Now test yourself answers
Chapter 1
Chapter 2
1
1 F – friction = ma
F – 400 = 1200 × 3
F = 3600 + 400 = 4000 N
2 F – friction = ma
3000 – friction = 1100 × 2
friction = 3000 – 2200 = 800 N
3 Downward gravitational force = 60 × 10 = 600 N
Resultant force = 600 − 480 N = 120 N
F 120
a=
=
= 2 m/s2
m
60
4 Newton’s first law gives the friction force as
400 N.
unbalanced force = m × a
thrust – 400 = 500 × 2
thrust = 1000 + 400 = 1400 N
5 forward thrust – friction = m × a
forward thrust – 400 = 1200 × 3
forward thrust = 400 + 3600 = 4000 N
6 Suppose the combined mass of the cyclist and
the bicycle is m.
unbalanced force = m × a
100 – friction = m × 1.0 = m
140 – friction = m × 1.5 = 1.5m
Subtracting, 40 = 0.5m
so, m = 80 kg and the cycle mass = 80 – 65 = 15 kg
Substituting, friction = 100 – 80 = 20 N
7 Mass is measured in kg, weight is measured in N.
Mass is a scalar quantity (it has no direction);
weight is a vector (it has direction).
Mass is the same regardless of location; weight
depends on location (e.g. weight at the top of a
mountain is less than weight at sea-level).
8 (a) 0 N
(b) 620 N vertically upwards.
9 The object’s direction of motion is constantly
changing, so its velocity is changing. The object
is therefore accelerating, so there must be a
resultant force on it.
10 The hammer will continue to move in a straight
line at 3 m/s until another force compels it to
change its velocity. This is a consequence of
Newton’s first law.
2
3
4
5
(a) Total distance = 5 × (105 + 150 + 105 + 150) =
2550 m
total distance 2550
(b) Average speed =
=
850
total time
= 3 m/s
(a) Rate of change of speed =
final speed – initial speed 27 – 3
= 3 m/s2
=
8
time taken
initial speed + final speed
(b) Average speed =
2
3 + 27
=
= 15 m/s
2
total distance travelled
(c) Average speed =
total time taken
total distance travelled
15 =
8
Total distance travelled = average speed ×
time = 15 × 8 = 120 m
total distance 100 cm
=
(a) (i) Average speed =
3.7 s
total time
= 27.0 cm/s
initial speed + final speed
(ii) Average speed =
2
0+v
= 27.0 cm/s
=
2
Maximum (final) speed = 2 × 27 = 54 cm/s
(iii) Rate of change of speed =
final speed – initial speed = 54 – 0
3.7
time taken
2
= 14.6 cm/s
(b) Assumption: rate of change of speed was
constant.
v – u 0 – 28
=
(a) a =
= –4 m/s2
7
t
Retardation (negative acceleration) = –4 m/s2
28 + 0
(b) Average speed =
= 14 m/s
2
Total distance = average speed × time = 14 × 7
= 98 m
(a) None is a vector. They are all scalars.
(b) Mass is a scalar, so it has no direction and
masses add like ordinary numbers.
Force is a vector, so it has direction. So
direction must be taken into account when
adding forces. (In this case, if, say, the forces
were in opposite directions, the total force
would be 4 N.)
CCEA GCSE Physics
1
Now test yourself answers
11 Weight is measured in N. Mass is measured
in kg. Julie probably has a mass of 35 kg and a
weight of 350 N.
12 The ball will start to accelerate, but as the
resistive force increases, the acceleration will
decrease. Eventually when the resistive force
is equal to the ball’s weight, the ball will move
with a constant downward velocity until it hits
the bottom of the cylinder.
13 There is no atmosphere on the Moon, so there
is nothing resisting the motion of either the
hammer or the feather. They will both fall with
the same acceleration and strike the surface at
the same time and with the same speed.
14 As the wind fills the canopy of the parachute,
it causes a considerable drag force. This
drag force increases with the speed of the
parachutist. It can be greater than the weight of
the parachutist and slow him down.
