1

1 A student suspends a spring from a clamp stand and measures the length l0 of the spring.

The diagram shows the apparatus.

l0

(not to scale)

The student then suspends loads of different weights from the spring and measures the length of
the spring for each load. He then plots a graph of the length of the spring against weight.
the

I
(You
I
This is the graph that the student plots. New Length can take any point
on

(ineating en
it
N Straight
0.80

length / m

0.60
-> Max weight
before Limit
- - - . . . - -
~ -

I
0.40
I

I
0.20
I
↳
I
Initial
Length 0
I

0 2.0 4.0 6.0 8.0 10.0 12.0

weight / N

(a) Using the graph, determine the initial length l0 of the spring.

0 12 M
l0 = ................................................. [1]
.
 2

(b) State what is meant by the limit of proportionality and, using the graph, determine the weight
of the load that causes this spring just to reach the limit of proportionality.
The being directly
point
where extension stops
limit of proportionality ........................................................................................................
to the
proportional load
...........................................................................................................................................

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

(Blue
10 4N
graph)
mon" +he weight = ............................................................................................................................
.

[2]

(c) Using the graph, determine the spring constant of this spring.
↳(k)
F kn

-
=

=
=

22H/m
En
u =

M =

New Length -

Original length
24 NIM
=0 46-0 12 . .
spring constant = ......................................... [3]
=0 .
34M
[Total: 6]

2 A force is a vector quantity.

State the names of two other quantities that are vectors.

1. ..............................................................................................................................................

2. .............................................................................................................................................. [2]

[Total: 2]

3 A force is a vector quantity.

State two features of a vector quantity.

1. ..............................................................................................................................................

2. .............................................................................................................................................. [2]

[Total: 2]

4 A rock climber, of total mass 62 kg, holds herself in horizontal equilibrium against a vertical cliff.
She pulls on a rope that is fixed at the top of the cliff and presses her feet against the cliff.

The diagram shows her position.

 3

Tr rope

cliff
T anticlockwise

0.90 m
I
Pirot ↑

60° i
rock climber
1.2 m
↓ centre of mass
~-
(not to scale)
clock Wise

(a) The climber’s centre of mass is 0.90 m from the cliff.

Calculate the moment about her feet due to her weight.

Moment =

Fxd
-weight X distance from pirot
=62x10 X 0 .
4 560 NM
=
560 Hm moment = ..................................................... [2]

(b) The line of the rope meets the horizontal line through her centre of mass at a distance of 1.2 m
from the cliff, as shown in the diagram. The rope is at an angle of 60° to the horizontal.

Determine the tension in the rope.

anticluchwise moment
Clockwise moment =

560NM =
TYx1 .
2

560 =
T Si60 x1 2 .

T 540N
20 tension = ...................................................... [3]
=

Sin60X1 1 . [Total: 5]

= 538 86= 540Hm

.
 4

5 Force is a vector.

Draw a circle around two other quantities in the list which are vectors.

acceleration density energy mass

momentum power refractive index

[2]

[Total: 2]

6 The diagram shows an object of mass 2.0 kg on a bench. This object is connected by a cord,
passing over a pulley, to an object of mass 3.0 kg.

card
cord
pulley 2.0 cm 2.0 kg object

F
bench

M 3.0 kg object a

8
The 2.0 kg object is released from rest and accelerates at 4.0 m / s .

Calculate the resultant force acting on the 2.0 kg object.

⑧ 2

F Mx4
=

ex4 8 0N
=
=
.

8 0 N
force = ..............................................
.

[2]

[Total: 2]
 5

7 The diagram shows water in a river moving parallel to the river bank at 4.0 m / s and a canoe
travelling in the river.

river bank

4 0 M/S
.

-
7 canoe travels at 2.5 m / s
38° relative to the water
- > water moving at 4.0 m / s
-
->

river bank

The canoe travels at 2.5 m / s relative to the water and heads at an angle of 38° to the river bank.

