1. An object of mass m1 has a kinetic energy K1.

Another object of mass m2 has a kinetic energy

K2. If the momentum of both objects is the same, the ratio is equal to
K1
K2

A. .
m2
m1

B. .
m1
m2

C. .
m2
m1

D. .
m1
m2
(1)

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

3
F/N
2

0
0 1 2 3
d / 10–2 m

1
 The work done by the force in moving the cart through a distance of 2 cm is
–2
A. 10 × 10 J.
–2
B. 7 × 10 J.
–2
C. 5 × 10 J.
–2
D. 2.5 × 10 J.
(1)

3. An electric motor is used to raise a weight of 2.0 N. When connected to a 4.0 V supply, the
current in the motor is 1.5 A. Assuming no energy losses, the best estimate for the maximum
steady speed at which the weight can be raised is
–1
A. 0.3 m s .
–1
B. 3.0 m s .
–1
C. 9.0 m s .
–1
D. 12.0 m s .
(1)

4. The diagram below shows the variation with displacement x of the force F acting on an object in
the direction of the displacement.

Q
S
P

0 W V T
0 x1 x2 x

2
 Which area represents the work done by the force when the displacement changes from x1 to x2?

A. QRS

B. WPRT

C. WPQV

D. VQRT
(1)

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

Law of conservation of energy Efficiency

A. E=W+H W
B. E=W+H W
E

C. E+H=W W
H

D. E+H=W W
E–H

(1)

3
 3
6. A machine lifts an object of weight 1.5 × 10 N to a height of 10 m. The machine has an overall
efficiency of 20%. The work done by the machine in raising the object is
3
A. 3.0 × 10 J.
4
B. 1.2 × 10 J.
4
C. 1.8 × 10 J.
4
D. 7.5 × 10 J.
(1)

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

A. 50 MN.

B. 200 kN.

C. 20 kN.

D. 200 N.
(1)

8. A stone of mass m is attached to a string and moves round in a horizontal circle of radius R at
constant speed V. The work done by the pull of the string on the stone in one complete
revolution is

A. zero.
2
B. 2πmV .

C. 2 πmV 2 .
R

D. 2 πmV .
R
(1)

4
9. The diagram below represents energy transfers in an engine.

input energy useful output energy

engine
EIN EOUT

wasted energy
EW

The efficiency of the engine is given by the expression

A. .
EW
E IN

B. .
EW
E OUT

C. .
E OUT
E IN

D. .
E OUT
EW
(1)

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

5
 Which one of the following is the correct expression for the work done by the force?

A. Fd

B. Fd sin θ

C. Fd cos θ

D. Fd tan θ
(1)

11. Which one of the following is a true statement about energy?

A. Energy is destroyed due to frictional forces.

B. Energy is a measure of the ability to do work.

C. More energy is available when there is a larger power.

D. Energy and power both measure the same quantity.

(1)

12. A body of mass m and speed v has kinetic energy EK. A second body of mass m moves at
2
speed 2v. The kinetic energy of this second body is

A. EK .
2

B. EK.

C. 2EK.

D. 4EK.
(1)

6
13. A box of mass m is moved horizontally against a constant frictional force f through a distance s
at constant speed v. The work done on the box is

A. 0.

B. mgs.
2
C. 1 mv .
2

D. fs.
(1)

14. An electric motor, with an input power of 250 W, produces 200 W of mechanical power. The
efficiency of the motor is

A. 20%.

B. 25%.

C. 55%.

D. 80%.
(1)

7
15. A spring is compressed by a force F.

For a compression e, the force F is given by F = ke. When the compression force is removed,
the spring returns to its original length in time t. The best estimate for the power developed by
the spring during its expansion is

A. ke
.
2t

B. ke
.
t

C. ke 2
.
2t

D. ke 3
.
t
(1)

8
16. The output power of an electric motor is determined using the arrangement shown below.

motor

wheel

belt

W1

W2

The belt has weights W1 and W2 attached to its ends. The wheel has circumference S. When the
wheel is rotating at R revolutions per second, the belt is stationary.

Which one of the following is a correct expression for the output power of the motor?