15 Hooke’s law states that for many materials,
the extension is directly proportional to the
applied load, up to a limit known as the limit of
proportionality.
16 If the deformation is elastic, the spring will return
to its original length when the load is removed.
If the deformation is plastic, the spring will no
longer return to its original length when the
load is removed.
17 The limit of proportionality is the point
beyond which extension is no longer directly
proportional to the applied force.
10
F
= 1 × 109 Pa
=
A 1.0 × 10 –8
F 9000
19 A = =
= 500 cm2
18
P
Since there are four tyres, the area of each in
contact with the ground = 500 / 4 = 125 cm2
18 P =
20 F = P × A = 61 000 × (0.9 × 0.9) = 49 410 N
Chapter 3
mass
75.6 g
= 12.6 g/cm3
=
volume 6.0 cm3
2 (a) mass = volume × density = 20 cm3 × 2.7 g/cm3
= 54 g
mass
54 g
(b) volume =
= 20 cm3
=
density 2.7 g/cm3
1 density =
2
CCEA GCSE Physics
3 volume = length × breadth × height
= 10 m × 5 m × 3 m = 150 m3
mass = volume × density = 150 m3 × 1.26 kg/m3
= 189 kg
4 volume of stone = 35 cm3 – 15 cm3 = 20 cm3
mass
60 g
density =
= 3 g/cm3
=
volume 20 cm3
5 mass = volume × density = 0.08 m3 × 800 kg/m3
= 64 kg
6 mass of air = 351.2 g – 350 g = 1.2 g
mass
density =
= 1.2 g = 0.0012 g/cm3
volume 1000 cm3
= 1.2 kg/m3
Chapter 4
1 oil, coal, gas, peat
2 chemical, electrical, heat, kinetic, light, sound
3 (a) A renewable energy resource is one that
is replaced by nature in less than a human
lifetime.
(b) A non-renewable resource is one that is used
faster than it can be replaced by nature. We
will eventually run out of non-renewable
energy.
4 Renewable: solar, tide, waves, wind.
Non-renewable: coal, oil, gas, uranium (for
nuclear fuel)
5 The production of electricity often uses very
polluting fuels like oil and coal.
6 Energy can neither be created nor destroyed, but
it can change its form.
7 (a) input: kinetic; useful output: kinetic
(b) A renewable energy resource is one that
is replaced by nature in less than a human
lifetime.
(c) solar, tides
8 (energy stored in the upper lake): gravitational
potential energy; (energy in the moving water):
kinetic energy; (output energy from the power
station): electrical energy
Device/situation
Input energy form
Microphone
Sound energy
→
Electrical energy
Loudspeaker
Electrical energy
→
Sound energy
Electric smoothing iron
Electrical energy
→
Heat energy
Coal burning in an open fire
Chemical energy
→
Heat energy
Weight falling towards the
ground
Gravitational potential energy
→
Kinetic energy
Candle flame
Chemical energy
→
Heat energy and light energy
Battery-powered electric drill
Chemical energy → Electrical
energy
→
Kinetic energy
10 Work requires movement. Holding a tray
provides no movement.
11 work = force × distance
work done
power =
time taken
useful energy out
efficiency =
total energy in
12 GPE is the energy possessed by a mass because
of its height above the ground.
Kinetic energy is the energy possessed by a
mass because it is moving.
GPE = mgh; KE = ½ mv2
13 There can never be more energy out of a
process than that which is input because of the
law of conservation of energy.
14 Efficiency is a ratio of two quantities which are
both measured in the same unit (joules).
15 Since GPE = mgh, 1 = m × 10 × 1
so m = 0.1 kg
16 (a) work = F × d = 8000 × 1.8 = 14 400 J
work done
(b) power =
time taken
5200 = 26 000
t
26 000
= 5s
t=
5200
(c) input power =
output power 5.2 kW
= 20 kW
=
0.26
efficiency
17 work = F × d = 550 N × 3.0 m = 1650 J
18 Speed decreases, potential energy increases,
total energy remains constant, kinetic energy
decreases.
Useful output energy form
Now test yourself answers
9
Chapter 5
1 (a) To reduce the entry of heat into the hold, which
could destroy the food.
