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Physics Exam Questions

This document contains a multi-part physics question about various concepts including forces, energy, and motion. It asks the student to: 1) Draw equivalency lines between units like joules, watts, newtons, and kg m/s^2. 2) Calculate the weight, contact area, and pressure exerted by a person standing on a floor. 3) Use given masses and accelerations in a pulley system to calculate time, velocity, and acceleration during an impact. The question covers various physics principles and requires calculations to find quantities like weight, time, velocity, acceleration, stress, and electrical power. It assesses students' understanding of core physics concepts.

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0% found this document useful (0 votes)

433 views146 pages

Physics Exam Questions

Uploaded by

P1ko

We take content rights seriously. If you suspect this is your content, claim it here.

Available Formats

Download as RTF, PDF, TXT or read online on Scribd

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1.

Draw a line from each unit on the left-hand side to the correct equivalent unit on the right-hand
side.
jo u le ( J )

kg m s2

w a tt (W )

N m

n e w to n (N )

J s1

[Total 2 marks]
2.

This question is about estimating the pressure exerted by a person wearing shoes standing on a
floor, see the figure below.

(i)

Estimate the weight in newtons of a person.

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

(ii)

Estimate the total area of contact in square metres between the shoes of this person and
the floor.

area = .................................................... m

2
[1]

(iii)

Hence estimate the pressure in pascals exerted by this person standing on the floor.

pressure = .................................................... Pa
[1]
[Total 3 marks]

Kingsdale Secondary School

The figure below shows two masses A and B tied to the ends of a length of string. The string
passes over a pulley. The mass A is held at rest on the floor.
p u lle y

B
1 .5 0 k g

2 .8 0 m
A
1 .2 0 k g

f lo o r

The mass A is 1.20 kg and the mass B is 1.50 kg.

(a)

Calculate the weight of mass B.

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

(b)

Mass B is initially at rest at a height of 2.80 m above the floor. Mass A is then released.
2
Mass B has a constant downward acceleration of 1.09 m s . Assume that air resistance
and the friction between the pulley and the string are negligible.
(i)

In terms of forces, explain why the acceleration of the mass B is less than the
acceleration of free fall g.
....................................................................................................................................
.............
[1]

(ii)

Calculate the time taken for the mass B to fall 1.40 m.

time = ...................................................... s
[3]
(iii)

Calculate the velocity of mass B after falling 1.40 m.

velocity = ................................................ m s

1
[2]

(iv)

1
Mass B hits the floor at a speed of 2.47 m s . It rebounds with a speed of 1.50 m
1
2
s . The time of contact with the floor is 3.0 10 s. Calculate the magnitude of
the average acceleration of mass B during its impact with the floor.

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acceleration = ................................................ m s

2
[2]
[Total 9 marks]

A lift has a mass of 500 kg. It is designed to carry a maximum of 8 people of total mass 560 kg.
4 2
The lift is supported by a steel cable of cross-sectional area 3.8 10 m . When the lift is at
ground floor level the cable is at its maximum length of 140 m, as shown in the figure below.
1
The mass per unit length of the cable is 3.0 kg m .

s te e l c a b le
140 m
lift s h a ft

g r o u n d f lo o r

(a)

Show that the mass of the 140 m long steel cable is 420 kg.

[1]
(b)

(i)

The lift with its 8 passengers is stationary at the ground floor level. The initial
2
upward acceleration of the lift and the cable is 1.8 m s . Show that the maximum
4
tension in the cable at point P is 1.7 10 N.

[4]
(ii)

Calculate the maximum stress in the cable.

stress = .................................................... Pa

Kingsdale Secondary School

[2]
[Total 7 marks]

An electron in a particle accelerator experiences a constant force. According to one student, the
acceleration of the electron should remain constant because the ratio of force to mass does not
change. In reality, experiments show that the acceleration of the electron decreases as its
velocity increases. Describe what can be deduced from such experiments about the nature of
accelerated electrons.
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
[Total 2 marks]

The figure below shows the velocity vector for a particle moving at an angle of 31 to the
horizontal.

8 .0 m s -1

(i)

On the figure above, show the horizontal (x-direction) and vertical (y-direction)
components of the velocity.
[2]

(ii)

Calculate the horizontal (x-direction) component of the velocity.

velocity = ................................................ m s

1
[1]
[Total 3 marks]

State the principle of conservation of energy.

Kingsdale Secondary School

[Total 1 mark]
8.

Describe one example where elastic potential energy is stored.

.........................................................................................................................................................
...............
[Total 1 mark]

Kingsdale Secondary School

The figure below shows a ship S being pulled by two tug-boats.

N o t t o s c a le
1 .5 0 k N
S

c a b le

d ir e c tio n o f
tra v e l o f
s h ip S

tu g -b o a t

The ship is travelling at a constant velocity. The tensions in the cables and the angles made by
these cables to the direction in which the ship travels are shown in the figure above.
(i)

Draw a vector triangle and determine the resultant force provided by the two cables.

resultant force = .................................................... kN

[3]
(ii)

State the value of the drag force acting on the ship S. Explain your answer.

(a)

Define a vector quantity.

(b)

Circle all the vector quantities in the list below.

acceleration

speed

time

displacement

weight
[1]
[Total 2 marks]

11.

In what form is energy stored when a metal wire is extended by a force?

Kingsdale Secondary School

.........................................................................................................................................................
...............
[Total 1 mark]

Kingsdale Secondary School

12.

The figure below shows a simple pendulum with a metal ball attached to the end of a string.

s tr in g

m
P
h
v

When the ball is released from P, it describes a circular path. The ball has a maximum speed v
at the bottom of its swing. The vertical distance between P and bottom of the swing is h. The
mass of the ball is m.
(i)

Write the equations for the change in gravitational potential energy, E , of the ball as it
p
drops through the height h and for the kinetic energy, E , of the ball at the bottom of its
k
swing when travelling at speed v.
E =
p
E =
k
[1]

(ii)

Use the principle of conservation of energy to derive an equation for the speed v. Assume
that there are no energy losses due to air resistance.

[2]
[Total 3 marks]
13.

The figure below shows a length of tape under tension.

p u ll
(i)

p u ll

Explain why the tape is most likely to break at point B.

(ii)

Explain what is meant by the statement: the tape has gone beyond its elastic limit.
...............................................................................................................................................

Kingsdale Secondary School

14.

Some countries in the world have frequent thunderstorms. A group of scientists plan to use the
energy from the falling rain to generate electricity. A typical thunderstorm deposits rain to a
2
7 2
depth of 1.2 10 m over a surface area of 2.0 10 m during a time of 900 s. The rain falls
3
3
3
from an average height of 2.5 10 m. The density of rainwater is 1.0 10 kg m . About
30% of the gravitational potential energy of the rain can be converted into electrical energy at
the ground.
(i)

8
Show that the total mass of water deposited in 900 s is 2.4 10 kg.

[2]
(ii)

Hence show that the average electrical power available from this thunderstorm is about 2
GW.

[3]
(iii)

Suggest one problem with this scheme of energy production.

15.

The force against length graph for a spring is shown in Fig. 1.

6
fo rc e /N
5
4
3
2
1
0

10
le n g th /1 0

12
m

Fig. 1
(a)

Explain why the graph does not pass through the origin.
...............................................................................................................................................
..............
...............................................................................................................................................
..............

Kingsdale Secondary School

[1]

Kingsdale Secondary School

(b)

State what feature of the graph shows that the spring obeys Hookes law.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]

(c)

The gradient of the graph is equal to the force constant k of the spring. Determine the
force constant of the spring.

force constant = ............................................... N m

1
[2]

(d)

Calculate the work done on the spring when its length is increased from 2.0 10
2
8.0 10 m.

m to

work done = ...................................................... J

[2]
(e)

One end of the spring is fixed and a mass is hung vertically from the other end. The mass
is pulled down and then released. The mass oscillates up and down. Fig. 2 shows the
displacement s against time t graph for the mass.

0 .4
s /m
0 .2
0

2 .0

4 .0

-0 .2
-0 .4
Fig. 2
Explain how you can use Fig. 2 to determine the maximum speed of the mass. You are
not expected to do the calculations.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
Kingsdale Secondary School

...............................................................................................................................................
..............
[2]
[Total 8 marks]
16.