Draw a scale diagram to determine the canoe’s resultant velocity and state the scale you used.

Scale :

/M/s =
2CM
I It is not recommended -
because drawing
will he
tool

Speed water = 4 .
0 M1S => 4 0x2
. =
0 .
0 cm

this he
Speec cance =

2 .
5 M1S =) 2 5x2
.
=
5 0 .
ch
* All or must measured

L
be ruler Call
answers ,
created e)
Jenyth or diagonal

=
e
643
.

=
5 .
2 CM 7
Ba U 0 M/S
.
2
R
-

)
= =
2

langgers
?

Panjangnya)
:

in
-
-
&
5 0 cm
.

IMCS = 2 0 Cm
scale ..............................................
.

2 6 M IS
magnitude of resultant velocity ..............................................
.

360
direction of resultant velocity (angle from the river bank) .............................................. [4]

[Total: 4]
 6

8 The diagram shows an object of mass 2.0 kg on a bench. This object is connected by a cord,
passing over a pulley, to an object of mass 3.0 kg.

card
cord
pulley 40. M/S 2.0 cm 2.0 kg object
-
F
U OM/5 I bench
W
↓
,

W = MXG
3.0 kg object
3 x10 = 30

2
The 2.0 kg object is released from rest and accelerates at 4.0 m / s .

Calculate the upward force F exerted by the cord on the 3.0 kg object.

18N
force F = .............................................. [3]

(Fret =

w-F) -> [Total: 3]

9 A battery provides energy to an electric car.

2
The electric car has an acceleration of 2.9 m / s when it moves from rest. The combined mass of
the car and its driver is 1600 kg.

Calculate the force required to produce this acceleration.

Mx 4
F =

= 1600 x 2 4
.

=4640N
4640N
force = .............................................. [2]

[Total: 2]

10 The diagram shows a boat stored in a shed. The boat is suspended from the ceiling of the shed
by two ropes.
 7

&0
1
ceiling

Barah
60° 60°

ropes
154 T T 75N
Atas
1600 ---

nat
-

boat

The tension T in each of the ropes is 75 N.

the boat. State the scale you used.

I
(a) Draw a vector diagram to determine the resultant of the forces exerted by the two ropes on
v 1
jud
:

Scale =3 IOM= / CM
Gabungin
78H= 7 .
5 cm

155
Resultant
608 ↑
~ - -

- - -

75N 13 CR =

130N
↑
T
1 52M.

* Use a ruler and protractor

10N =ICM
scale = ..............................................
130N
magnitude of resultant force = ..............................................
vertically upwards
direction of resultant force = .............................................. [4]
 8
(look at the blue
(ne
(b) Determine the mass of the boat. diagra
W =
my
W
m
=

I
13 my
mass = .............................................. [1]
130N
= =

1344
-
10
/ [Total: 5]
 9

11 The diagram shows two forces acting on an object.

60° 30 N

20 N

Draw a scale diagram to determine the resultant force acting on the object. State the scale you
use.

scale .........................................................................................................................................

magnitude of resultant force = .................................................................................................

direction of resultant relative to the direction of the 20 N force = ............................................. [4]

[Total: 4]
 10

12 A vertical tube contains a liquid. A metal ball is held at rest by a thread just below the surface of
the liquid, as shown in the diagram.

(not to scale)

The diameter of the tube is much greater than the diameter of the ball. The ball is released and it
accelerates downwards uniformly for a short period of time.

The ball reaches terminal velocity.

Describe and explain the motion of the ball from when it is released until it reaches terminal velocity.

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

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

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

.................................................................................................................................................. [3]

[Total: 3]

13 The diagram shows a model car travelling on a flat circular track.

The speed of the car increases and at point P on the diagram the car does not stay on the track.
 11

(a) Suggest, in terms of the force acting on the car, why the car does not stay on the track at point
P.