(b) Polystyrene or urea formaldehyde.
(c) The material traps air, which is an excellent
insulator.
2 (a) It takes 40 years for the annual savings to
amount to the cost of installing double glazing.
(b) Double glazing reduces the entry of unwanted
sound into the home. This might be important
if the house is close to an airport, busy road or
noisy factory.
3 The payback time is 1.5 years, so the cost is
1.5 years × £90 = £135
4 (a) Black materials are best at emitting heat
radiation. So the pipes radiate the heat taken
from the food into the environment.
(b) The thin metal fins provide a very large
surface area. The bigger the radiating surface,
the more effective the fridge is in dissipating
the unwanted heat.
5 (a) Top
(b) The hot air rises from the bottom of the
oven. So the top is likely to be hotter than the
bottom.
(c) Successful cooking sometimes relies on
the oven being at the same temperature
throughout. The fan forces the air to circulate,
rather than simply relying on convection.
CCEA GCSE Physics
3
Now test yourself answers
6 Radiation from outside the house can cause the
inside of the house to become very hot. Painting
the roof white reduces the absorption and
increases the reflection of heat from the Sun.
White surfaces are worse absorbers and better
reflectors than dark surfaces.
Chapter 6
Chapter 7
1 (a) electrons
(b) neutrons
(c) electrons
(d) protons and neutrons
(e) electrons
23
2 11Na
3 They all have the same number of protons (same
atomic number). They all have a different number
of neutrons (so they have a different mass
number).
4 Carbon-14,146C
5 (a) gamma
(b) alpha
(c) beta
(d) gamma
(e) alpha
(f) gamma
(g) alpha
6
Atomic
Radiation
number (Z)
Mass number (A)
1 In a transverse wave the particles vibrate
perpendicular to the direction of wave motion. In
a longitudinal wave the particles vibrate parallel
to the direction of wave motion.
2 Transverse — water waves, visible light;
longitudinal — sound, ultrasound
3 Wavelength — distance between consecutive
crests; frequency — number of waves passing a
fixed point in 1 second; amplitude — maximum
displacement of wave from equilibrium position
4 Microwaves can cause heating
5 See page 60
6 Distance between consecutive compressions
increases
7 Wavelength Frequency
Speed
5m
100 Hz
500 m/s
12 m
50 Hz
600 m/s
3 cm
60 kHz
1800 m/s
0.05 m
4 Hz
20 cm/s
0.5 m
5 kHz
2.5 km/s
α-emission
Decreases by 2 Decreases by 4
16 mm
50 Hz
80 cm/s
β-emission
Increases by 1
Unchanged
6 × 10 4 m
5000 Hz
3 × 108 m/s
γ-emission
Unchanged
Unchanged
U → 234
Th + 42He
7 (a) 238
92
90
(b) 14
C → 14
N + –10 e
6
7
8 (a) Beta decay – no change in mass number, but
a change in atomic number (different nuclear
species)
(b) Alpha decay – mass number decreases by 4
(c) Alpha decay – mass number decreases by 4
9 (a) 1000 → 500 → 250 represents 2 half-lives, so
half-life = 14.4 hours/2 = 7.2 hours
(b) 200 → 100 → 50 → 25 represents 3 half-lives,
so half-life = 18 hours/3 = 6 hours
(c) 500 → 250 → 125 → 62.5 represents
3 half-lives, so half-life = 86.4 years/3
= 28.8 years
4
10 (a) 64 → 32 → 16 → 8 → 4 → 2 → 1 represents
6 half-lives = 6 × 5.27 years = 31.62 years
(b) 128 → 64 → 32 → 16 → 8 → 4 → 2 → 1
represents 7 half-lives = 7 × 8 days = 56 days
(c) 32 → 16 → 8 → 4 → 2 → 1 represents
5 half-lives = 5 × 138 days = 690 days
CCEA GCSE Physics
8 Amplitude = ½ × 24 = 12 cm
Frequency = number of waves per second
30 waves
=
= 0.5 Hz
60 s
Wavelength = distance between successive crests
40 cm
= 10 cm
=
4
Speed = f × λ= 0.5 × 10 = 5 cm/s
9 (a) Diagram showing:
– normal perpendicular to barrier at point of
incidence
– reflected ray from point of incidence so
that angle i = angle r
– three wavefronts perpendicular to
reflected ray, which are parallel to each
other and the same distance apart as the
incident waves.
