Work, Power & Energy

1. A solid rubber ball has a diameter of 8.0cm. It is released from rest with the top of the ball 80cm
above a horizontal surface. It falls vertically and then bounces back up so that the maximum
height reached by the top of the ball is 45 cm, as shown.

80

60

40

20

If the kinetic energy of the ball is 0.75 J just before it strikes the surface, what is its kinetic energy
just after it leaves the surface?

A 0.36 J B 0.39 J C 0.40 J D 0.42 J

2. A wind turbine has blades that sweep an area of 2000m2. It converts the power available in the
wind to electrical power with an efficiency of 50%.

What is the electrical power generated if the wind speed is 10 m s–1? (The density of air is 1.3 kg
m–3.)

A 130 kW B 650 kW C 1300kW D 2600kW

3. The diagram shows a wheel of circumference 0.30 m. A rope is fastened at one end to a force
meter. The rope passes over the wheel and supports a freely hanging load of 100 N. The wheel
is driven by an electric motor at a constant rate of 50 revolutions per second.

When the wheel is turning at this rate, the force meter reads 20 N.
 What is the output power of the motor?

A 0.3 kW B 1.2 kW C 1.8 kW D 3.8 kW

4. A ball is thrown vertically upwards.

Neglecting air resistance, which statement is correct?

A The kinetic energy of the ball is greatest at the greatest height attained.

B By the principle of conservation of energy, the total energy of the ball is constant throughout its
motion.

C By the principle of conservation of momentum, the momentum of the ball is constant

throughout its motion.
D The potential energy of the ball increases uniformly with time during its ascent.

5. A bow of mass 400 g shoots an arrow of mass 120g vertically upwards. The potential energy
stored in the bow just before release is 80 J. The system has an efficiency of 28%.

What is the height reached by the arrow when air resistance is neglected?

A 4m B 19 m C 187m D 243m

6. A train on a mountain railway is carrying 200 people of average mass 70kg up a slope at an
angle of 30° to the horizontal and at a speed of 6.0 m s–1. The train itself has a mass of 80 000
kg. The percentage of the power from the engine which is used to raise the passengers and the
train is 40 %.

What is the power of the engine?

A 1.1 MW B 2.8 MW C 6.9 MW D 14 MW

7. A ball of mass m is thrown up to height h in air with an initial velocity v, as shown.

v
h

P Q

Air resistance is considered negligible. The acceleration of free fall is g.

What is the total work done by the gravitational force on the ball during its flight from P to Q?

A zero B ½mv 2 C mgh D 2mgh

8. A spring of unextended length 40 mm is suspended from a fixed point. A load of 16 N is applied

to the free end of the spring. This causes the spring to extend so that its final length is five times
its original length. The spring obeys Hooke’s Law.

What is the energy stored in the spring due to this extension?

A 1.3 J B 1.6 J C 2.6 J D 3.2 J

9. The diagram shows an arrangement used to find the output power of an electric motor.

The wheel attached to the motor’s axle has a circumference of 0.5 m and the belt which passes
over it is stationary when the weights have the values shown.

motor

wheel

20 N

50 N

If the wheel is making 20 revolutions per second, what is the output power of the motor?

A 300 W B 500 W C 600 W D 700 W

10. What is the internal energy of a system?

A the amount of heat supplied to the system

B the random energy of the atoms of the system
C the total kinetic energy of the system
D the total potential energy of the system

11. The diagram shows a barrel of weight 1.0 × 103 N on a frictionless slope inclined at 30o to the
horizontal.

A force is applied to the barrel to move it up the slope at constant speed. The force is parallel to
the slope.

What is the work done in moving the barrel a distance of 5.0 m up the slope?

A 2.5 × 103 J B 4.3 × 103 J C 5.0 × 103 J D 1.0 × 104 J

12. A car travelling on a level road at a steady 20 m s–1 against a constant resistive force develops a
power of 40 kW.

What is the magnitude of the resistive force?

A 200 N B 800 N C 2000N D 4000N

13. A turbine at a hydroelectric power station is situated 30 m below the level of the surface of a
large lake. The water passes through the turbine at a rate of 340 m3 per minute.

The overall efficiency of the turbine and generator system is 90%.

What is the output power of the power station? (The density of water is 1000 kgm–3.)

A 0.15 MW B 1.5 MW C 1.7 MW D 90 MW

14. The pump of a water pumping system uses 2.0 kW of electrical power when raising water. The
pumping system lifts 16 kg of water per second through a vertical height of 7.0m.