The figure below shows one possible method for determining the Young modulus of a metal in
the form of a wire.
w o o d b lo c k s

c la m p

m e ta l w ir e

m a rk e r
p u lle y

BEN C H TO P

m asses

Describe how you can use this apparatus to determine the Young modulus of the metal. The
sections below should be helpful when writing your answers.
The measurements to be taken:
In your answer, you should use appropriate technical terms, spelled correctly.
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
The equipment used to take the measurements:
In your answer, you should use appropriate technical terms, spelled correctly.

Kingsdale Secondary School

17.

The figure below shows graphs of velocity v against time t for two cars A and B travelling along
a straight level road in the same direction.
26
v / m s1

22
20
18
16
14

12
10
8
6

t / s

At time t = 0, both cars are side-by-side.

(i)

Describe the motion of car A from t = 0 to t = 10 s.

(ii)

Calculate the distance travelled by car A in the first 4.0 s.

distance = ..................................................... m
[2]
(iii)

Use the figure above to find

the time at which both cars have the same velocity

time = ...................................................... s
[1]

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the time t at which car A overtakes car B.

t = ...................................................... s
[2]
[Total 7 marks]
18.

The figure below shows the path of water from a hose pipe.
h o s e p ip e
7 .0 m s -1
P
p a th o f
w a te r

1 .3 m

g ro u n d
3 .6 m

The end of the horizontal hose pipe is at a height of 1.3 m from the ground. The initial horizontal
1
velocity of the water is 7.0 m s . The horizontal distance from the end of the hose pipe to the
point where the water hits the ground is 3.6 m. You may assume that air resistance has
negligible effect on the motion of the water jet.
(a)

On the figure above, draw an arrow to show the direction of the acceleration of the water
at point P.
(Mark this arrow A).
[1]

(b)

Describe the energy conversion that takes place as the water travels from the end of the
hose pipe to the ground.
In your answer, you should use appropriate technical terms, spelled correctly.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[2]

(c)

Explain why the horizontal component of the velocity remains constant at 7.0 m s

...............................................................................................................................................
..............
Kingsdale Secondary School

...............................................................................................................................................
..............
[1]
(d)

Show that the water takes about 0.5 s to travel from the end of the pipe to the ground.

[1]
(e)

Show that the speed of the water when it hits the ground is 8.6 m s

[3]
[Total 8 marks]
19.

Define the newton.

20.

State why the equation F = ma cannot be applied to particles travelling at speeds very close to
the speed of light.
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
[Total 1 mark]

21.

The figure below shows the horizontal forces acting on a car of mass 900 kg when it is travelling
at a particular velocity on a level road.

The total forward force between the tyres and the road is 200 N and the air resistance (drag) is
80 N.
(i)

Calculate the acceleration of the car.

Kingsdale Secondary School

acceleration = ................................................ m s

2
[2]

(ii)

Explain why we cannot use the equation v = u + at to predict the velocity of the car at a
later time even when the forward force is constant.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]
[Total 3 marks]

22.

Define torque of a couple.

Kingsdale Secondary School

23.
T

The figure below shows a person being lifted vertically upwards by a rope.

r o p e

The mass of the person is 72 kg. The upward vertical acceleration of the person is 1.4 m s
Calculate the tension T in the rope.

T = ...................................................... N
[Total 3 marks]
24.

(a)

Explain why moment of a force and torque of a couple have the same unit N m.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]

(b)

The figure below shows an irregular shaped metal plate of constant thickness that can
swing freely about point P.
P
0 .3 0 m

0 .4 0 m
6 .0 N

(i)

The weight of the plate is 6.0 N. With the plate in the position as shown in the
figure, calculate the clockwise moment of the weight of the plate about an axis
through point P.

moment = .................................................. N m
[1]
(ii)

Explain why the moment of the weight reduces to zero when the plate reaches the
bottom of the swing.
....................................................................................................................................
.............
....................................................................................................................................
.............

Kingsdale Secondary School

[1]
[Total 3 marks]

25.

Describe an experiment to determine the centre of gravity of the metal plate shown in the figure
below.
P
0 .3 0 m

0 .4 0 m
6 .0 N

The figure below shows a section of the human forearm in equilibrium.

b ic e p
F
o b je c t

e lb o w

3 .5 c m
14 cm
32 cm

18 N
60 N

The weight of the object in the hand is 60 N. The centre of gravity of this object is
32 cm from the elbow. The bicep provides an upward force of magnitude F. The distance
between the line of action of this force and the elbow is 3.5 cm. The weight of the forearm is 18
N. The distance between the centre of gravity of the forearm and the elbow is 14 cm.
By taking moments about the elbow, determine the magnitude of the force F provided by the
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bicep.

F = ...................................................... N
[Total 3 marks]

Kingsdale Secondary School

27.

The figure below shows a 20 N force acting at an angle of 38 to the horizontal.

20 N

h o r iz o n ta l

Determine the horizontal and vertical components of this force.

horizontal component = ...................................................... N

[1]
vertical component = ...................................................... N
[1]
[Total 2 marks]
28.

The figure below shows a metal block held in equilibrium by two wires.
38

w ir e

20 N

w ir e

20 N

b lo c k

not to scale

The tension in each wire is 20 N.

(i)

Show that the weight W of the metal block is about 25 N.

[2]
(ii)

The metal block has a volume of 2.9 10

3
m . Calculate the density of the metal.

density = .............................................. kg m

3
[3]
[Total 5 marks]

Kingsdale Secondary School

29.

Define stopping distance of a car.

30.

State two factors that affect the braking distance of a car. Describe how each factor affects the
braking distance.
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
[Total 4 marks]

31.

Describe how Global Positioning System (GPS) is used to locate the position of a car on the
Earths surface.
In your answer, you should use appropriate technical terms, spelled correctly.
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
[Total 4 marks]

34.

State a similarity and a difference between distance and displacement.

(i)
similarity: ..............................................................................................................................
..............
...............................................................................................................................................

Kingsdale Secondary School

..............
[1]
(ii)
difference: .............................................................................................................................
.............
...............................................................................................................................................
..............
[1]
[Total 2 marks]

Kingsdale Secondary School

32.

A metal wire of length 1.2 m is clamped vertically. A weight is hung from the lower end of the
7
wire. The extension of the wire is 0.35 mm. The cross-sectional area of the wire is 1.4 10
2
11
m and the Young modulus of the metal is 1.9 10 Pa.
Calculate
(i)

the strain of the wire

strain = .........................................................
[1]
(ii)

the tension in the wire.

tension = ...................................................... N
[2]
[Total 3 marks]
33.

There is great excitement at the moment about structures known as carbon nanotubes (CNTs).
CNTs are cylindrical tubes of carbon atoms. These cylindrical tubes have diameter of a few
nanometres and can be several millimetres in length. Carbon nanotubes are one of the
strongest and stiffest materials known. Recently a carbon nanotube was tested to have an
ultimate tensile strength of about 60 GPa. In comparison, high-carbon steel has an ultimate
tensile strength of about 1.2 GPa. Under excessive tensile stress, the carbon nanotubes
undergo plastic deformation. This deformation begins at a strain of about 5%. Carbon
nanotubes have a low density for a solid. Carbon nanotubes have recently been used in high
quality racing bicycles.
(i)

The diameter of CNTs is a few nanometres. What is one nanometre in metres?

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

Explain what is meant by plastic deformation.

(ii)

How many times stronger are CNTs than high-carbon steel?

Kingsdale Secondary School

[1]
(iii)

State two advantages of making a bicycle frame using CNT technology rather than highcarbon steel.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[2]
[Total 5 marks]

Kingsdale Secondary School

34.

The figure below shows two airports A and C.

5
An aircraft flies due north from A for a distance of 360 km (3.6 10 m) to point B. Its average
1
speed between A and B is 170 m s . At B the aircraft is forced to change course and flies due
east for a distance of 100 km to arrive at C.
(i)

Calculate the time of the journey from A to B.

time = ....................................................... s
[1]
(ii)

Draw a labelled displacement vector triangle below. Use it to determine the magnitude of
the displacement in km of the aircraft at C from A.

displacement = ....................................................km
[3]
[Total 4 marks]
35.

State a similarity and a difference between distance and displacement.

Kingsdale Secondary School

(ii)
difference: .............................................................................................................................
.............
...............................................................................................................................................
..............
[1]
[Total 2 marks]
36.