(b) Frequency, wavelength and speed are all
unchanged by reflection.
Wave
X-rays
10 (a) Dispersion is the splitting up of white light into
its coloured components.
(b) Dispersion occurs in certain media (e.g. glass)
because each colour travels at a different
speed so bends by a slightly different amount
on refraction.
11 (a) (i) angle of incidence = 34°
(ii) faster in air
(b) Red light bends more than blue when
refracted in glass, so red light is faster than
blue light in glass.
12 (Sound waves bend away from the normal
because sound travels faster in water than in air.)
Now test yourself answers
10 (a) Diagram should show:
– normal perpendicular to barrier at point of
incidence and at both sides of barrier
– refracted ray bent towards normal at point
of incidence so that angle i > angle r
– three waves perpendicular to reflected ray,
which are parallel to each other and closer
together than the incident waves.
(b) Frequency never changes on refraction.
Wavelength and speed both decrease when
water waves enter shallower water.
11 (a) There are many similarities between the
behaviour of water waves and the behaviour of
light waves — we say they are analogous.
(b) When water waves and light waves reflect,
then
angle of incidence = angle of reflection
reflected wavelength = incident wavelength
there is no change in wavelength,
frequency or speed.
12 The missing waves are: X-rays, visible light,
infrared and microwaves.
These are entered in the table in order of
increasing wavelength.
normal
air
water
sound
13
Visible Infrared Microwaves
light
light
1 × 10 –10 6 × 10 –7 1 × 10 –5 1 × 10 –3
Typical
wavelength/m
13 d = speed × time from emitter to wall
= 340 m/s × (½ × 0.0025 s) = 0.425 m
Chapter 8
1 The normal is a line drawn perpendicular to the
mirror at the point of incidence. The angle of
reflection is the angle between the normal and
the reflected ray. The angle of incidence is the
angle between the normal and the incident ray.
2 The angle of incidence is always equal to the
angle of reflection.
3 The image is virtual, the same size as the object,
laterally inverted and the same distance behind
the mirror as the object is in front of the mirror.
4 0° (a common mistake is to say the angle is 90°)
5 angle of reflection = angle of incidence = 50°
6 angle of incidence = ½ × 130° = 65°
7 Student is 20 cm further from mirror and image is
20 cm further from mirror. So distance between
student and image has increased by 40 cm.
8 Refraction is the bending of light as it passes from
one material into another and changes its speed.
9 (a) Light refracts towards the normal when it
slows down.
(b) Light refracts away from the normal when it
speeds up.
14 The critical angle is the angle of incidence in the
medium resulting in an angle of refraction of 90°
in air.
15 The light is travelling in an optically dense
material (like glass) towards a boundary with an
optically rare material (like air).
The angle of incidence at the boundary is greater
than the critical angle.
16 and 17 See text.
18 (a) 0°
(b) Since the triangle is equilateral, the angle at A
is 60°. Angle of incidence at surface AC is 60°.
(c) Angle of incidence at AC is greater than the
critical angle, so the light is totally internally
reflected at AC.
(d) Angle of incidence on BC is 0°. So angle of
refraction in air on BC is also 0°.
(e)
CCEA GCSE Physics
5
Now test yourself answers
19 For upper diagram all statements are true; for
lower diagram: all statements are false.
20 Speed of light in the core is slower than in the
cladding, otherwise total internal reflection
could not occur at the core–cladding boundary.