What is the efficiency of the pumping system?

A 1.8% B 5.6% C 22% D 55%

15. A body travelling with a speed of 20 m s–1 has kinetic energy Ek.

If the speed of the body is increased to 80 m s–1, what is its new kinetic energy?

A 4Ek B 8Ek C 12Ek D 16Ek

16. An electrical generator is started at time zero. The total electrical energy generated during the
first 5 seconds is shown in the graph.

50
energy / J
40

30

20

10

0
0 1 2 3 4 5
time / s

What is the maximum electrical power generated at any instant during these first 5 seconds?

A 10 W B 13 W C 30 W D 50 W

17. What is the average power output of a laser that can deliver 0.20J of energy in 10ns?

A 2 nW B 20 mW C 200 kW D 20 MW
18. A weight W hangs from a trolley that runs along a rail. The trolley moves horizontally through a
distance p and simultaneously raises the weight through a height q.

trolley
rail
Y

r q
X
weight W p

As a result, the weight moves through a distance r from X to Y. It starts and finishes at rest.

How much work is done on the weight during this process?

A Wp B W(p + q) C Wq D Wr

19. The engine of a car exerts a force of 600 N in moving the car 1.0km in 150 seconds.

What is the average output power of the engine?

A 4.0 W B 4.0 kW C 90 kW D 90 MW

20. A mass at point X inside a uniform gravitational field experiences a gravitational force of 0.200N.
It has 1.00 J of gravitational potential energy.

The mass is then moved to point Y.

What is its new gravitational potential energy?

A 0.90 J B 0.94 J C 1.06 J D 1.10 J

21. A small mass is placed at point P on the inside surface of a smooth hemisphere. It is then
released from rest. When it reaches the lowest point T, its speed is 4.0 m s–1.

The diagram (not to scale) shows the speed of the mass at other points Q, R and S as it slides
down. Air resistance is negligible.
 The mass loses potential energy E in falling from P to T.

E
At which point has the mass lost potential energy ?
4

A Q
B R
C S
D none of these

22. An escalator is 60 m long and lifts passengers through a vertical height of 30m, as shown.

30 m
60 m

To drive the escalator against the forces of friction when there are no passengers requires a
power of 2.0 kW.

The escalator is used by passengers of average mass 60 kg and the power to overcome friction
remains constant.

How much power is required to drive the escalator when it is carrying 20 passengers and is
travelling at 0.75 m s–1?

A 4.4 kW B 6.4 kW C 8.8 kW D 10.8 kW

23. An electric motor has an input power Pin, useful output power Pout and efficiency η.

How much power is lost by the motor?

24. A shot-put champion accelerates a 7.0 kg metal ball in a straight line. The ball moves from rest
to a speed of 12 m s–1 in a distance of 1.2m.

What is the average resultant force on the metal ball?

A 70 N B 210 N C 420 N D 840 N

25. A ball drops onto a horizontal surface and bounces elastically.

What happens to the kinetic energy of the ball during the very short time that it is in contact with
the surface?

A Most of the kinetic energy is lost as heat and sound energy.

B The kinetic energy decreases to zero and then returns to its original value.
C The kinetic energy remains constant because it is an elastic collision.
D The kinetic energy remains constant in magnitude but changes direction.

26. A mass attached to the lower end of a spring bounces up and down.

At which points in the path of the mass do the gravitational potential energy of the mass (GPE),
the elastic potential energy in the spring (EPE) and the kinetic energy of the mass (KE) have
their highest values?

GPE EPE KE

A bottom middle top

B bottom top middle
C top bottom middle
D top bottom top
27. A mass m is situated in a uniform gravitational field.

gravitational
P Q field lines
x

When the mass moves through a displacement x, from P to Q, it loses an amount of potential
energy E.

Which row correctly specifies the magnitude and the direction of the acceleration due to gravity
in this field?

magnitude direction
E
A mx →

E
B mx ←

E
C x →

E
D x ←

28. A small electric motor is mounted on a bench, as shown. The motor is connected to a 6.0V
supply and the current in the motor is 0.50 A. The motor is 50% efficient.

What is the time taken to lift a mass of 200 g up through a height of 90cm?

A 0.59 s B 0.85 s C 1.2 s D 2.7 s

29. A projectile is launched at 45° to the horizontal with initial kinetic energy E.

Assuming air resistance to be negligible, what will be the kinetic energy of the projectile when it
reaches its highest point?