The figure below shows a graph of velocity against time for an object travelling in a straight line.
v e lo c ity
v

tim e

The object has a constant acceleration a. In a time t its velocity increases from u to v.
(a)

Describe how the graph of the figure above can be used to determine
(i)

the acceleration a of the object

In your answer, you should use appropriate technical terms, spelled correctly.

the displacement s of the object.

(b)

Use the graph of the figure above to show that the displacement s of the object is given
by the equation:
1

2
s = ut + 2 at

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[2]
(c)

In order to estimate the acceleration g of free fall, a student drops a large stone from a tall
building. The height of the building is known to be 32 m. Using a stopwatch, the time
taken for the stone to fall to the ground is 2.8 s.
(i)

Use this information to determine the acceleration of free fall.

acceleration = .................................................m s

2
[2]

(ii)

One possible reason why your answer to (c)(i) is smaller than the accepted value
of 9.81 ms2 is the reaction time of the student. State another reason why the
answer is smaller than 9.81 m s2.
....................................................................................................................................
.............
....................................................................................................................................
.............
[1]
[Total 7 marks]

37.

A skydiver jumps from a stationary hot-air balloon several kilometres above the ground.
(a)

In terms of acceleration and forces, explain the motion of the skydiver immediately after
jumping
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
at a time before terminal velocity is
reached .....................................................................................
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............

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at terminal
velocity. .......................................................................................................................
.....
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[6]
(b)

In the final stage of the fall, the skydiver is falling through air at a constant speed. The
skydivers kinetic energy does not change even though there is a decrease in the
gravitational potential energy. State what happens to this loss of gravitational potential
energy.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]

(c)

The figure below shows a sketch graph of the variation of the velocity v of a skydiver with
time t.
v / m s -1

0
0

t / s

Suggest the changes to the graph of the figure above, if any, for a more massive
(heavier) skydiver of the same shape.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[2]
[Total 9 marks]

Kingsdale Secondary School

38.

Define work done by a force.

39.

A car has a total mass of 810 kg. Its speed changes from zero to 30 m s
(i)

in a time of 12 s.

Calculate the change in the kinetic energy of the car.

change in kinetic energy = ....................................................... J

[2]
(ii)

Calculate the average power generated by the car engine. Assume that the power
generated by the engine of the car is entirely used in increasing the kinetic energy of the
car.

power = ......................................................W
[1]
(iii)

The actual efficiency of the car is 25%. The car takes 18 kg of petrol to fill its tank. The
1
energy provided per kilogram of petrol is 46 MJ kg . The drag force acting on the car at
1
a constant speed of 30 m s is 500 N.
1

Calculate the work done against the drag force per second.

work done per second = .................................................. J s

1
[1]

Calculate the total distance the car can travel on a full tank of petrol when travelling
1
at a constant speed of 30 m s .

distance = ......................................................m

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[3]
[Total 7 marks]
40.

Define power.
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
[Total 1 mark]

41.

Explain why the efficiency of a mechanical device can never be 100%.

42.

The figure below shows a wooden block motionless on an inclined ramp.

b lo c k

ra m p

The angle between the ramp and the horizontal is .

(i)

The weight W of the block is already shown on the figure. Complete the diagram by
showing the normal contact (reaction) force N and the frictional force F acting on the
block
[2]

(ii)

Write an equation to show how F is related to W and .

43.

Circle from the list below a material that is ductile.

jelly

copper

ceramic

glass
[Total 1 mark]

44.

On the axes of the figure below, sketch a stress against strain graph for a typical ductile

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material.
s tre s s

0
0

s tr a in

[Total 2 marks]

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45.

The figure below shows a kitchen cupboard securely mounted to a vertical wall. The cupboard
rests on a support at A.
s c re w
w a ll

F
c u p b o a rd
75 cm

A
su p p o rt

12 cm
200 N

The total weight of the cupboard and its contents is 200 N. The line of action of its weight is at a
distance of 12 cm from A. The screw securing the cupboard to the wall is at a vertical distance
of 75 cm from A.
(i)

State the principle of moments.

In your answer, you should use appropriate technical terms, spelled correctly.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[2]

(ii)

The direction of the force F provided by the screw on the cupboard is horizontal as shown
in the figure above. Take moments about A. Determine the value of F.

F = ...................................................... N
[2]
(iii)

The cross-sectional area under the head of the screw in contact with the cupboard is 6.0
5 2
10 m . Calculate the pressure on the cupboard under the screw head.

pressure = .....................................................Pa
[2]
(iv)

State and explain how your answer to (iii) would change, if at all, if the same screw was
secured much closer to A.

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In February 1999 NASA launched its Stardust spacecraft on a mission to collect dust particles
from the comet Tempel 1. After a journey of 5.0 10 12 m that took 6.9 years, Stardust returned
to Earth with samples of the dust particles embedded in a special low-density gel. When a dust
particle hits the gel, it buries itself in the gel creating a cone-shaped track as shown in the figure
below. The length of the track is typically 200 times the diameter of the dust particle.

n o t t o s c a le
c o n e -s h a p e d tra c k

gel

(a)

Calculate the average speed in m s

of Stardust during its voyage.

speed = .................................................m s

1
[2]

(b)

Calculate the average stopping force produced by the gel for a dust particle of diameter
0.70 mm and mass 4.0 106 kg travelling at a velocity of 6.1 103 m s1 relative to
Stardust.

force = .......................................................N
[3]
[Total 5 marks]
47.

Define ultimate tensile strength of a material.

Kingsdale Secondary School

[Total 1 mark]
48.

State Hookes law.

Kingsdale Secondary School

49.

The figure below shows a mechanism for firing a table tennis ball vertically into the air.

b a ll

p la tfo r m
s p r in g

s p r in g f ix e d
to p la te

p la te
p u ll a n d r e le a s e
to fir e b a ll

The spring has a force constant of 75 N m

spring.
(i)

1
. The ball is placed on the platform at the top of the

The spring is compressed by 0.085 m by pulling the platform. Calculate the force exerted
by the compressed spring on the ball immediately after the spring is released. Assume
both the spring and the platform have negligible mass.

force = .......................................................N
[2]
(ii)

The mass of the ball is 2.5 10

kg. Calculate the initial acceleration of the ball.

acceleration = .................................................m s

2
[1]

(iii)

Calculate the maximum height that could be gained by the ball. Assume all the elastic
potential energy of the spring is converted into gravitational potential energy of the ball.

Kingsdale Secondary School

height = ......................................................m
[3]
[Total 6 marks]
50.

(i)

Define speed of an object. Explain how you would determine the constant speed of a
conker at the end of length of string being whirled in a horizontal circle.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[3]

(ii)

Define velocity of an object.

(iii)

By reference to speed and velocity, explain the difference between a scalar quantity and
a vector quantity, using as an example the terms speed and velocity.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[2]
[Total 6 marks]

51.

Explain the following terms in relation to motion of a road vehicle.

Kingsdale Secondary School

(i)

braking distance
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]

(ii)

thinking distance
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]
[Total 2 marks]

Kingsdale Secondary School

52.

Fig. 1 shows a long rope that is tied at one end to a high support. A girl swings forwards and
backwards across a pool using the other end of the rope.
2 .5
x /m
2 .0

s u p p o rt

1 .5

ro p e

1 .0

0 .5

1 .0

2 .0

3 .0

4 .0

5 .0

6 .0
t/s

Fig. 1

Fig. 2

Fig.2 shows the variation with time t of the displacement x of the girl from A to B and back to
A.
(i)

State what the gradient of the graph represents and explain why the graph shows both
positive and negative gradients.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[2]

(ii)

Mark on Fig.2 with a cross a position where the speed of the girl is zero (label this Z).
[1]

(iii)

1. Explain how you can determine using Figure 2 that the maximum speed of the girl is
1
about 1.4ms .
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
2. Estimate the uncertainty in the value of the maximum speed obtained in this way.

Kingsdale Secondary School

(a)

Define acceleration.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]

(b)

An aircraft of total mass 1.5 105 kg accelerates, at maximum thrust from the engines,
from rest along a runway for 25 s reaching the required take-off speed of 65 m s 1.
Assume that the acceleration of the aircraft is constant. Calculate
(i)

the net force acting on the aircraft to produce this acceleration

force = ..................................... N
[3]
(ii)

the distance travelled by the aircraft in this time.

distance = ................................. m
[2]
(c)

At a particular airport, the length of the runway for the same take-off speed is less than
your answer in (b)(iii). State and explain what change could be made to the aircraft to
enable it to reach the required take-off speed on this shorter runway.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............