21–23 See text
Chapter 9
1 (a) Two of the cells cancel each other. So the
voltage of each cell is the battery voltage or
1.6 V
(b) 3 × 1.6 V = 4.8 V
2 (a) 3000 mA
(b) 200 mA
(c) 0.2 mA
3 (a) Q = It = 6 A × 10 s = 60 C
(b) Q = It = 0.3 A × 60 s = 18 C
(c) Q = It = 500 × 10 –6 A × (60 × 60) s = 1.8 C
V 20 V
= 2A
4 I= =
R 10 Ω
V 15 V
=
= 5Ω
I
3A
6 V = I × R = 2 A × 25 Ω = 50 V
V 15 V
7 (a) R = =
= 6Ω
I 2.5 A
(b) V = I × R = 2 A × 6 Ω = 12 V
5 R=
V
6V
= 0.5 A
8 (a) I = =
R 12 Ω
(b) V = I × R = 1.5 A × 12 Ω = 18 V
V
6V
=
= 60 Ω
I 0.1 A
V
3V
= 5Ω
10 R = =
I 0.6 A
V 2.5 V
= 0.5 A
I= =
R
5Ω
9 R=
11 (a) First circuit: Rtotal = R1 + R2 + R3 = 3 + 6 + 9 = 18 Ω
V
3V
= 0.17 A
current from cell I = =
R 18 Ω
Second circuit: since the resistors are both
R 4
4 Ω, Rtotal = = = 2 Ω
2 2
V 8V
I= =
= 4A
R 2Ω
(b) Voltage across each resistor in parallel
= battery voltage = 8 V
V 12
= 4Ω
12 (a) Circuit resistance R = =
I
3
so each resistance is 8 Ω
6
CCEA GCSE Physics
R
2Ω
=
= 0.8 m
2.5 Ω/m
k
(b) R = kL = 2.5 × 1.2 = 3 Ω
14 (a) Resistance of 80 cm length of wire is
0.8 × 3 = 2.4 Ω
Loop consists of two ‘half-loops’ in parallel,
each of resistance 1.2 Ω
So total resistance of parallel arrangement
1.2
=
= 0.6 Ω
2
(b) Resistance of a parallel arrangement is
always less than the smaller resistance in the
loop. So, as the clip moves along the loop, the
resistance decreases, eventually to zero.
15 (a) 75 cm length has resistance 1.5 times that of
the 50 cm length or 2.4 Ω.
(b) Doubling diameter quadruples the crosssectional area and brings resistance down
by a factor of 4. So resistance of new 50 cm
1.6
length is
= 0.4 Ω
4
(c) Resistance is increased by a factor of 1.5
by increasing the length, then quartered by
doubling the cross-sectional area.
1.6 × 1.5
= 0.6 Ω
So the total resistance is
4
13 (a) L =
Chapter 10
energy
3 600 000 J
1 power = =
= 1000 W
time
(60 × 60) s
2 (a) 1500 W
(b) energy = power × time = 1500 W × 10 s
= 15 000 J
V 240 V
3 (a) I = =
= 0.25 A
R 960 Ω
(b) P = IV = 0.25 A × 240 V = 60 W
4 (a) I = P = 1200 W = 5 A
240 V
V
(b) Power would decrease.
V2
.
R
So P decreases when V decreases
(R is roughly constant)
P = IV and V = IR, so P =
5
Name of
appliance
Power
rating
Current
drawn
Resistance
Filament
lamp
60 W
0.25 A
960 Ω
Coffee
machine
120 W
0.5 A
480 Ω
Iron
1440 W
6A
40 Ω
Electric oven
2440 W
10 A
24 Ω
Immersion
heater
3 kW
12.5 A
19.2 Ω
1 Field lines show the direction of the magnetic
field. Crossing field lines would be a
contradiction.
2 A neutral point is one where there is no resultant
magnetic field.
3 (a) Remember that copper is not a magnetic
material, so the compass points to the Earth’s
north pole.
copper rod
N
(b) The diagram follows the same lines as the
field around the magnet.
bar magnet
N
N
S
4 Both rods become magnetised. The left end of
each rod becomes a south pole, the right end
becomes a north pole. In the space between
the rods a north pole faces a south pole. The
attractive force between these two opposite poles
causes the rods to move closer together. So, the
gap between the iron rods decreases.