A 0.50 E B 0.71 E C 0.87 E D E

30. A constant force F, acting on a car of mass m, moves the car up a slope through a distance s at
constant velocity v. The angle of the slope to the horizontal is α.

Which expression gives the efficiency of the process?

mgs sinα mv mv 2 mg sinα

A Fv B Fs C 2Fs D F

31. The diagram shows a particle X, with kinetic energy Ek, about to collide with a stationary particle
Y. Both particles have the same mass.

X Y

After colliding, X and Y travel onwards together as a single larger particle.

How much kinetic energy is lost in the collision?

A 0 B Ek C Ek D 3Ek
4 2 4

32. A box of weight 30 N is released from rest on a ramp that is at an angle of 30° to the horizontal.
The box slides down the ramp so that it falls through a vertical distance of 8.0 m. A constant
frictional force of 10 N acts on the box while it is moving.

What is the kinetic energy of the box after falling through this distance?

A 80 J B 160 J C 240 J D 400 J

33. A positive charge experiences a force F when placed at point X in a uniform electric field. The

charge is then moved from point X to point Y.

Distances r and s are shown on the diagram.

What is the change in the potential energy of the charge?

A decreases by Fs
B increases by Fs
C decreases by Fr
D increases by Fr

34. A van driver adjusts the force on a van’s brakes so that the van travels at constant speed down a
hill from P to Q.

The magnitude of the change in the van’s kinetic energy is ∆Ek. The magnitude of the change
in its gravitational potential energy is ∆Ep.

Which statement is correct?

A ∆Ek > ∆Ep

B ∆Ek = ∆Ep
C ∆Ep > ∆Ek > 0
D ∆Ek = 0

35. A team of nine dogs can pull a sledge with a combined force of 800N at a speed of 1.5m s–1 for
360 minutes.

What is the average work done by each dog during this time?

A 4.8 × 104 J B 4.3 × 105 J C 2.9 × 106 J D 2.6 × 107 J

36. Which statement is correct?

A A ball lands on the ground and bounces. The kinetic energy changes sign, because the ball
changes direction.

B A car drives up a slope at a steady speed. The power generated by the engine equals the
potential energy gained per unit time.
C An electric heater can be 100% efficient.
D It is impossible for momentum to be conserved in a collision.

37. The diagram shows a pump called a hydraulic ram.

In one such pump the long approach pipe holds 500 kg of water. A valve shuts when the speed
of this water reaches 2.0 m s–1 and the kinetic energy of this water is used to lift a small quantity
of water by a height of 15 m.

The efficiency of the pump is 10%.

Which mass of water could be lifted 15 m?

A 0.15 kg B 0.68 kg C 1.5 kg D 6.8 kg

38. A conveyor belt is driven at velocity v by a motor. Sand drops vertically on to the belt at a rate of
m kg s–1.

What is the additional power needed to keep the conveyor belt moving at a steady speed when
the sand starts to fall on it?

39. A uniform solid block has weight 500N, width 0.4 m and height 0.6 m. The block rests on the
edge of a step of depth 0.8 m, as shown.
 The block is knocked over the edge of the step and rotates through 90° before coming to rest
with the 0.6 m edge horizontal.

What is the change in gravitational potential energy of the block?

A 300 J B 400 J C 450 J D 550 J

40. The diagram shows a hydroelectric power station.

The reservoir is linked to the turbines by a pipe of uniform cross-sectional area.

Water flows from X to Y at constant speed. Which statement about the change of energy of the
water as it moves from X to Y is correct?

A It gains both gravitational potential energy and kinetic energy.

B It loses both elastic potential energy and kinetic energy.
C It loses both elastic potential energy and gravitational potential energy.
D It loses gravitational potential energy and gains elastic potential energy.

41. A fisherman lifts a fish of mass 250 g from rest through a vertical height of 1.8 m. The fish gains
a speed of 1.1 m s–1.

What is the energy gained by the fish?

A 0.15 J B 4.3 J C 4.4 J D 4.6 J

42. Water from a reservoir is fed to the turbine of a hydroelectric system at a rate of 500 kg s–1. The
reservoir is 300 m above the level of the turbine.

The electrical output from the generator driven by the turbine is 200 A at a potential difference of
6000 V.

What is the efficiency of the system?

