 2.08 + 1.25 = 13.75 A
So only 3 appliances can be connected at once
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Supplement
20 a
Some electrons can move easily from atom to atom and can be considered to be ‘free’
electrons.
b
All electrons are firmly bound to atoms and there are no ‘free’ electrons available to
produce a current.
21 D
22 a
Parallel plates with opposite charges perpendicular field lines, direction of field
marked correctly
b
Positive point charge radiating field lines, direction of field marked correctly
23 a
b
Rearrange I = Q/t to give Q = It = 5 A × 4 s = 20 C
Q = It = 5 A × 2 × 60 s = 600 C
24 a
I = Q/t = 30 C / 15 s = 2 A
b
I = Q/t = 60 C / 60 s = 1 A
25 C
26 a
B
b
i
V1/V2 = R1/R2 = 5/15 =
1
3
V = V1 + V2 = 10 V so V1 = 10 V ×
ii
V2 = 10 V ×
3
4
E = IVt = QV = 0.5 C × 6 V = 3 J
b
E = IVt = 3 A × 6 V × 20 s = 360 J
b
4
= 2.5 V
= 7.5 V
27 a
28 a
1
E = IVt = QV so Q = E/V = 48 J / 12 V = 4 C
I = Q/t = 4 C / 10 s = 0.4 A
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29 a
b
Connect four cells in series
E = IVt = QV = 2 C × 6 V = 12 J
30- a
coulomb C
b
ampere A
c
volt V
d
volt V
e
ohm Ω
31 a
Resistors in parallel: 1/R = 1/R1 + 1/R2 = 1/4 + 1/12 = 4/12 Ω−1
so R = 12/4 = 3 Ω
b
Rearrange R = V/I to give I = V/R = 6 V / 3 Ω = 2 A
c
I1 = V/R1 = 6 V / 4 Ω = 1.5 A
d
I2 = V/R2 = 6 V / 12 Ω = 0.5 A
32 a
Axes labelled, straight line with positive gradient through origin
b
Axes labelled, straight line curving at high current with decreasing gradient
33 a
High resistance when p.d. applied in one direction (reverse bias); low resistance when
p.d. applied in the opposite direction (forward bias)
b
Resistance increases as lamp heats up.
34 a
Doubled
b
Halved
c
Doubled
d
Halved
35 B
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36
Axes labelled, very low current for negative voltages / increasing current for positive
voltages
37 Analogue voltages vary continuously; digital voltages have discrete values, for example,
high or low .
38 a
Two from: LDR, thermistor, microphone, pressure switch
b
Two from: lamp, LED, loudspeaker, relay, motor, heater
39 a
i
Increases
ii
Switches on
iii Lamp lights
b
As a light-operated intruder alarm
Exam-style questions
Core
1
a
No damaged insulation, exposed wires, loose connections or short circuits [1]; plug
correctly wired [1]
b
Water lowers the resistance of the path to earth [1] so the current increases. [1]
c
The current through wire [1] is too high. [1]
d
It ensures the current-carrying capacity of the wiring [1] is not exceeded. (The fuse melts
and breaks the circuit if the current becomes greater than the fuse rating.) [1]
Supplement
2
a
All at same brightness because they have the same voltage across them; [1] if one
lamp fails, the rest remain lit. [1]
b
i
R = V/I so I = V/R [1] = 24 V / 80 Ω = 0.3 A [1]
ii
Itotal = 20 × 0.3 A [1] = 6.0 A [1]
iii Idrawn = 6.0 A − 0.3 A [1] = 5.7 A [1]
3
a
i
Rtotal = 18 Ω + 12 Ω = 30 Ω [1]
R = V/I so I = V/R = 9 V / 30 Ω = 0.3 A [1]
ii
V1/V2 = R1/R2 = 18/12 = 3/2 [1]
V = V1 + V2 = 9 V [1] so V1 = 9 V × 3/5 = 5.4 V [1]
iii V2 = 9 V × 2/5 = 3.6 V [1]
b
i
Rtotal = 33 Ω + 12 Ω = 45 Ω [1]
R =V/I so I = V/R = 9 V / 45 Ω = 0.2 A [1]
ii
V1/V2 = R1/R2 = 33/12 = 11/4 [1]
V = V1 + V2 = 9 V [1] so V1 = 9 V × 11/15 = 6.6 V [1]
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iii V2 = 9 V × 4/15 = 2.4 V [1]
4
c
Increases [1]
a
i
Increases [1]
ii
Increases [1]
iii Decreases [1]
b
V = VLDR + VR = 6 V [1]
so when VLDR = 3.5 V, VR = (6 − 3.5)V = 2.5 V [1]
For a potential divider, V1/V2 = R1/R2 so VLDR/VR = RLDR/R
Rearranging gives RLDR = VLDR × R/VR [1] = 3.5 V × 10 Ω / 2.5 V = 14 Ω [1]
4B Electromagnetic effects
Core
1
B
2