Kingsdale Secondary School

[2]
[Total 8 marks]
54.

(a)

Define
(i)

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

(ii)

a joule.
....................................................................................................................................
.............
....................................................................................................................................
.............
[1]

(b)

A force F acts on an object. The object moves at an angle to this force. Explain why the
work done W by the force in the direction of motion of the object is not just
W = Fx
but is equal to
W = Fx cos
In your answer, you should use appropriate technical terms, spelled correctly.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]
[Total 3 marks]

55.

The diagram below shows a part of a fairground ride with a carriage on rails.

3 .9 m

30o

The carriage of mass 500 kg is travelling towards a slope inclined at 30 to the horizontal. The
carriage has a kinetic energy of 25 kJ at the bottom of the slope. The carriage comes to rest
after travelling up the slope to a vertical height of 3.9 m.
Kingsdale Secondary School

(i)

Show that the gravitational potential energy gained by the carriage is 19 kJ.
[2]

(ii)

Calculate the total work done against the resistive forces as the carriage moves up the
slope.

work done = ........................................... kJ

[1]
(iii)

Calculate the magnitude of the resistive force acting against the carriage as it moves up
the slope.

resistive force = ....................................... N

[2]
[Total 5 marks]

56.

(a)

State Hookes law.

(b)

The diagram below shows the variation of the applied force F with the extension
x for a particular spring.

Kingsdale Secondary School

10
fo rc e / N

100

e x te n s io n /
x (x 1 0 3 m )

(i)

Use the diagram to determine the force constant of the spring.

force constant = ..................................N m

1
[2]

(ii)

Determine the elastic potential energy stored in the spring when a force of 20 N is
applied.

energy stored = ......................................... J

[2]
(iii)

State one assumption made in your calculation of the energy in (ii).

(iv)

The energy stored in the spring is used to propel a metal ball of mass m
horizontally. There is 100% transfer of energy from the spring to the ball. Show how
the speed v of the metal ball is proportional to the extension x of the spring. Find

Kingsdale Secondary School

the constant of proportionality.

[2]
[Total 9 marks]
57.

A car of mass 800 kg is travelling at a speed of 20 m s

(i)

1
. Calculate

the kinetic energy of the car

kinetic energy = ......................................... J

[2]
(ii)

the deceleration of the car when the braking distance is 24 m.

deceleration = ...................................... m s

2
[2]
[Total 4 marks]

58.

Describe in terms of the forces acting on the driver how wearing a seat belt and having an
airbag in a car can help to protect the driver from injury in a head on collision.
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
[Total 4 marks]

Kingsdale Secondary School

59.

The wearing of seat belts became law in the UK in January 1983. The diagram below shows the
annual deaths due to road accidents in Scotland since 1950.

Num ber of
d e a th s

9
8
7
6
5
4
3
2
1

0
0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
0
0
0
1950

1960

1970

1980

1990

2000

Year

The percentage of car drivers wearing seat belts in 1983 and at present has remained static at
93 %. On average, cars are travelling faster now than in 1983. Suggest another factor which
may have been responsible for the decrease in deaths.
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
.........................................................................................................................................................
...............
[Total 1 mark]
60.

(a)

Define the Young modulus of a material.

(b)

Explain why the quantity strain has no units.

62.

(a)

Explain what is meant by a brittle material.

Kingsdale Secondary School

(b)

Define the ultimate tensile strength of a material. Suggest why an engineer designing a
suspension bridge should know the value of this quantity for all his materials.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[2]
[Total 3 marks]

Kingsdale Secondary School

62.

(a)

State two conditions that are necessary for an object to be in equilibrium.

(b)

The diagram below shows a computer resting on a tabletop that is hinged at

point A.
0 .8 0 m
c o m p u te r

ta b le to p
A

B
F
0 .2 5 m
200 N

The tabletop has a mass of 5.0 kg and its centre of gravity is 0.40 m from the axis of the
hinge A. The computer has a weight of 200 N acting through a point 0.25 m from the
hinge A. The tabletop is supported to maintain it in a horizontal position by a force F
acting vertically at B. The distance AB is 0.80 m.

Calculate the force F applied at B that is required to maintain the tabletop in equilibrium.

force F = .................................................. N
[3]
(c)

Explain why the force F and the 200 N force shown in the figure above cannot be a
couple.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]
[Total 6 marks]

Kingsdale Secondary School

63.

The figure below shows the path of a ball thrown from A and passing through positions B, C and
D.

The ball is thrown from A with a velocity v. A vector arrow on the figure. represents the
magnitude and direction of the velocity of the ball at A.
(a)

On the figure draw arrows to represent the horizontal and vertical components of the
velocity of the ball at A.
[1]

(b)

State how the components of the velocity of the ball at B, C and D compare with the
components at A. Assume air resistance is negligible.
(i)

The vertical component at B

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

The horizontal component at B

............................................................
[1]
(ii)

The vertical component at C

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

The horizontal component at C

...............................................................
[1]
(iii)

The vertical component at D

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

The horizontal component at D

............................................................
[1]
(c)

Explain the answers you have given for the components of the velocity of the ball at
positions B, C and D.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............

Kingsdale Secondary School

[4]
[Total 8 marks]

Kingsdale Secondary School

64.

Explain, with reference to a car, the quantities

(i)

braking force
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]

(ii)

braking distance.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]
[Total 2 marks]

65.

A car of mass 1380 kg, travelling at 31.1 m s

48.2 m. Calculate
(i)

, is brought to rest by the brakes in

the initial kinetic energy of the car

kinetic energy = .............................. J

[3]
(ii)

the average deceleration of the car

deceleration = .............................. m s

2
[2]

(iii)

the average braking force.

braking force = .............................. N

[2]
[Total 7 marks]
66.

Define the quantities

(i)

work

..............
[1]
(ii)

power.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]
[Total 2 marks]

67.

The figure below shows a crane that is used to move heavy objects.

The motor M in the crane lifts a total mass of 1500 kg through a height of 25 m at a constant
velocity of 1.6 m s1.
Calculate
(i)

the tension in the lifting cable

tension = .............................. N
[2]
(ii)

the time taken for the mass to be raised through the height of 25 m

time = .............................. s
[1]
(iii)

the rate of gain of potential energy of the mass

rate of gain of potential energy = .............................. J s

Kingsdale Secondary School

[3]
(iv)

the minimum output power of the motor used to raise the mass.

power = .............................. W
[1]
[Total 7 marks]
68.

Define
(i)

the moment of a force

(ii)

the torque of a couple.

Kingsdale Secondary School

69.

The figure below shows a uniform rectangular beam supported by two straps. The beam is in
equilibrium.
0 .5 0 m
X

Y
1 .0 m

w e ig h t = 3 6 0 0 N
4 .0 m

The weight of the beam is 3600 N and its length is 4.0 m. The strap A is positioned 0.50 m from
one end of the beam and the strap B is positioned 1.0 m from the other end.
(i)

Use the principle of moments to show that the upward force X at strap A is 1440 N.

[2]
2

Hence determine the force Y at the strap B.

force = .............................. N
[2]
(ii)

Discuss whether the forces X and Y provide a couple.

(iii)

The area of strap A in contact with the underside of the beam is 2.3 10
the average pressure exerted on the beam by strap A.

Kingsdale Secondary School

2
m . Calculate

pressure = .............................. unit ..............................

[3]
[Total 9 marks]

70.

The results given in the table below are obtained in an experiment to determine the Young
modulus of a metal in the form of a wire. The wire is loaded in steps of 5.0 N up to 25.0 N and
then unloaded.

(i)

unloading

load / N

extension / mm

extension /mm

0.0

0.00

5.0

0.24

10.0

0.47

0.48

15.0

0.71

20.0

0.96

0.95

25.0

1.20

Using the results in the table and without plotting a graph, state and explain whether the
deformation of the wire
1

is plastic or elastic

obeys Hookes law.

Explain how the extension and length of the wire may be determined experimentally.
...............................................................................................................................................

Kingsdale Secondary School

(iii)

7 2
The wire tested is 1.72 m long and has a cross-sectional area of 1.80 10 m . Use the
extension value given in the table for a load of 25.0 N to calculate the Young modulus of
the metal of the wire.

Young modulus = .............................. Pa

[3]
[Total 8 marks]

72.

In this question, two marks are available for the quality of written communication.
Below is a graph of the displacement against time for the motion of a radio-controlled model car.