A 8.0% B 8.2% C 80% D 82%

43. The gas in an engine does work on a piston of cross-sectional area 80cm2. The pressure on the
piston has a constant value of 4.6 × 105 Pa.
25 cm

force of gas
pushing
piston

final position initial position

of piston of piston

How much work is done by the gas on the piston when it moves through a distance of 25 cm?

A 9.2 × 102 J B 9.2 × 104 J C 9.2 × 106 J D 9.2 × 108 J

44. A loaded aeroplane has a total mass of 1.2 × 105 kg while climbing after take-off. It climbs at an
angle of 23° to the horizontal with a speed of 50 m s–1. What is the rate at which it is gaining
potential energy at this time?

A 2.3 × 106 J s–1

B 2.5 × 106 J s–1

C 2.3 × 107 J s–1

D 2.5 × 107 J s–1

45. When a horizontal force F is applied to a frictionless trolley over a distance s, the kinetic energy
of the trolley changes from 4.0 J to 8.0 J.

If a force of 2F is applied to the trolley over a distance of 2s, what will the original kinetic energy
of 4.0 J become?

A 16 J B 20 J C 32 J D 64 J

46. A gas is contained inside a sealed syringe, as shown.

graduated gas syringe

gas

The volume of gas at room temperature is 2.0 cm3.

Atmospheric pressure is 101 kPa.

What is the work done by the gas when it is heated and expands to a volume of 6.0 cm3?

A 404 µJ B 404 mJ C 404 J D 404 kJ

47. A combined heat and power (CHP) station generates electrical power and useful heat. The
diagram shows the input and output for a CHP station.

wasted
power 60
MW

useful heating power

input power
160 MW
from fuel

useful electrical
power 100 MW

What is the efficiency of the CHP station for producing useful power?

A 31% B 38% C 50% D 81%

48. In ‘normal driving conditions’, an electric car has a range of 150 km. This uses all of the 200 MJ
energy stored in its batteries.

With the batteries initially fully charged, the car is driven 100 km in ‘normal driving conditions’.
The batteries are then recharged from a household electrical supply delivering a constant
current of 13.0 A at a potential difference (p.d.) of 230V.

What is the minimum time required to recharge the batteries?

A 0.95 hours
B 12.4 hours
C 18.6 hours
D 27.9 hours

49. A car of mass 500 kg is at rest at point X on a slope, as shown.

The car’s brakes are released and the car rolls down the slope with its engine switched off. At
point Y the car has moved through a vertical height of 30 m and has a speed of 11 m s–1.

mass = 500 kg
speed =0ms–1

30 m
speed = 11 m s–1

Y
 What is the energy dissipated by frictional forces when the car moves from X to Y?

A 3.0 × 104 J B 1.2 × 105 J C 1.5 × 105 J D 1.8 × 105 J

50. In which situation is no work done?

A The air in a bicycle tyre is released because of a puncture.

B A ball is dropped and falls to the ground.
C A box moves at constant speed across a smooth horizontal surface.
D A crane lifts a steel girder at constant speed.

51. An electric railway locomotive has a maximum mechanical output power of 4.0 MW. Electrical
power is delivered at 25 kV from overhead wires. The overall efficiency of the locomotive in
converting electrical power to mechanical power is 80 %.

What is the current from the overhead wires when the locomotive is operating at its maximum
power?

A 130 A B 160 A C 200 A D 250 A

52. A trolley starts from rest at X. It rolls down to Y and eventually comes to rest at Z.

Which row is a possible summary of the energy changes during this process?

X to Y Y to Z

A p.e. → k.e. k.e. → p.e. key

B p.e. → k.e. k.e. → p.e. + heat p.e. = potential energy
C p.e. → k.e. + heat k.e. → p.e. k.e. = kinetic energy
D p.e. → k.e. + heat k.e. → p.e. + heat
53. An object of weight 15.0 N is pulled along a horizontal surface at a constant velocity of 2.00 ms–1.
The force pulling the object is 12.0 N at 30° to the horizontal, as shown.

2.00 m s–1
12.0

N 30

15.0 N

What is the power used to move the object?

A 12.0 W B 20.8 W C 24.0 W D 30.0 W

54. Some gas in a cylinder is supplied with thermal energy q.

The gas does useful work in expanding at constant pressure p from volume V0 to volume VF, as
shown.

volume V0

gas
pressure
p

volume VF

Which expression gives the efficiency of this change?

pV0 VF p(VF −V0 ) (VF − V0 )
A B C D
q V0 q q V0 q
55. The power P required to move an object through a medium at constant speed depends on the
speed v and the resistive force F acting on the object.