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

........................................................................................................................................... [1]

(b) On the diagram, draw and label an arrow with the letter S to show the direction of motion of
the car as it leaves the track at point P. [1]

[Total: 2]

14 The diagram shows a uniform rod of wood suspended from a pivot.

(not to scale)

The rod is held stationary by a horizontal force F acting as shown.

The mass of the rod is 0.080 kg.
 12

(a) Calculate the weight W of the rod.

weight = .............................................. [1]

(b) Calculate the moment of W about the pivot.

moment = .............................................. [2]

(c) Calculate the moment of F about the pivot.

moment = .............................................. [1]

(d) Calculate the force F.

force = .............................................. [2]

[Total: 6]

15 Speed is a scalar quantity.

State one other scalar quantity.

.................................................................................................................................................. [1]

[Total: 1]

16 Velocity is a vector quantity.

State one other vector quantity.

.................................................................................................................................................. [1]

[Total: 1]
 13

17 The diagram shows a uniform rod of wood suspended from a pivot.

(not to scale)

The rod is held stationary by a horizontal force F acting as shown.

The angle between the rod and the vertical is increased.

State whether the force F needed to hold the rod stationary must be increased, decreased or stay
the same.
Explain your answer.

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

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

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

.................................................................................................................................................. [2]

[Total: 2]
 14

18 A sky-diver jumps out of a hot-air balloon, which is 4000 m above the ground. At time = 30 s, she
opens her parachute.

The graph is the speed-time graph of her fall.

Describe, in terms of the forces acting on the sky-diver, her motion between leaving the balloon
and opening her parachute.

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

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

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

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

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

.................................................................................................................................................. [4]

[Total: 4]

19 The diagram shows a model car travelling at constant speed on a flat circular track.
 15

The speed of the car is 0.30 m / s. In one complete revolution around the track, the car travels
3.9 m.

(a) Calculate the time taken for the car to complete one revolution around the track.

time = .............................................. [2]

(b) On the diagram, draw and label with the letter F an arrow to show the resultant force acting
on the car. [1]

[Total: 3]

20 The graph is the extension–load graph for a light spring S.

 16

(a) Using information from the graph, determine the spring constant k of spring S.

k = .............................................. [2]

(b) A second spring, identical to spring S, is attached to spring S. The two springs are attached
to a rod, as shown in the diagram. A load of 4.0 N is suspended from the bottom of spring S.
The arrangement is in equilibrium.

(i) State the name of the form of energy stored in the two springs when they are stretched.

................................................................................................................................ [1]
 17

(ii) Determine the extension of the arrangement in the diagram.

extension = .............................................. cm [1]

(iii) The load is carefully increased to 6.0 N in total.

Calculate the distance moved by the load to the new equilibrium position as the load
increases from 4.0 N to 6.0 N.

distance moved = .............................................. [1]

[Total: 5]
2
21 Calculate the force required to give a mass of 71 kg an acceleration of 6.4 m / s .

force = .............................................. [2]

[Total: 2]
 18

22 A chest expander is a piece of equipment used by athletes in a gym. The diagram shows a chest
expander that consists of five identical springs connected in parallel between two handles.

Two athletes are stretching the chest expander by pulling on the two handles in opposite directions.

The springs obey Hooke’s law.

Explain what is meant by this statement.

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

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

.................................................................................................................................................. [2]

[Total: 2]

23 The diagram shows a uniform metre rule PQ in equilibrium.

The distance PQ is 100 cm. The mass of the metre rule is 0.12 kg and its weight is W.

(a) On the diagram, draw and label:

1. an arrow to show the force W acting on PQ at the centre of mass

2. an arrow to show the force R acting on PQ at the pivot.

[2]
 19

(b) By taking moments about the pivot, calculate F.

F = .............................................. [4]

(c) Calculate R.

R = .............................................. [2]

[Total: 8]

24 A chest expander is a piece of equipment used by athletes in a gym. The diagram shows a chest
expander that consists of five identical springs connected in parallel between two handles.

