Table Of ContentSection A: Forces and Motion
1. a) 7.75 m/s.
b) 0.00775 km/s.
c) 27.9 km/h.
2. a) 500 seconds and
b) 8⅓ minutes.
3. 39 735 360 000 000 kilometres (roughly 40 trillion kilometres).
4. a) Graph (b) (the steepest straight line).
b) Graph (d) (change in gradient from positive, moving away from the start, to negative moving
back).
c) Graph (c) (the gradient is continuously increasing).
d) Graph (a) (straight line, less steep than graph (b)).
5. a) 25 m/s.
e
b) 3.125 m/s2. uid
G
6. a) 3.5 m/s2. on
si
vi
b) At a constant velocity of 14 m/s. e
R
c) 140 m (area under graph = area of triangle + area of rectangle (cid:2) (2 × 14 + 8 × 14) m). s
c
si
y
d) 7 m/s. h
P
7. a) b) The sum or resultant of balanced
forces is zero as they are equal
in size, but opposite in direction.
8. a) b) When the string is cut the tension
force will no longer act on the
balloon.
c) The forces will no longer be balanced; there will be a resultant force upwards which will cause
the balloon to accelerate vertically upwards.
d) As soon as the balloon starts to move it will be subjected to a (viscous) drag force opposing its
upward motion through the air. This force will increase with the speed of the balloon, so the
balloon will accelerate quickly at first, then more and more slowly until the three forces balance
once again. The balloon will then rise at a steady terminal speed.
1111
9. An unbalanced force can cause an object to accelerate (speed up), decelerate (slow down) or change
the direction in which it is moving.
10. a) Between A and C (the straight part of the graph) Hooke’s Law is obeyed. At C Hooke’s Law
ceases to be obeyed.
b) The elastic limit or the limit of proportionality.
11. a) 54 000 000 N (b) The drag force due to its movement through the water. (c) It must be greater
than the drag force by 54 000 000 N to cause the acceleration.
12. a) 8500 N.
b) 1.9 m/s2. (If the LEM weighed 7500 N on the Moon, its mass = weight ÷ Moon gravity, approx
4490 kg).
c) As the rocket expels the products of burning fuel, the mass of the rocket decreases; if the thrust
is constant then the acceleration will increase.
13. 0.008 kg (or 8 grams).
14. a) Car C. It has the largest area under the graph line.
e
d
ui b) Car A. The horizontal section of the graph shows no braking (constant velocity) because the
G
n driver has yet to react to the hazard – in the graph for car A this is the shortest. The reaction time
o
si for the other two graphs could be because the driver was tired, under the influence of alcohol or
vi
e other drugs, was distracted by use of a mobile phone or because visibility was poor (any two).
R
s
c c) If you cannot see the car in front you cannot ensure you have left enough braking distance and
si
y you are likely to take longer to realise that there was an emergency stop required. The faster you
h
P
are going and the longer you take to react (graph C) the greater the distance needed to come to a
halt.
d) The slope of the braking part of the graph would be less steep because you could not brake as
hard without skidding. This would mean that the total stopping distance (thinking distance +
braking distance) would be greater still.
15. a) The hammer and feather hit the Moon’s surface at the same instant. It showed that in the
absence of an atmosphere, all objects fall with the same acceleration.
b) The hammer would hit the ground after a shorter time than it did on the Moon, because the
Earth’s gravity is about six times stronger than the Moon’s. The feather would also accelerate
more quickly, but the effect of air resistance would mean it soon reached a terminal velocity and
therefore took noticeably longer to reach the ground.
16. a) The acceleration is virtually constant because the resultant force on the object is virtually
constant.
b) When the speed of the object increases, the drag force due to air resistance increases. Eventually
this becomes significant and the resultant force becomes noticeably smaller – so too does the
acceleration.
c) The terminal velocity.
d) Zero. The forces on the object are balanced.
2
17. a) 30 kg m/s.
b) The same, 30 kg m/s, but in the opposite direction.
c) 0.3 m/s.
18. 3.2 m/s.
19. a) 360 000 N.
b) The average force is now only 28 800 N. Large decelerations involve huge forces – these are
transmitted to the human occupant, when they hit the windscreen for example, and cause
extensive damage to bones and internal organs.