30
d is p la c e m e n t
/m
20

20
tim e /s

Use the graph to describe and explain, without calculation

(a)

how the velocity changes from time t = 0 to time t = 20 s

Kingsdale Secondary School

...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[5]
(b)

how the acceleration changes from time t = 0 to time t = 20 s.

Kingsdale Secondary School

Define the quantities

(i)

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

(ii)

strain.
...............................................................................................................................................
..............
[1]
[Total 2 marks]

76.

Explain the term centre of gravity of an object.

Kingsdale Secondary School

73.

A champion BMX cyclist wishes to become a professional and seeks help from an A-level
Physics student in creating an act. The student suggests two stunts; one involving a horizontal
take-off on to a sloping ramp and the other involving a loop-the-loop manoeuvre.
(a)

The student begins by finding out the maximum speed the cyclist can produce on level
ground. Two flags are positioned 240 m apart on a flat road. The cyclist is told to
accelerate to the first flag and to pedal as hard as he can until the second flag is passed.
This is shown in Fig. 1

240 m
Fig. 1
The student gets the cyclist to repeat the test three times and records the following
results:
14.8 s

17.2 s

15.6 s
1
.

Show that the mean speed the cyclist can maintain over the 240 m is about 15 m s

[2]
(b)

The student designs the stunt shown in Fig. 2 where the cyclist must take off at 15 m s
from a horizontal launch pad and land smoothly just at the edge of a sloping ramp.

1 5 m s1
la u n c h p a d
y
x
ra m p

g ro u n d

Fig. 2
The student reasons that in order to land smoothly, the direction of the velocity of the
cyclist on reaching the edge of the ramp must be at the same 45 angle as the ramp
itself.
Ignore air resistance in all calculations.
(i)

Explain why the vertical component of velocity on reaching the ramp must be 15 m

Kingsdale Secondary School

The student calculated the vertical fall y to the ramp to be about 11 m. Show how
he arrived at this result.

[2]
(iii)

The student calculated the horizontal jump x to the ramp to be about 23 m. Show
how he arrived at this result.

[1]
(iv)

The total mass of the cyclist and bike is 86 kg. Show that the kinetic energy of the
cyclist on reaching the ramp is about 19 kJ.

[3]
[Total 9 marks]

75.

The figure below shows a vacuum cleaner of weight W being pushed with a force P. The force
P acts at 30 to the horizontal.

dust
c o lle c to r

P = 2 4 .0 N

30
flo o r
W = 6 5 .0 N

Kingsdale Secondary School

The weight W is 65.0 N and the magnitude of force P is 24.0 N.

(a)

(i)

Calculate

the horizontal component of the force P

horizontal component = ................................N

the vertical component of the force P.

vertical component = ................................N

[3]
(ii)

Show that the total downward vertical force is 77.0 N.

[1]
(iii)

Hence determine the magnitude of the resultant of the forces W and P.

resultant force = ................................N

[2]
(iv)

The vacuum cleaner is not switched on and is pushed in such a way that it travels
at a constant velocity to the left. There are other forces acting on the vacuum
cleaner. State and explain the magnitude of the resultant of these other forces.
....................................................................................................................................
.............
....................................................................................................................................
.............
[2]

(b)

(i)

3 2
The total area of the vacuum cleaner in contact with the floor is 4.2 10 m .
Calculate the pressure exerted on the floor by the total downward vertical force.

pressure = ................................Pa
[2]
(ii)

State and explain what happens to this pressure if the handle is lifted so that its
angle with the horizontal direction is more than 30. The force P and the total area
in contact with the floor remain constant.
....................................................................................................................................
.............
....................................................................................................................................

Kingsdale Secondary School

.............
....................................................................................................................................
.............
[1]
[Total 11 marks]
88.

(i)

Define velocity.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]

(ii)

Kingsdale Secondary School

74.

The web site www.britishwindenergy.co.uk gives the following information for wind turbines.
rotor diameters

30 m 65 m
1
1
4 m s 25 m s
1
15 m s wind speed
15 50 revolutions per minute

useable wind speeds

maximum power output occurs at
rate of turning of rotor
maximum theoretical efficiency at wind speed 15 m s
average power output

60%
30% of theoretical maximum

data sourced from British Wind Energy Association, www.bwea.com

In this question about wind turbines you will need to use some of this information.
(a)

Consider the mass of the cylinder of air which travels past the blades of a turbine in one
1
second. Take the wind speed to be 15 m s and the diameter of the rotor to be 40 m.
See the figure below.
The density of air is 1.3 kg m

3
.

40 m

15 m

Calculate
(i)

the volume of the cylinder of air passing the rotor in one second

volume = ................................................... m

3
[2]

(ii)

the mass of air passing the rotor in one second

mass = ..................................................... kg
[1]
(iii)

the kinetic energy of this mass of air

Kingsdale Secondary School

kinetic energy = ...................................................... J

[2]
(iv)

the maximum theoretical power output.

power = ..................................................... W
[2]
(b)

(i)

Calculate the average power output from the wind turbine in (a).

average power output = ..................................................... W

[1]
(ii)

How many of these turbines would be required to replace one 1000 MW

conventional power station?

number = .........................................................
[1]
(c)

(i)

Wind power is often said to be free. Give another reason why wind power is
desirable.
....................................................................................................................................
.............
....................................................................................................................................
.............
[1]

(ii)

Explain why wind power cannot be relied upon.

(d)

Suggest reasons why

(i)

maximum useable wind speed does not produce maximum power

Kingsdale Secondary School

turbines have to be stopped when the wind speed is too high

(iii)

government policy is to aim for only 10% of national electrical supply to be provided
by wind power.
....................................................................................................................................
.............
....................................................................................................................................
.............
....................................................................................................................................
.............
....................................................................................................................................
.............
[3]
[Total 18 marks]

Kingsdale Secondary School

77.

The figure below shows a lawn mower which is carried by two people.
B

9 0 .0 c m

2 0 .0 c m

g ra s s
c u ttin g s
c o lle c to r

la w n m o w e r
A

w e ig h t 3 5 0 N

(i)

g ro u n d

The two people apply forces A and B at each end of the lawn mower. The weight of the
lawn mower is 350 N.
1

Explain why the weight of the lawn mower does not act in the middle of the lawn
mower, that is 55 cm from each end.
....................................................................................................................................
.............
....................................................................................................................................
.............
[1]

Use the principle of moments to show that the force B is 64 N.

[2]
3

Determine the force A.

A = ................................N
[1]

(ii)

State and explain what happens to the forces A and B if the person that applies force B
moves his hands along the handle towards the middle of the lawn mower.
...............................................................................................................................................
..............

Kingsdale Secondary School

The figure below shows the path of a tennis ball after passing over the net.

te n n is
b a ll

1 .2 0 m

net

lin e
11 .9 m
As the ball passes over the net it is travelling horizontally at a height of 1.20 m. The ball strikes
the ground on a line 11.9 m from the net.
(a)

Assume that there is no air resistance acting on the ball.

(i)

Show that the time taken for the ball to reach the line after passing over the net is
0.495s.

[3]
(ii)

At the instant the ball strikes the line calculate

the horizontal component of its velocity

horizontal component = ................................m s

1
[2]

the vertical component of its velocity.

vertical component = ................................m s

Kingsdale Secondary School

[2]
(b)

2
The mass of the tennis ball is 6.00 10 kg. Calculate the loss in gravitational potential
energy of the ball from the time it passes over the net until it hits the line.

loss in potential energy = ................................ J

[2]
[Total 9 marks]
79.

Define the Young modulus.

80.

The figure below shows a violin.

w ir e s u p p o r t
G
w ooden pegs

Two of the wires used on the violin, labelled A and G are made of steel. The two wires are both
500 mm long between the pegs and support. The 500 mm length of wire labelled G has a mass
3
3
3
of 2.0 10
kg. The density of steel is 7.8 10 kg m .
(i)

Show that the cross-sectional area of wire G is 5.1 10

2
m .

[2]
Kingsdale Secondary School

(ii)

The wires are put under tension by turning the wooden pegs shown in the figure. The
11
Young modulus of steel is 2.0 10 Pa.
4
Calculate the tension required in wire G to produce an extension of 4.0 10 m.

tension = ................................N
[3]
(iii)

Wire A has a diameter that is half that of wire G. Determine the tension required for wire
4
A to produce an extension of 16 10 m.

tension = ................................N
[1]
(iv)

State the law that has been assumed in the calculations in (ii) and (iii).
...............................................................................................................................................
..............
[1]
[Total 7 marks]

Kingsdale Secondary School

81.