Use a larger current, more turns on solenoid
3
Speed of rotation of the coil, number of turns on the coil, strength of the magnetic field
4
Circular field lines around wire, field direction and current direction marked correctly
5
a
Upwards
b
Upwards
6
a.c. voltages can be stepped up and down easily using transformers
7
C
8
a
Rearrange Vp/Vs = Np/Ns to give Vs = Vp × Ns / Np = 240 V × 30/600 = 12 V
b
Step-down
Supplement
9
a
It does not move
b
It swings to right
c
It swings further to left
d
It swings to right
10 Current flows to the right
11 a
N
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b
S
c
N
12 a
P = IV so I = P/V = 80 000 W / 400 000 V = 0.2 A
b
Energy loss = I2R = 0.2 A × 0.2 A × 15 Ω = 0.6 J/s
13 a
i
B
ii
Reverse current direction
iii Left
b
14 a
b
i
Inside solenoid
ii
Outside solenoid
Rearrange IpVp = IsVs to give Is = IpVp / Vs = 0.15 A × 240 V / 12 V = 3.0 A
90% efficiency gives Is = 3.0 A× 90/100 = 2.7 A
15 Upwards (towards the positive plate)
16 Upwards
Exam-style questions
Core
1
a
The current through the coil reaching the ‘pull-on’ value. [1]
b
It becomes magnetised by current in coil [1] and attracts the iron armature. [1]
c
Contact is made at X [1] allowing current to flow in circuit PQ. [1]
d
It is used to control power in a second circuit; [1] especially useful if second circuit
requires a larger current. [1]
2
a
Graph: axes labelled correctly [1]; easy-to-read scales chosen and at least half of graph
paper used [1]; points clearly and correctly plotted to half a small square [1]; well judged,
best-fit, thin continuous line joining all points [1]
b
Linear/straight line, through origin [1]
c
0.75 A [1]
d
50 N [1]
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e
Q could lift a heavier load with a given current. [1]
Supplement
3
a
They maintain contact with the brushes as the coil rotates. [1]
b
Axes labelled correctly [1], one cycle [1] of sine wave sketched [1]
4
c
Horizontal [1]
d
a.c. [1]
a
It causes the coil to turn [1]
b
Increase current in coil [1]; increase number of turns on coil [1]; increase strength of
magnet [1]
c
The coil would turn faster. [1]
d
It causes a change of direction of the current in the coil every half-turn [1] so that the
direction of the couple on the coil stays constant [1].
5
a
Rearrange Vp/Vs = Np/Ns to give Ns = Vs × Np/Vp [1] = 1000 V × 100/250 [1] = 400 [1]
b
P = IV [1] = 0.8 A × 250 V = 200 W [1]
c
Rearrange IpVp = IsVs to give Is = IpVp/Vs [1] = 0.8 A × 250 V / 1000 V [1] = 0.2 A [1]
d
It reduces the efficiency. [1]
5 Nuclear physics
Core
1
G
2
a
A=Z+N
b
Z
c
i
4
2
ii
0
−1
iii
1
0
He
e
n
3
Nuclides that have the same proton number (Z) but different nucleon numbers (A)
4
a
14
b
i
6
ii
6
iii 6
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5
6
7
8
9
c
Yes
a
α-particles
b
γ-rays
c
γ-rays
d
α-particles
e
β-particles
f
α-particles
a
+1
b
0
c
+2
d
−1
e
0
f
+2
a
β-particles
b
α-particles
c
γ-rays
d
β-particles
e
γ-rays
f
α-particles
g
β-particles
a
Electrons are removed from atoms/molecules; leaving behind positive ions
b
Using a Geiger counter/GM tube or a charged electroscope
B
10 a
b
Average time for half the nuclei in a sample to decay
Radiation from the environment with example from cosmic rays, radioactive sources in
the air (radon gas) and rocks around us, food and drink
11 Number of counts has fallen by half, so age is one half-life: 5700 years
Supplement
12 Downwards
13 a
b
i
Decreases
ii
Increases
β; the radiation will pass easily through the paper and be readily detected by a Geiger
counter
14 Most of the incident α-particles passed straight through while some were deflected through an
large angle and a few particles completely rebounded.