20. Although it is clearly the astronaut who is doing the throwing she cannot apply a force to the box
without experiencing a force herself, equal in size (magnitude) but opposite in direction. The force
she feels is the reaction force to the action force she applied on the box.
21. Least (d), (force acts through the turning point or pivot so turning moment is 0). Next (c) (because it
is clearly less than (a) and (a) is just less than (b): (d), (c), (a), (b).
22. a) The order is (d), (a), (b), (c). e
d
ui
b) The most stable object is (d) and (c) is the least stable. G
n
o
23. 400 N (left-hand diagram); 300 N (right-hand diagram). si
vi
e
R
24. The Sun generates energy in the form of light (and heat of course) by the continuous fusion reaction s
c
going on; the Moon merely reflects some of the Sun’s energy back to Earth. si
y
h
P
25. a) The gravitational force of attraction between objects which have large mass.
b) The order is (c), (a), (b). The more massive the bodies and the closer they are together, the
bigger the gravitational force attracting the bodies is. (c) exerts a smaller force on the satellite
than (a) because the satellite is further away; (b) exerts a larger force on the satellite than (a)
because it has greater mass.
26. a) 10 N and 1 kg; on the Earth a mass of 1 kg experiences a force due to gravity of approximately
10 N. Both spring balances are correctly calibrated for use on the Earth.
b) 1.7 N and 0.17 kg; the gravitational field at the surface of the Moon is about one-sixth of that at
the Earth’s surface. The mass is still 1 kg but the spring balance calibrated on the Earth will give
a false reading; this is because the extension of the spring depends on the weight of the 1 kg
mass.
27. Our solar system is made up of a star called the sun which is orbited by a number of planets. Some
of these planets have moons orbiting them, including the Earth. There are billions of stars in the our
galaxy which is called the Milky Way. The universe itself is made up billions of galaxies.
28. A is a galaxy, B is a comet, C is a star, D is a planet.
Remember that the comet has the ‘tail’ and eccentric orbit. The planet Saturn has rings and a galaxy
is a huge group of billions of stars.
3
29. A is the orbit of a planet, B is the orbit of a comet. Comets have highly eccentric orbits, planets have
orbits that are nearly circular.
30. Earth orbital speed: 108 000 km/h, 30 000 m/s.
Mercury orbital speed: 1.8 million km/h, 480 000 m/s. [All figures rounded to no more than
3 sig. fig.]
e
d
ui
G
n
o
si
vi
e
R
s
c
si
y
h
P
4
Section B: Electricity
1. B.
2. Paper clip used as a fuse!
A loose strand from live wire (brown).
Neutral wire (blue) has damaged insulation.
Outer plastic casing is not secured under cable anchor.
Screw missing from the cable anchor (left).
3. The fuse melts if the current exceeds a safe level , breaking the circuit. Its purpose is to prevent
cables and appliances from overheating and causing fires. Key points: breaks circuit, too much
current, risk of fire.
4. The earth wire ensures that any exposed metal parts of an electrical appliance are at 0V by providing
a very low resistance path to the earth. In the event of a live wire touching the metal casing a large
fault current will result. This will blow a fuse or trip a circuit breaker, switching the mains supply to
the appliance off. Key points: metal casing cannot become ‘live’, fuse blows.
e
d
5. A hair drier. There are no exposed metal parts that can become ‘live’. ui
G
n
6. Electric fire, toaster, electric kettle, hair drier, electric iron. o
si
vi
e
7. When an electric current passes round a circuit, electrical energy is converted to heat wherever there R
s
is resistance. In a lighting circuit the cables carrying electricity to the lamp have very low resistance c
si
so very little heat is generated in the cables (so they shouldn’t overheat). The same current in the y
h
P
high resistance filament produces a great deal of heat making it get hot enough to glow white hot and
give out light. Key points: in a series circuit the current is the same throughout; you want the heat to
be generated where you need it, not to be wasted in the cables.
8. a) The circuits in a house are protected by fuses or circuit breakers to break the circuit if the
current reaches a level that will cause the circuit cables to overheat. (Faults like a live wire
touching an earthed casing cause large fault currents.)
b) Use I = P/V to find the working current for an appliance. The working current is the normal, or
safe current.
i) I = 900 W/230 V so the working current is 3.9 A; a 3A fuse will therefore quickly blow, so
the correct fuse is rated at 5A; choose the smallest fuse available that can handle the
working current.
ii) 3 A.
iii) 10 A (Remember to convert 1.2 kW to 1200 W when substituting into the formula).