A. W1 × SR

B. W2 × SR

C. (W2 − W1) × SR

D. (W2 + W1) × SR
(1)

9
17. Forces of magnitude F1 and F2 act tangentially on the edge of a wheel of circumference S. The
wheel is made to complete one revolution about its centre, in the direction shown below.

F1 F2

Which one of the following is a correct expression for the work done on the wheel?

A. F1 × S

B. F2 × S

C. (F2 − F1) × S

D. (F2 + F1) × S
(1)

18. A body moving along a straight-line has mass 3.0 kg and kinetic energy 24 J. The motion is then
opposed by a net force of 4.0 N. The body will come to rest after travelling a distance of

A. 2.0 m.

B. 6.0 m.

C. 8.0 m.

D. 12 m.
(1)

10
19. An object of weight 50 N is dragged up an inclined plane at constant speed, through a vertical
height of 12 m. The total work done is 1500 J.

The work done against friction is

A. 2100 J.

B. 1500 J.

C. 900 J.

D. 50 J.
(1)

20. A machine lifts an object of weight W at constant speed through a vertical distance h. The
efficiency of the machine is 25%. The total input energy to the machine is

A. 0.25Wh.

B. 0.75Wh.

C. 2.5Wh.

D. 4.0Wh.
(1)

11
21. The graph below shows the variation with displacement x of the force F acting on an object.
The force F always acts in the same direction as the displacement.

Q
FQ

0 xQ x
0

At point Q, the displacement is xQ and the force is FQ.

Which of the following gives the work done by the force on the body as the displacement
increases from zero to xQ and then returns to zero?

A. Zero

B. 1
2 FQ xQ

C. FQ xQ

D. 2FQ xQ
(1)

12
22. Water flows out from a tank down a pipe, as shown below.

tank

water
water flow
pipe

The pipe is always full of water.

Which of the following gives the change in the kinetic energy and in the gravitational potential
energy of the water as the water flows down the pipe?

kinetic energy gravitational potential energy

A. constant decreases
B. constant increases
C. increases decreases
D. increases increases

(1)

23. Engine X is stated to be more powerful than engine Y.

Which of the following is the correct comparison of the engines?

A. Engine X produces a larger force than engine Y.

B. Engine X produces more useful energy than engine Y.

C. Engine X produces more useful energy per unit time than engine Y.

D. Engine X produces more power for a longer time than engine Y.

(1)

13
24. A force of magnitude F1 accelerates a body of mass m from rest to a speed v. A force of
magnitude F2 accelerates a body of mass 2m from rest to a speed 2v.

The ratio
work done by F2
is
work done by F1

A. 2.

B. 4.

C. 8.

D. 16.
(1)

25. An object of mass m falls from rest in a vacuum. As the object falls it loses an amount E of
gravitational potential energy. The speed of the object is then

A. 2E .
m

B. m .
2E

C. 2E .
m

D. m .
2E
(1)

14
26. This question is about the breaking distance of a car and specific heat capacity.
–1
(a) A car of mass 960 kg is free-wheeling down an incline at a constant speed of 9.0 m s .

speed = 9.0 m s -1

15°

The slope makes an angle of 15° with the horizontal.

3
(i) Deduce that the average resistive force acting on the car is 2.4×10 N.

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

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

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

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

(ii) Calculate the kinetic energy of the car.

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

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

15
(b) The driver now applies the brakes and the car comes to rest in 15 m. Use your answer to
(a)(ii) to calculate the average braking force exerted on the car in coming to rest.

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

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

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

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

(c) The same braking force is applied to each rear wheel of the car. The effective mass of
–1 –1
each brake is 5.2 kg with a specific heat capacity of 900 J kg K . Estimate the rise in
temperature of a brake as the car comes to rest. State one assumption that you make in
your estimation.

estimate:

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

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

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

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

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

assumption:

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

.....................................................................................................................................
(4)
(Total 9 marks)

16
27. This question is about the kinematics and dynamics of circular motion.

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

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

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

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

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

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

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

marble

0.80 m C

0.35 m

ground B

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

Consider the marble when it is at point C.

(b) (i) On the diagram opposite, draw an arrow to show the direction of the resultant force
acting on the marble.
(1)

17
(ii) State the names of the two forces acting on the marble.