5 As shown in Figure 11.10 on page 116, point the
centre finger of the left hand in the direction of
the current and the first finger in the direction
of the magnetic field. The direction in which the
thumb is pointing gives the direction of the force.
(ii)
6 (a) (i)
N
N
force
(b) When the north pole is pulled out of the
coil, the magnetic flux linked with the coil is
changing, but this time in the opposites sense,
so EMI occurs and there is an induced current
in the opposite direction.
(c) The person giving the kinetic energy to the
magnet
9 (a) When the switch is closed there is a sudden
increase in the current in the primary coil.
This causes a sudden increase in the magnetic
field linked to the secondary coil. So there
is EMI in the secondary coil and a current is
detected. The effect is momentary because
the current in the primary coil does not
increase indefinitely.
(b) When the switch is opened there is a sudden
decrease in the current in the primary
coil. This causes a sudden decrease in the
magnetic field linked to the secondary coil.
So there is EMI in the secondary coil and a
current is detected.
(c) Because the magnetic field linked to the
secondary coil in (b) is collapsing, while in (a)
it is increasing, the directions of the current in
the two situations are opposite to each other.
(d) Switch the current in the primary coil on and
off repeatedly, or replace the battery and
switch with a source of a.c.
10 (a) Yes — the magnetic field/flux linked with the
wire is changing.
(b) No — the circuit is incomplete (not closed), so
no current can flow.
(c)
Now test yourself answers
Chapter 11
force
S
S
(b) (i)
(ii)
S
S
current OUT of
paper
force
N
current OUT
of paper
force
N
7 (a) (i), (ii) and (iii) are all d.c. (because the lines do
not cross the time axis).
(b) (iv) and (v) are both a.c.
8 (a) (i) Electromagnetic induction
(ii) When the magnet is stationary there is no
change in the magnetic flux linked with
the coil, so there is no electromagnetic
induction. So no current flows. When the
north pole moves into the coil, the magnetic
flux linked with the coil is changing, so EMI
occurs and there is an induced current.
11 (a) There is a momentary deflection on the
centre-zero ammeter. The needle then returns
to zero.
(b) There is a momentary deflection on the
centre-zero ammeter, but in the opposite
direction to that observed in (a). The needle
then returns to zero.
12 (a) The wind causes the cups to turn. This causes
the magnet to spin. The spinning magnet
produces a changing flux in the coil, inducing
an a.c. which is detected on the voltmeter.
CCEA GCSE Physics
7
Now test yourself answers
(b) The greater the speed of the wind, the faster
the cups turn, the faster the magnet spins and
the greater the induced voltage.
(c) Use of a stronger magnet (or using a coil of
more turns per unit of length) would make the
anemometer more sensitive.
13 (a) 25 kJ
(b) High voltages mean that to deliver a given
amount of power the current is low (from
P = I × V). A low current means less heat is
lost in the power cables.
(c) At the consumer distribution system.
(d) To reduce the voltage to a safer value that is
suitable for electrical appliances.
Chapter 12
1 Mars
2 Jupiter
3 There are many, many more asteroids than
comets.
4 The Hubble telescope is a satellite because it
orbits the Earth. It is artificial because it was put
into space by humans.
5 Moons
6 A cloud of gas (mainly hydrogen) and dust from
which stars are formed.
8
CCEA GCSE Physics
7 The loss of gravitational potential energy as the
particles in the nebula come together.
8 They are not hot enough at the core to bring
about nuclear fusion.
9 Nuclear fusion
10 15 000 000 °C
11 Radiation pressure
12 When almost all the hydrogen is used up,
the outward radiation pressure from nuclear
processes is greater than gravity, so the star
expands. It changes to a red colour as it cools
down.
13 A black dwarf star
14 A red supergiant
15 The absorption spectrum shows dark lines
corresponding to these elements.
16 The increase in the wavelengths of light from
distant galaxies.
17 They are moving away from us.
18 Cosmic microwave background radiation
19 CMBR is the ‘after-glow’ or ‘echo’ of the Big
Bang.
20 Planets outside our Solar System.
21 Oxygen and water are essential for life (as we
know it).