The figure below shows a vehicle that is used for carrying people off-road.

An off-road vehicle is designed so that it can be driven on rough and uneven ground. The mass
of the vehicle and occupants is 3000 kg.
(a)

Explain how the tyres are designed to reduce the pressure of the vehicle on the surface
over which it is travelling.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[1]

(b)

The braking distance of the vehicle when travelling on a normal road at 26 m s

is 52

Calculate
(i)

the kinetic energy of the vehicle and occupants before braking occurs

kinetic energy = ................................ J

[3]
(ii)

the average deceleration of the vehicle when braking

deceleration = .................. unit.................

[2]
(iii)

the average braking force acting during the deceleration.

braking force = ................................ N

Kingsdale Secondary School

[2]
[Total 8 marks]

Kingsdale Secondary School

82.

(i)

State and explain how two different road conditions affect the braking distance of a car.
1. ..........................................................................................................................................
...............
...............................................................................................................................................
..............
2. ..........................................................................................................................................
...............
...............................................................................................................................................
..............
[2]

(ii)

The braking distance for a small car is shorter than for the off-road vehicle described
above when they are tested travelling on the same road surface at the same speed.
Discuss one difference between the small car and the off-road vehicle that could explain
this.
...............................................................................................................................................
..............
...............................................................................................................................................
..............
...............................................................................................................................................
..............
[2]
[Total 4 marks]

83.

In this question, two marks are available for the quality of written communication.
A skydiver jumps from an aircraft that is flying horizontally at a height of 5000 m with a constant
speed.
(a)

Describe and explain the motion of the skydiver as she descends towards the ground
from the moment she jumps until she opens her parachute. In your description of her
motion use the terms speed, acceleration and force.
...............................................................................................................................................
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Kingsdale Secondary School

(b)

In some competitions the skydiver attempts to travel at the highest possible speed over a
vertical distance of 1000 m. Discuss and explain the different methods that could be used
by the skydiver to achieve the highest possible speed.
...............................................................................................................................................
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[4]
Quality of Written Communication [2]
[Total 12 marks]

85.

(i)

Sketch on the figure below a graph to show the relationship between the tensile force F
applied to a copper wire and the extension x produced. Continue the graph to the
breaking point of the wire.

x
[1]
(ii)

Label your graph to show the regions where the wire is undergoing
1

elastic deformation

plastic deformation.
[2]
[Total 3 marks]

Kingsdale Secondary School

84.

The diagram below shows a simple model to demonstrate the forces exerted by back muscles
for a person bending over at an angle of 30 to the horizontal.

40 c
m

head

25 c
m

back
X
15
30

F
p iv o t

The back muscles may be considered to act as a single force F through a point on the back
situated 25 cm from the pivot and making a constant angle of 15 with the back. The weight W
of the upper body acts through a point X, situated a distance of 40 cm from the pivot.
(a)

Calculate for an upper body weight W of 450 N, the size of the force F needed by the
back muscles to keep the back at an angle of
(i)

30 to the horizontal

F = ..................................................... N
[4]
(ii)

70 to the horizontal.

F = ..................................................... N
[1]
(b)

Explain including reference to your answers to (a), the body position which should be
adopted when lifting heavy loads from the ground.
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Kingsdale Secondary School

During a bungee jump, the jumper falls a distance of 150 m before stopping for the first time.
The jumpers mass is 80 kg.
(a)

Assuming that frictional losses are negligible, complete the following table to show the
energy changes between the top and the bottom of the fall. One value has been given.
energy at the top / J

gravitational potential energy

of jumper

energy at the bottom / J

kinetic energy of jumper

elastic potential energy of
elastic rope
[3]
(b)

The elastic rope being used has an unstretched length of 50 m and spring constant of 24
1
N m . Calculate the tension in the rope when the jumper stops at the bottom.

tension = .................................................... N
[1]
(c)

For a rope obeying Hookes law show that the elastic potential energy stored in the rope
is given by

1
2
E = 2 kx
where k is the elastic spring constant and x is the extension.

[2]
(d)

(i)

Another jumper has a mass of 100 kg. For this bungee jump a rope of unstretched

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1
length 45 m and a spring constant 26.7 N m is used. Show that this data is valid
for the same 150 m fall before stopping for the first time.

[2]

(ii)

In fact, the rope used by the second jumper is a shorter length of the rope used by
the first jumper. Explain why the spring constant for the shorter rope is larger.
....................................................................................................................................
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[1]
[Total 9 marks]

87.

The figure below illustrates a conveyor belt for transporting young children up a snow-covered
bank so that they can ski back down.

24 m

4 .0 m
c o n v e y o r b e lt

A child of mass 20 kg travels up the conveyor belt at a constant speed. The distance travelled
up the slope is 24 m and the time taken is 55 s. The vertical height climbed in this time is 4.0 m.
(a)

For the child on the conveyor belt, calculate

(i)

her speed

speed = ............................ m s

1
[2]

(ii)

her kinetic energy

Kingsdale Secondary School

kinetic energy = ............................ J

[2]
(iii)

the increase in her potential energy for the complete journey up the slope.

potential energy = ............................ J

[2]
(b)

(i)

The conveyor belt is designed to take a maximum of 15 children at any one time.
Calculate the power needed to lift 15 children of average mass 20 kg through a
height of 4.0m in 55s

power = ............................ W
[2]
(ii)

The belt is driven by an electric motor. State two reasons why the motor needs a
greater output power than that calculated in (b)(i).
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[2]
[Total 10 marks]

Kingsdale Secondary School

89.

Fig. 1 shows a ruler clamped at one end. A mass M is attached to the other end of the ruler and
is then made to oscillate up and down.

m ass M
A

Fig. 1
Fig. 2 shows the variation with time t of the velocity v of the mass M as it oscillates from A to B
and back to A.
4 .0
v / c m s 1
2 .0

0 .1 0
A

0 .2 0

0 .3 0

0 .4 0
B

0 .5 0

0 .6 0

t/s

0 .7 0

0 .8 0
A

2 .0

4 .0

Fig. 2
(i)

For the graph shown in Fig. 2, state what is represented by

the area between the graph and the time axis

.........................................................................................................................
[1]
2

the gradient of the graph at a particular time.

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

(ii)

Use Fig. 2 to determine the distance travelled by the mass M from time t = 0 to
time t = 0.20 s.

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distance = ............................ cm
[2]

(iii)

Use Fig. 2 to describe how the acceleration of the mass M varies as the mass moves
from A to B.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[2]

(iv)

Use Fig. 2 to calculate the average acceleration of the mass M between

t = 0.25 s and t = 0.55 s.
acceleration = ............................ cm s

2
[2]
[Total 8 marks]

90.

(i)

Define pressure.
.........................................................................................................................
.........................................................................................................................
[1]

Kingsdale Secondary School

(ii)

Define moment of a force.

91.

(a)

The figure below shows a device used for compressing materials.

380 m m

120 m m
H

le v e r a r m

p lu n g e r

F = 20N

c r u s h e d m a te r ia l
c r o s s - s e c tio n a l
a re a
4 .0 x 1 0 3 m 2

c y lin d e r

A vertical force F of 20 N is applied at one end of a lever system. The lever is pivoted
about a hinge H. The plunger compresses the material in the cylinder.

(i)

Two forces acting on the lever arm are its weight and the force F. On the figure
above, draw and label two other forces acting on the lever arm.
[2]

(ii)

By taking moments about H, show that the force acting on the plunger is
83 N. The weight of the lever arm may be neglected.
[2]

Kingsdale Secondary School

(b)

(i)

3 2
The cross-sectional area of the plunger is 4.0 10 m . Calculate the pressure
exerted by the plunger on the material in the cylinder.
pressure = ............................ Pa
[2]

(ii)

State two methods of increasing the pressure exerted by the plunger.

92.

The figure below shows three ropes attached to a ring R. Three cylinders x, y and z, are
supported by these ropes from two pulleys.

p u lle y
p u lle y

X
Z = 360N
90
x

z
53

Y = 450N

360N

(a)

(i)

3 3
The cylinder z has a weight of 360N and a volume of 4.7 10 m .