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

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

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

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

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

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

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

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

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

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

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

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

...........................................................................................................................
(4)
(Total 12 marks)

18
28. This question is about estimating energy changes for an escalator (moving staircase).

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

30m

40°
A

(a) The escalator is 30 m long and makes an angle of 40° with the horizontal. At full
capacity, 48 people step on at point A and step off at point B every minute.
2
(i) Calculate the potential energy gained by a person of weight 7.0 × 10 N in moving
from A to B.

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

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

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

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

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

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

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

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

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

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

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

19
 .....................................................................................................................................

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

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

.....................................................................................................................................
(3)
(Total 7 marks)

29. Kinematics

(a) State the principle of conservation of energy.

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

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

(b) An aircraft accelerates from rest along a horizontal straight runway and then takes-off.
Discuss how the principle of conservation of energy applies to the energy changes that
take place while the aircraft is accelerating along the runway.

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

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

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

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

20
 3
(c) The mass of the aircraft is 8.0 × 10 kg.

(i) The average resultant force on the aircraft while travelling along the runway is 70
–1
kN. The speed of the aircraft just as it lifts off is 75 m s . Estimate the distance
travelled along the runway.

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

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

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

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

(ii) The aircraft climbs to a height of 1250 m. Calculate the potential energy gained
during the climb.

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

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

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

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

21
When approaching its destination, the pilot puts the aircraft into a holding pattern. This means
–1
the aircraft flies at a constant speed of 90 m s in a horizontal circle of radius 500 m as shown
in the diagram below.

500 m

(d) For the aircraft in the holding pattern,

(i) calculate the magnitude of the resultant force on the aircraft;

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

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

(ii) state the direction of the resultant force.

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

.........................................................................................................................
(1)
(Total 11 marks)

22
30. Block on an inclined plane

A block is held stationary on a frictionless inclined plane by means of a string as shown below.

string

block

inclined plane

(a) (i) On the diagram draw arrows to represent the three forces acting on the block.
(3)

(ii) The angle θ of inclination of the plane is 25°. The block has mass 2.6 kg. Calculate
–2
the force in the string. You may assume that g = 9.8 m s .

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

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

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

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

–1
(b) The string is pulled so that the block is now moving at a constant speed of 0.85 m s up
the inclined plane.

(i) Explain why the magnitude of the force in the string is the same as that found in (a)
(ii).

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

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

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

23
(ii) Calculate the power required to move the block at this speed.

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

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

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

(iii) State the rate of change of the gravitational potential energy of the block. Explain
your answer.

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

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

.........................................................................................................................
(2)
(Total 11 marks)

24
31. Mechanical power

(a) A car drives up a straight incline that is 4.8 km long. The total height of the incline is 0.30
km.

–1
The car moves up the incline at a steady speed of 16 m s . During the climb, the average
2
friction force acting on the car is 5.0 × 10 N. The total weight of the car and the driver is
4
1.2 × 10 N.

(i) Determine the time it takes the car to travel from the bottom to the top of the
incline.

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

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

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

(ii) Detemine the work done against the gravitational force in travelling from the
bottom to the top of the incline.

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

(iii) Using your answers to (a)(i) and (a)(ii), calculate a value for the minimum power
output of the car engine needed to move the car from the bottom to the top of the
incline.

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

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

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

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

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

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

25
(b) From the top of the incline, the road continues downwards in a straight line. At the point
where the road starts to go downwards, the driver of the car in (a), stops the car to look at
the view. In continuing his journey, the driver decides to save fuel. He switches off the
engine and allows the car to move freely down the hill. The car descends a height of 0.30
km in a distance of 6.4 km before levelling out.

2
The average resistive force acting on the car is 5.0 × 10 N.

Estimate

(i) the acceleration of the car down the incline.

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

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

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

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

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

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

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

(ii) the speed of the car at the bottom of the incline.

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

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

(c) In fact, for the last few hundred metres of its journey down the hill, the car travels at
constant speed. State the value of the frictional force acting on the car whilst it is moving
at constant speed.

...................................................................................................................................
(1)
(Total 15 marks)

26