15 a
i
131
ii
54
b
131 − 53 = 78
c
77
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Exam-style questions
Core
1
a
Two from: damage living cells and tissues leading to cancer; eye cataracts; radiation
burns/sickness; death; cause gene mutation [2]
b
Two from: radioactive tracers in medicine or agriculture; thickness testing and flaw
detection in industry; dating of materials; sterilization; radiotherapy; smoke detectors [2]
c
Two from: use lead or concrete shielding; handle sources with long forceps/remotely; keep
away from the eyes; keep in lead boxes [2]
Supplement
2
a
The break-up of a large nucleus [1] into two smaller nuclei of nearly equal size [1]
b
i
A = 235 +1 − 90 − 1 − 1 [1] = 144 [1]
ii
Z = 92 + 0 − 56 − 0 − 0 [1] = 36 [1]
i
Kinetic energy of emitted particles [1]
ii
Heats water to produce steam, which then drives a generator [1]
c
3
a
The union of two light nuclei [1] into one heavier nucleus [1]
b
i
A = 3 + 3 − 1 − 1 [1] = 4 [1]
ii
Z = 2 + 2 − 2 − 1 [1] = 1 [1]
i
He [1]
ii
H [1]
c
4
d
Electromagnetic radiation [1]
a
i
A = 241 − 237 [1] = 4 [1]
ii
Z = 95 − 93 [1] = 2 [1]
b
α-particle [1]
c
It causes ionisation of the air [1]
6 Space physics
Core
1
C
2
B
3
a
The Earth orbits the Sun once in every 365 days; the Earth is tilted on its axis
b
The northern hemisphere is tilted away from the Sun and the southern hemisphere is tilted
towards the Sun
4
C
5
B
6
a
C
b
A
c
D
d
B
Supplement
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7
B
8
a
The orbital speed of Mercury is greater than that of the Earth and the circumference of
its orbit is less, because it is nearer the Sun
b
Mars is further from the Sun than the Earth and it does not have much atmosphere
c
The mass, and hence the gravitational field of the Earth, is too low to be able to
retain a light gas such as hydrogen.
9
T = distance/speed = 2 × π × 108 × 106 km / 35 km/s = 19.4 × 106 s
= 19.4 × 106 s / 60 × 60 × 24 = 224 days
10 Stars are formed when a cloud of hydrogen collapses under gravitational attraction to form a
protostar. As the mass of the protostar increases it becomes hotter, and when the core is
hot enough nuclear fusion of hydrogen into helium begins. The protostar turns into a
stable star when the inward force of gravity is balanced by outward force arising from the
high temperature of the star.
11 Energy, fusion, collapse, expand, temperature, carbon, planetary, dwarf
12 High mass star → red giant → supernova → neutron star OR black hole
13 A planetary nebula, B white dwarf, C supernova , D neutron star, E black hole
14 B
15 1 Cosmic microwave background radiation (CMBR)
2 Redshift in the light from distant galaxies shows the speed of recession increases with
distance
16 Ho = v/d so d = v/Ho = 350 km/s / (2.2 × 10−18 s−1) = 160 × 1018 km
= 160 × 1018 km / (1013 km/light year) = 16 million light years
17 1100 million light years = 1100 × 106 × 1013 km = 1.1 × 1022 km
Ho = v/d = 24 000 km/s / (1.1 × 1022 km) = 2.2 × 10−18 s−1
Exam-style questions
Core
1
2
a
Because the Earth rotates [1] on its axis every 24 hours [1]
b
At noon, [1] on or about 21 June [1].
a
The high temperature of the star [1] causes hydrogen gas in its surface layers to glow. [1]
b
It is redshifted (its wavelength increases) [1] in comparison with light from glowing
hydrogen on Earth [1]
c
Measurement of the redshift of light from distant galaxies [1] shows that the further away a
galaxy is [1] the greater is the redshift [1] and so the faster the galaxy is receding. [1]
Supplement
3
a
A protostar is formed from the gravitational collapse of interstellar clouds of gas and dust
containing hydrogen. [1]
b
A star is powered by the release of energy during the nuclear fusion [1] of hydrogen into
helium. [1]
c
When most of the hydrogen in the core is used up. [1]
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d
When the star becomes unstable, the inward force of gravity is sufficient to cause the core
to collapse. [1] The outer layers of gas expand and cool, [1] and the star becomes a red
giant. [1]
4
a
v = 2 π r / T [1]
so vN/vE = (2 π rN/TN) / (2 π rE/TE) [1] = (rN × TE) / (rE × TN) [1] = 30/165 = 0.18 [1]
5
b
Slower [1]
a
Light from glowing hydrogen and other gases in stars in distant galaxies [1] have a longer
wavelength than they do on Earth, [1] that is, they are shifted towards the red end of the
electromagnetic spectrum. [1]
6
b
v = Ho d [1] where v is the speed of recession of a galaxy a distance d away and Ho is
Hubble’s constant [1]
a
d = v/Ho [1] = 60000 km/s / (2.2 × 10−18 s−1) [1] = 2.7 × 1022 km [1]
b
d = 2.7 × 1022 km / (1013 km/light year) [1] = 2.7 × 109 light years
Time to reach Earth = 2.7 × 109 years [1]
c
Time = d/v = 2.7 × 1022 km / 60000 km/s [1] = 43 × 1016 s [1]
Since 1 year = 365 × 24 × 60 × 60 s = 3.2 × 107 s [1]
Time = 43 × 1016 / 3.2 × 107 years [1] = 14 × 109 years [1]
d
It is the approximate age of the universe. [1]
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