Kingsdale Secondary School

Calculate
1

the mass of the cylinder z

mass = ............................ kg
[1]

the density of the cylinder z.

density = ............................ unit ........
[3]

(ii)

The ring R is in equilibrium. Use a labelled vector triangle to determine the tension
X.

tension X = ............................ N
[4]

(b)

(i)

Explain why the sum of the magnitudes of the tensions in any two ropes does not
equal the tension in the other rope.
................................................................................................................
................................................................................................................
................................................................................................................
[2]

(ii)

Show that the sum of the vertical components of the tensions X and Z is equal to
the tension Y.

[2]
[Total 12 marks]

Kingsdale Secondary School

93.

Below is a stress-strain graph up to the point of fracture for a rod of cast iron.

200
s tre s s / 1 0

fra c tu re
p o in t

Pa
160

120

0 .2

0 .4

0 .6

0 .8

1 .0

1 .2
s t r a in / 1 0

(a)

1 .4
3

4 2
The rod of cast iron has a cross-sectional area of 1.5 10 m .
Calculate

(i)

the force applied to the rod at the point of fracture

force = ............................ N
[2]
(ii)

the Young modulus of cast iron.

Young modulus ............................. = N m

2
[3]

Kingsdale Secondary School

(b)

Use the graph or otherwise to describe the stress-strain behaviour of cast iron up to and
including the fracture point.
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[3]
[Total 8 marks]

94.

In this question, two marks are available for the quality of written communication.
State and explain two factors that affect the braking distance of a car.
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[Total 4 marks]

Kingsdale Secondary School

95.

State and explain two safety features in a car that are designed to protect the driver during a
collision.
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[4]
Quality of Written Communication [2]
[Total 6 marks]

96.

State what is meant by speed and velocity

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97.

State what is meant by elastic and plastic

98.

(i)

Below is a list of five quantities. Underline those that are scalar quantities.
acceleration

energy

force

power

speed
[1]

(ii)

What is a vector quantity?

Kingsdale Secondary School

99.

The figure below shows the direction of two forces of 16 N and 12 N acting at an angle of 50 to
each other.

16N
50

12N
Using the figure, draw a vector diagram to determine the magnitude of the resultant of the two
forces.
magnitude of resultant force ................................ N
[Total 4 marks]

Kingsdale Secondary School

100. The figure below shows a gannet hovering above a water surface.

gannet

30m

w a te r

6 .0 m
fis h

The gannet is 30 m above the water. It folds in its wings and falls vertically in order to catch a
fish that is 6.0 m below the surface.
Ignore air resistance.
(a)

Calculate

(i)

the speed that the bird enters the water

Speed = .............................. m s

1
[2]

(ii)

the time taken for the bird to fall to the water surface.
time = ........................................ s
[2]

Kingsdale Secondary School

(b)

The bird does not continue to travel at the acceleration of free fall when it enters the
water. State and explain the effect of the forces acting on the bird as it falls
(i)

through the air

(ii)

through the water.

Kingsdale Secondary School

101. The figure below shows the path of a ball that has been thrown by a girl towards a vertical wall.

w a ll
p a th o f b a ll

3 .3 m
10m s

4 .9 m
2
1
The girl throws the ball, of mass 5.0 10
kg, with a velocity of 10 m s
at 53 to the
horizontal. In this question, ignore air resistance.
(a)

(i)

Show that the horizontal component of the velocity is 6.0 m s

.
[1]

(ii)

In moving to the wall, the ball travels 4.9 m horizontally and 3.3 m vertically.
Calculate the time taken for the ball to travel from the girls hand to the wall.

time = ........................................ s
[2]
(iii)

Calculate the gain in potential energy of the ball from leaving the girls hand to
when it hits the wall.
Gain in potential energy = ........................................ J
[3]

Kingsdale Secondary School

(b)

The ball is moving horizontally at 6.0 m s

when it hits the wall. The ball is in contact

1
with the wall for 0.16 s and rebounds horizontally at 4.0 m s .
Calculate, for the time that the ball is in contact with the wall
(i)

the change in velocity of the ball

change in velocity = ..........................m s

1
[1]

(ii)

the horizontal acceleration of the ball (assumed to be constant)

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

(iii)

the horizontal force acting on the ball

magnitude of the force = ...................................N

direction of the force .....................................
[3]

(iv)

the loss in kinetic energy of the ball when rebounding from the wall.

loss in kinetic energy = ................................. J

[3]
[Total 15 marks]

Kingsdale Secondary School

102. The figure below shows two forces, each of magnitude 1200 N, acting on the edge of a disc of
radius 0.20 m.

1200 N

0 .2 0 m

r o t a t in g d is c
1200 N

(a)

(i)

Define the torque of a couple.

(ii)

Calculate the torque produced by these forces.

torque = ............................N m
[2]

Kingsdale Secondary School

(b)

This torque is needed to overcome friction and keep the disc rotating at a constant rate.
(i)

Show that the work done by the two forces when the disc rotates one complete
revolution is about 3000 J.

[2]
(ii)

Calculate the power required to keep the disc rotating at 40 revolutions

per second.

power = ............................... W
[2]
[Total 7 marks]

103. Fig. 1 shows part of the force-extension graph for a spring. The spring obeys Hookes law for
forces up to 5.0 N.

3 .0
fo rc e / N
2 .0

1 .0

15
e x te n s io n / m m

Fig. 1
(a)

Calculate the extension produced by a force of 5.0 N.

extension = ............................. mm
[2]

Kingsdale Secondary School

(b)

Fig. 2 shows a second identical spring that has been put in parallel with the first spring. A
force of 5.0 N is applied to this combination of springs.

f ix e d s u p p o r t

5 .0 N

F ig . 2
For the arrangement shown in Fig. 2, calculate

(i)

the extension of each spring

extension = ............................. mm
[2]
(ii)

the total strain energy stored in the springs.

strain energy = ................................. J

[2]

(c)

11
The Young modulus of the wire used in the springs is 2.0 10 Pa. Each
spring is made from a straight wire of length 0.40 m and cross-sectional
7 2
area 2.0 10 m . Calculate the extension produced when a force of 5.0 N is applied to
this straight wire.

extension = ................................m
[3]

Kingsdale Secondary School

(d)

Describe and explain, without further calculations, the difference in the strain energies
stored in the straight wire and in the spring when a 5.0 N force is applied to each.
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[2]
[Total 11 marks]

Kingsdale Secondary School

104. State the factors that control the braking distance of a car. For each factor, explain the effect on
the braking distance.
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[5]
Quality of Written Communication [2]
[Total 7 marks]

Kingsdale Secondary School

105. The following is a list of scalar and vector quantities.

acceleration, density, displacement, energy, power, speed, time, weight.
In the blank spaces provided in the table below, list the quantities as either scalars or vectors.
scalar

vector

[Total 4 marks]

Kingsdale Secondary School

106. The figure below shows the path of a ball as it is passed between three players. Player A
passes a ball to player B. When player B receives the ball, she immediately passes the ball to
player C. The distances for each pass are shown on the figure.

p la y e r C
10m
p la y e r B

14m
12m

p la y e r A
The ball takes 2.4 s to travel from player A to player C.

(i)

Calculate, for the total journey of the ball

the average speed of the ball

average velocity = ............................ m s

1
[2]

the magnitude of the average velocity of the ball.

average speed = ............................ m s

1
[2]

Kingsdale Secondary School

(ii)

Explain why the values for the average speed and average velocity are different.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
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[2]
[Total 6 marks]

107. State the two conditions necessary for a system to be in equilibrium.

108. The figure below shows a painters plank resting on two supports A and B.

0 .5 5 m
0 .1 5 m

0 .1 5 m

B
1 .0 0 m

1 .0 0 m

80N

650N

The plank is uniform, has a weight 80 N and length 2.00 m. A painter of weight 650 N stands
0.55m from one end.