Each spring has an unstretched length of 0.63 m.

Two athletes are stretching the chest expander by pulling on the two handles in opposite directions.

Each athlete pulls the handle towards himself with a force of 1300 N.

(a) State the tension in each spring.

tension = .............................................. [1]

 20

(b) The chest expander stretches and each spring is now 0.94 m long.

Calculate the spring constant k of each spring.

k = .............................................. [2]

[Total: 3]

25 The diagram shows a model fire engine. Its brakes are applied.

0.80 kg of water is emitted in the jet every 6.0 s at a velocity of 0.72 m / s relative to the model.

(a) The brakes of the model are released.

State and explain the direction of the acceleration of the model.

Statement .........................................................................................................................

Explanation .......................................................................................................................

........................................................................................................................................... [2]

(b) In (a) the model contains a water tank, which is initially full.

State and explain any change in the magnitude of the initial acceleration if the brakes are first
released when the tank is nearly empty.

Statement .........................................................................................................................

Explanation .......................................................................................................................

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

........................................................................................................................................... [3]

[Total: 5]
 21

26 The diagram shows an object suspended from two ropes. The weight of the object is 360 N. The
magnitude of the tension in each rope is T.

In the space below, determine the tension T by drawing a vector diagram of the forces acting on
the object.

State the scale you have used.

scale ..............................................

T = .............................................. [5]

[Total: 5]

27 The diagram shows a uniform plank AB of length 2.0 m suspended from two ropes X and Y.
 22

The weight W of the plank is 210 N. The force in rope X is P. The force in rope Y is Q.

(a) State, in terms of P, the moment of force P about B.

........................................................................................................................................... [1]

(b) Calculate:

(i) the moment of W about B

moment = .............................................. [1]

(ii) the force P

force P = .............................................. [2]

(iii) the force Q.

force Q = .............................................. [2]

[Total: 6]
 23

28 Complete the table by writing in the right-hand column the name of the quantity given by the product
in the left-hand column.

product quantity

mass × acceleration

force × time

[2]

[Total: 2]

29 Crystalline rocks are solids made of atoms.

A sculptor makes a statue from a block of crystalline rock using a cutting tool.

Explain why he must apply a large force to the tool to remove a small piece of rock.

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

.................................................................................................................................................. [2]

[Total: 2]
 24

30 The diagram shows a horizontal rod of length 2.4 m and weight 160 N. The weight of the rod acts
at its centre. The rod is suspended by two vertical ropes X and Y. The tension in each rope is 80 N.

The rod is in equilibrium.

Using data from the diagram, explain why.

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

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

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

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

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

.................................................................................................................................................. [4]

[Total: 4]

31 An athlete of mass 64 kg is bouncing up and down on a trampoline.

At one moment, the athlete is stationary on the stretched surface of the trampoline.The figure shows
the athlete at this moment.

springs

The stretched surface of the trampoline begins to contract. The athlete is pushed vertically upwards
and she accelerates. At time t, when her upwards velocity is 6.0 m / s, she loses contact with the
surface.
 25

(a) Calculate her kinetic energy at time t.

kinetic energy = ....................................................... [2]

(b) Calculate the maximum possible distance she can travel upwards after time t.

maximum distance = ....................................................... [3]

(c) In practice, she travels upwards through a slightly smaller distance than the distance calculated
in (b).

Suggest why this is so.

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

........................................................................................................................................... [1]

[Total: 6]
 26

32 The figure shows a uniform, rectangular slab of concrete ABCD standing upright on the ground.
The slab has height 0.60 m, width 0.30 m and mass 18 kg. A force of 40 N acts horizontally to the
left at B.

A B
40 N

0.60 m

D C
0.30 m

The ground is rough so that the slab does not slide.

State and explain what happens to the slab as the horizontal force at B is gradually increased.