The resistive force F also depends on the speed v.

Which row shows a possible relationship between speed v, resistive force F and power P ?

resistive force F power P

A proportional to v constant
B proportional to v proportional to v

C proportional to v 2 proportional to v 2
D proportional to v 2 proportional to v 3

56. Which amount of energy is not 2400 J?

A the decrease in gravitational potential energy of a body of mass 60 kg when it moves vertically
downwards through 40 m near the Earth’s surface
B the energy transferred in 15 s by a machine of power 160 W

C the kinetic energy of a body of mass 12 kg moving at a speed of 20 m s–1

D the work done by a gas expanding against a constant external pressure of 120 kPa when its
volume increases by 0.020 m3

57. A hammer with 10J of kinetic energy hits a nail and pushes it 5.0mm into a plank.

Both the hammer and nail come to rest after the collision.

What is the approximate average force that acts on the nail while it moves through 5.0 mm?

A 0.050 N B 2.0 N C 50 N D 2000N

58. A parachutist is falling at constant (terminal)

velocity. Which statement is not correct?

A Gravitational potential energy is converted into kinetic energy of the air.

B Gravitational potential energy is converted into kinetic energy of the parachutist.
C Gravitational potential energy is converted into thermal energy of the air.
D Gravitational potential energy is converted into thermal energy of the parachutist.

59. A boy on a bicycle starts from rest and rolls down a hill inclined at 30° to the horizontal.

The boy and bicycle have a combined mass of 25 kg.

There is a frictional force of 30 N, which is independent of the velocity of the bicycle.

What is the kinetic energy of the boy and the bicycle after rolling 20 m down the slope?

A 1850 J B 2450J C 3050J D 3640J

60. An escalator in an underground station has 250 people standing on it and is moving with a
velocity of 4.3 m s–1. The average mass of a person is 78kg and the angle of the escalator to the
horizontal is 40°.

What is the minimum power required to lift these people?

A 54 kW B 64 kW C 530 kW D 630 kW

61. An electric motor operating a lift has an output power of 20 kW.

motor

cable
20 m

Lift
And passengers

1500 kg

The lift and passengers have a combined mass of 1500 kg. The motor raises the lift through a
distance of 20 m.

How long does it take?

A 6s B 15 s C 30 s D 60 s

62. A bungee jumper jumps from a platform and is decelerated by an elastic bungee cord, as shown.

platform bungee
jumper

bungee cord bungee

cord

ground ground
not to
before jumping scale during the jump

When the jumper makes the jump, his initial gravitational potential energy is converted into his
kinetic energy and into elastic potential energy in the cord.
 At which part of the jump are all three types of energy non-zero?

A on the platform before the jump

B on the way down before the cord has started to extend
C on the way down as he decelerates
D at the bottom of the jump when he is stationary

63. An object of mass 0.30 kg is thrown vertically upwards from the ground with an initial velocity of
8.0 m s–1. The object reaches a maximum height of 1.9m.

How much work is done against air resistance as the object rises to its maximum height?

A 4.0 J B 5.6 J C 9.6 J D 15 J

64. A racing car has an output power of 300 kW when travelling at a constant speed of 60 m s–1.

What is the total resistive force acting on the car?

A 5 kN B 10 kN C 50 kN D 100 kN

65. The diagram shows the design of a water wheel which drives a generator to produce electrical
power. The flow rate of the water is 200 kg s–1. The generator supplies a current of 32A at a
voltage of 230 V.

water

direction of rotation
8.0 m
generator

Ignoring any changes in kinetic energy of the water, what is the efficiency of the system?

A 14% B 16% C 22% D 47%

Mark Scheme

1 B 2 B 3 B 4 B 5 B 6 C 7 A 8 A 9 A 10 B
11 A 12 C 13 B 14 D 15 D 16 C 17 D 18 C 19 B 20 C
21 B 22 B 23 D 24 C 25 B 26 C 27 A 28 C 29 A 30 D
31 C 32 A 33 A 34 D 35 C 36 C 37 B 38 D 39 C 40 D
41 D 42 D 43 A 44 C 45 B 46 B 47 D 48 B 49 B 50 C
51 C 52 D 53 B 54 C 55 D 56 A 57 D 58 B 59 A 60 C
61 B 62 C 63 A 64 A 65 D