9. a) Energy = current × voltage × time.
b) i) E = 0.22 A × 230 V × (2.5 × 60 × 60)s. Ans: 455 400J (Remember to convert current
into amps and time into seconds if necessary, as
shown in this example.)
1111
ii) Here you do not need to calculate the current in the lamp (which happens to be 3A) – just
use:
Energy = power × time: E = 36 W × (50 × 60)s Answer: 108 000 J.
10. Air flows backwards and forwards through the mouth organ; in an AC circuit the electric charges
move backwards and forward in the circuit as the current changes direction continuously.
11. a) Rubbing has caused a small amount of electric charge to be transferred between the comb and
the cloth; this means that both the comb and the cloth will now be electrically charged.
(Remember that objects are usually uncharged or neutral because the numbers of positively
charged protons and negatively charged electrons balance exactly. If electrons are removed from
the cloth and transferred to the comb, the comb becomes negatively charged leaving the cloth
positively charged.)
b) Metal rulers conduct electricity. As soon as charge starts to build up it can flow away through
the metal.
c) The tiny droplets of ink are given charge and the paper attracts the charged droplets.
12. a) Katie’s strip attracts the polythene strip because it is positively charged and opposite charges
e attract. It repels the acetate strip because like charges (positive in this case) repel.
d
ui
G b) Shazia must have a negatively charged strip.
n
o
si c) Joe has not managed to charge his strip, so both the suspended charged strips are attracted.
vi
e
R d) Amar must have been charging a polythene strip as this gains electrons from the cloth, leaving it
s with a positive charge, which attracts the negatively charged polythene strip.
c
si
y
h
P 13. An electric current is the rate of flow of charge in a circuit. The amp is the unit of current and the
unit of electric charge is the coulomb . The relationship between current, charge and time is given by
the equation charge = current × time .
14. a) Electrons.
b) Negative.
c) From the negative terminal to the positive terminal.
15. a) Voltage is the measure of how much energy in joules is transferred per coulomb of charge that
passes through a component.
b) 12 J per coulomb of charge. The energy is converted into heat and light.
16. a) i) Series ii) Parallel
b) In the series circuit all the lamps turn off. In the parallel circuit the remaining two good lamps
still light up.
2
c) They are connected in series. This means that the blade cannot be made to spin unless the lid is
in place; this means that you cannot accidentally turn it on when your fingers are next to the
blade!
17. (b), (c), (d), (a).
18. a) A filament lamp. As the current increases it get very hot and its resistance increases.
b) A diode. When reverse biased it has a very large resistance; when forward biased by 0.7V its
resistance becomes very small.
c) A resistor. Provided its temperature doesn’t change significantly its resistance is constant.
d) A filament lamp. Note that the axes in this graph are the opposite way round from graph (a).
The first three graphs plot current on the vertical axis against voltage on the horizontal – in these
the steeper the line the lower the resistance of the component is.
19. a) X is a variable resistor, Y is a thermistor and Z is a light dependent resistor (LDR).
b) In (a): Moving the slider upwards makes the resistance smaller, so the current increases.
In (b): Making the thermistor colder makes its resistance larger, so the current decreases.
e
d
In (c): Shining more light on the LDR makes its resistance smaller, so the current increases. ui
G
n
o
20. a) V =I × R. si
vi
b) I = V/R. e
R
s
c) R = V/I. c
si
y
h
21. V = 0.02 A × 1800 Ω Ans: 36 V. P
I = 6 V/250 Ω Ans: 0.24 A.
R = 9 V/0.0002 A Ans: 45 000 Ω.
22. a) “Without R” is intended to mean connection of the LED directly across the 9 V battery when the
switch is closed. The result would be a large current passing through the LED destroying it.
b) The voltage across R is (9 – 1.8)V Ans: 7.2 V (Voltage across the LED + voltage
across R = 9 V).
c) R = 7.2 V/0.012 A Ans: 600 Ω.
3
Section C: Waves
1. a) A transverse wave.
b) The tank is level.
c) The corks do not move across the tank with the ripples, but they do move up and down, which
requires energy.
d) Because as the wave front becomes larger and larger, the energy at any point on the wave front
must get smaller.