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

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

.................................................................................................................................................. [2]

[Total: 2]
 27

33 The figure shows a kitchen cupboard resting on a support and attached to a wall by a screw.

wall screw

cupboard
F

G
0.75 m

support 0.24 m
75 N

The weight of the cupboard and its contents is 75 N. G is the position of the centre of mass of the
cupboard.

The clockwise and anticlockwise moments about point P are equal.

Calculate the force F exerted by the screw.

F = ....................................................... [3]

[Total: 3]
 28

34 A metre rule balances when the 50 cm mark is directly above a pivot.

The figure shows an apple and a 0.40 N weight placed on the rule so that the rule remains balanced
at the 50 cm mark.

0.40 N
apple weight
50 cm
mark

25 cm
45 cm
pivot

The centre of mass of the apple is 25 cm from the pivot and the centre of mass of the weight is
45 cm from the pivot.

The apple is not moved. The weight is removed from the rule and the pivot is moved to the left until
the rule balances as shown in the figure below.

apple
50 cm
mark

pivot

Explain why the arrangement in the figure above balances.

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

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

.................................................................................................................................................. [2]

[Total: 2]

35 The figure shows a heavy ball B of weight W suspended from a fixed beam by two ropes P and Q.
 29

beam

P Q
30 N 30 N

45° 45°
B

P and Q are both at an angle of 45° to the horizontal. The tensions in P and Q are each 30 N.

(a) In the space below, draw a scale diagram to find the resultant of the tensions in P and Q. Use
a scale of 1.0 cm to represent 5.0 N. Label the forces and show their directions with arrows.

resultant = ..................................... [4]

(b) State the direction of the resultant. ................................................................................... [1]

(c) State the magnitude of W.

magnitude of W = .............................................. [1]

 30

[Total: 6]

36 The figure shows a top view of two bar magnets and a vertical rigid conducting rod carrying a
current. The direction of the current in the rod is coming out of the paper.

vertical rod perpendicular

to paper

The rod has a mass of 350 g and the resultant force acting on the rod is 0.21 N. The rod is free to
move.

Calculate the initial acceleration of the rod.

acceleration = ........................... [2]

[Total: 2]

37 The weight of a skydiver is 750 N.

The weight of the skydiver acts downwards, as shown in the diagram.

While the skydiver is falling, another force acts upwards.

The upward force varies as the skydiver falls.

 31

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

weight = 750 N
(not to scale)

The skydiver is accelerating between time = 0 and time = 20 s of the fall.

Between time = 20 s and time = 40 s the skydiver is falling at a constant speed.

(a) On the diagram, write the name of the upward force on the dotted line above the upward force.

[1]

(b) Suggest a value for the upward force on the skydiver at time = 10 s.

.................................................... N [1]

(c) Determine the value of the upward force on the skydiver at time = 30 s.

.................................................... N [1]

[Total: 3]
 32

38 A sailor uses a winch to raise a sail on a boat. Diagram A shows the sailor turning the winch.

sail

winch

Diagram A

The sailor applies a force of 200 N at a distance of 30 cm from the pivot in the winch, as shown in
diagram B.

200 N
winch

pivot
30 cm

Diagram B

Calculate the moment of this force about the pivot.

moment of force = ................................................ N cm [3]

[Total: 3]
 33

39 A rock climber, of total mass 62 kg, holds herself in horizontal equilibrium against a vertical cliff.
She pulls on a rope that is fixed at the top of the cliff and presses her feet against the cliff.

The diagram shows her position.

rope

cliff

0.90 m

60°

rock climber
1.2 m
centre of mass
(not to scale)

State the two conditions needed for equilibrium.

1. ..............................................................................................................................................

2. .............................................................................................................................................. [2]

[Total: 2]
 34

40 The diagram shows the handle used to open and close a cupboard door on an aeroplane.

60 N
pivot
20 cm

(not to scale)

A force of 60 N acts at a distance of 20 cm from the pivot of the handle.

Calculate the moment of the 60 N force about the pivot.

moment = .............................................. N cm [3]

[Total: 3]