2. It reminds her of a longitudinal wave. Sound waves are also longitudinal waves.
3. a)
e
d
ui
G
n
o
si
vi
e
R
s
c
si
y
h
P
i) Wavelength, λ, the distance between two successive crests.
ii) Frequency, f, the number of waves produced per second.
iii) Period, T, the time for one complete cycle of the wave.
b) i) Metre (cm or nm also).
ii) Hertz.
iii) Second.
c) Speed = frequency × wavelength.
d) Frequency (Hz) = 1/Period (s) or f = 1/T.
4. a) Upper: 20 kHz lower: 20 Hz.
b) i) Air: λ = 340 m/s ÷ 20 000 Hz Ans: 0.017 m.
λ = 340 m/s ÷ 20 Hz Ans: 17 m.
ii) Water: λ = 1500 m/s ÷ 20 000Hz Ans: 0.075m.
λ = 1500 m/s ÷ 20 Hz Ans: 75m.
1111
5.
This illustrates the answer to (b) (iii).
Increased diffraction means the
waves curve and spread out more.
Less diffraction means that the
spreading and curving is less
noticeable.
a) Diffraction. The left-hand diagram above shows how ripples behave when they pass through a
narrow gap.
b) i) The waves would diffract less because the wavelength would be smaller.
ii) The waves would diffract more because the wave speed is reduced, therefore the
wavelength is greater.
iii) Reducing the gap size will increase the amount of diffraction. See the right-hand diagram
above.
6.
e
d
ui
G
n
o
si 7. a) They are all transverse waves that travel at the speed of light in a vacuum.
vi
e
R b) X-rays have a much higher frequency and much shorter wavelength than infrared. (You can feel
s infrared radiation as heat; X-rays cannot be immediately detected but, in large doses, kill cells
c
si
y and can cause cancer. X-rays can pass right through soft tissue and low density material,
h
P infrared can only pass through certain types of material.)
8. Red, orange, yellow, green, blue, indigo, violet.
9. Microwave: used in microwave ovens; can cause burning in deep tissue indirectly.
Infrared: used for taking night-time images; can cause burns directly.
Visible light: essential for our vision; only hazardous if the light source is very bright, like the Sun
which causes damage to the retina.
Ultraviolet: used influorescent lamps; causes skin burns and cancer.
X-rays: used for imaging bones in the body; can cause cancer.
Gamma rays: used for sterilising medical equipment; can cause cancer, cell death.
10. Light waves are transverse, electromagnetic waves.
EM waves require no material medium in which to travel, the transverse waves on the rope are
mechanical, requiring a medium – in this case the rope. Waves on a rope cannot travel at anything
remotely approaching the speed of light!
11. a) i) B. ii) A. iii) C. iv) D. v) E.
b) The angle of incidence = the angle of reflection.
2
12. a)
b) This is a virtual image, that is it cannot be formed on a screen and is not formed by real rays of
light. The dotted lines show where the reflected light appears to come from.
The image is the right way up (though left and right are reversed) and the same size as the
object. The image appears to be the same distance behind the mirror as the object is in front of
the mirror.
13. a)
e
d
ui
G
n
o
si
vi
e
R
b) n = sin i / sin r. s
c
si
c) The angles of incidence, i, and refraction, r, are labelled on the diagram. Note that these angles hy
P
are measured from the normal – a construction line at right angles to the surface of the water
where the ray enters the water.
d) Shown in yellow on the diagram – the ray is refracted more when the refractive index is greater.
14. 40°.
15. a) The reflection that occurs when a ray of light meets the boundary between the material that it is
travelling in and another (less optically dense) material at an angle which is greater than the
critical angle. At GCSE this will be a reflection when light travelling in a glass block (or
similar) or in water meets the boundary with the air. Total internal reflection does not occur
when light is travelling in air into glass, perspex, water, etc.
b) Use refractive index, n = 1/sin c, rearranged to give sin c = 1/n,so sin c = 1/1.4 = 0.7143
Therefore the critical angle, c = inverse sin (0.7143)
[This maybe expressed as sin-1 0.7143 on some calculators.]
Therefore, c = 45.6°.
16. a)
3