(i)

Show that the force acting on the plank at the support B is approximately 540 N by taking
moments of all the forces about the support at A.
[3]

Kingsdale Secondary School

100

(ii)

Calculate the force acting on the plank at support A.

force at A = ....................................... N
[2]

(iii)

Describe and explain what happens to the forces on the plank at A and B if the painter
moves towards the support at A. Quantitative values are not required.
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[3]
[Total 8 marks]

109. (a)

Define acceleration.
.........................................................................................................................
.........................................................................................................................
[1]

Kingsdale Secondary School

101

(b)

The following figure shows the velocity v of a ball against time t as it falls vertically from
rest to when it hits the ground at A.

v /m s 1
6 .0

5 .0
4 .0
3 .0
2 .0
1 .0
0

0 .2

0 .4

0 .6

0 .8

1 .0

1 .2

t/s

1 .0
2 .0
3 .0
4 .0
5 .0
6 .0

Use the figure to show the distance that the ball falls is approximately 1.6m.
[2]

Kingsdale Secondary School

102

(c)

The ball is in contact with the ground for 20 ms and then rebounds vertically with an initial
1
upwards velocity of 5.1m s .
(i)

Calculate the acceleration of the ball as it rebounds while in contact with the
ground.
acceleration = ............................ m s

2
[3]

(ii)

Sketch on the figure above the velocity against time graph for the ball after it has
bounced off the ground until it reaches its maximum height.
[3]

(d)

The ball has a mass of 0.025 kg and rebounds to a height of 1.3 m.

(i)

Calculate the loss in the potential energy of the ball from the initial point of release
at 1.6 m to when it reaches 1.3 m.
loss in potential energy ............................ unit .................
[3]

(ii)

Explain the loss in the potential energy.

110. (i)

Define work done.

Kingsdale Secondary School

103

(ii)

Define the watt.

111. The braking distance x of a car depends on its initial kinetic energy E . The figure below shows
k
the relationship between E and x.
k

400

300
E k/kJ
200

100

(i)

x /m

Calculate the gradient of the graph.

gradient = ............................ J m

1
[2]

(ii)

Explain why the gradient of the graph is equal to the braking force acting on the car.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[2]

(iii)

The car has a mass of 800 kg. Calculate the deceleration of the car when braking.

Kingsdale Secondary School

104

deceleration = ............................ m s

2
[2]

(iv)

The car is loaded so that the total mass is 1200 kg. Describe and explain how the braking
distance changes for the same braking force and initial velocity.
.........................................................................................................................
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.........................................................................................................................
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[2]
[Total 8 marks]

112. (i)

Define strain.
.........................................................................................................................
.........................................................................................................................

(ii)

Define stress.
.........................................................................................................................
.........................................................................................................................
[Total 2 marks]

Kingsdale Secondary School

105

113. In this question, two marks are available for the quality of written communication.
Describe an experiment to determine the Young modulus of a metal in the form of a wire.
Your description should include

a labelled diagram of the apparatus

the measurements to be taken

an explanation of how the equipment is used to obtain the measurements

an explanation of how the measurements would be used to determine the Young

modulus.

diagram of the apparatus

[3]

measurements to be taken
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..................................................................................................................................
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[2]

Kingsdale Secondary School

106

how the equipment is used to obtain the measurements

determination of the Young modulus

Kingsdale Secondary School

107

114. The four sketch graphs below, plotted against time, show changes which occur in a small
fraction of a second and which result in almost vertical lines on the graphs. Three of these
sketch graphs are possible for ordinary objects and one of them is impossible.

d is p la c e m e n t

v e lo c ity

tim e

a c c e le r a t io n

tim e

r e s u lta n t
fo rc e

(a)

tim e

Identify the impossible graph, giving a reason for your selection.

Impossible graph is ..............................
[1]
Reason why it is impossible ...........................................................................
........................................................................................................................
[1]

Kingsdale Secondary School

108

(b)

Describe three everyday situations, one for each, which illustrate how the remaining
graphs can arise. State to which graph each description refers.
graph letter ...............
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
[3]

graph letter ...............

Kingsdale Secondary School

109

graph letter ...............

115. (i)

Define velocity.
.........................................................................................................................
.........................................................................................................................
[1]

(ii)

Define acceleration.
.........................................................................................................................
.........................................................................................................................
[1]
[Total 2 marks]

Kingsdale Secondary School

110

116. During some car races, the cars often stop to refuel and change tyres.
(i)

Suggest why a car stops to refuel rather than taking enough fuel at the start in order to
complete the race without stopping.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[2]

(ii)

Explain why the smooth tyres used in dry conditions are changed to those with a tread in
wet weather.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[2]
[Total 4 marks]

117. (a)

The figure below illustrates a racetrack near a refuelling station.

ra c e tra c k
ro u te o f c a r B

X
ro u

rA
to
1 2 re fu
0 m e lli
ng

160 m

s ta t
io n

out
re tu rn r

r
e to

tra
ace

ca
fo r

r e fu e llin g
s t a tio n

Kingsdale Secondary School

111

1
The cars A and B are in a race and both have a speed of 80 m s . Car A has a lead
over car B of 17.0 s at X when A leaves the racetrack to refuel. Car A travels 120 m from
X to the refuelling station.
Calculate the following values for car A, from the point where it leaves the racetrack until
it comes to rest at the refuelling station. Assume the deceleration is constant.
(i)

the average deceleration

deceleration = ............................ m s

2
[3]

(ii)

the time taken

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

(b)

Car A refuels in 9.0 s and then takes 4.0 s to travel to Y. During the refuelling of car A,
1
car B continues to travel at 80 m s . Calculate the time difference between the cars A
and B as car A arrives back on the racetrack at Y.
time = ............................ s
[4]
[Total 9 marks]

Kingsdale Secondary School

112

118. In this question, two marks are available for the quality of written communication.
The figure below shows the path of a ball after it is thrown from T. The ball reaches a maximum
height at point P and then returns to the ground at G.

Kingsdale Secondary School

113

(a)

Assuming no air resistance, describe and explain how the vertical and horizontal
components of the velocity of the ball change as it travels from T to G.
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[5]

Kingsdale Secondary School

114

(b)

Assuming no air resistance, describe the changes in the kinetic and potential energies of
the ball as it travels from T to G.
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[4]

(c)

Describe how the motion of the ball is affected when air resistance is taken into
consideration.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[3]
Quality of Written Communication [2]
[Total 14 marks]

Kingsdale Secondary School

115

119. A girl travels down a pulley-rope system that is set up in an adventure playground. Fig. 1 shows
the girl at a point on her run where she has come to rest.

Fig. 1

The girl exerts a vertical force of 500 N on the pulley wheel. All the forces acting on the pulley
wheel are shown in Fig. 2.

fo rc e o f ro p e
on w heel
T2

fo rc e o f ro p e
on w heel
T

h o r iz o n ta l

f o r c e o f g ir l
on w heel
500 N
Fig. 2

Kingsdale Secondary School

116

(a)

Explain why the vector sum of the three forces must be zero.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[1]

(b)

(i)

Sketch a labelled vector triangle of the forces acting on the pulley wheel.
[3]

(ii)

Determine by scale diagram or calculation the forces T and T the rope exerts on
1
2
the pulley wheel.
[3]
[Total 7 marks]

120. The figure below shows a stationary oil drum floating in water.

c r o s s - s e c tio n a l
a re a 0 .2 5 m 2

0 .7 5 m
w a te r

2
The oil drum is 0.75 m long and has a cross-sectional area of 0.25 m . The air pressure above
5
the oil drum is 1.0 10 Pa.

(a)

Calculate the force acting on the top surface of the oil drum due to the external air
pressure.
force = ............................ N
[2]

Kingsdale Secondary School

117

(b)

The average density of the oil drum and contents is 800 kg m

weight of the oil drum and contents.

3
. Calculate the total

weight = ............................ N
[3]

(c)

Calculate the force acting upwards on the base of the drum.

force = ............................ N
[1]
[Total 6 marks]

121. The figure below shows a crate resting on the flat bed of a moving lorry.

c ra te

d ir e c tio n o f t r a v e l
fla t b e d

(a)

The lorry brakes and decelerates to rest.

(i)

Describe and explain what happens to the crate if the flat bed of the lorry is
smooth.
................................................................................................................
................................................................................................................
................................................................................................................
................................................................................................................
[2]

(ii)

A rough flat bed allows the crate to stay in the same position on the lorry when the
lorry brakes. Show on the figure above (with an arrow labelled F) the direction of
the force that must act on the crate to allow this.
[1]

(b)

Using your answers to (a) or otherwise explain how seat belts worn by rear seat
passengers can reduce injuries when a car is involved in a head-on crash.

Kingsdale Secondary School

118

122. Fig. 1 shows a spring that is fixed at one end and is hanging vertically.

fix e d e n d o f s p r in g

m ass M

Fig. 1
A mass M has been placed on the free end of the spring and this has produced an extension of
250 mm. The weight of the mass M is 2.00 N.

Kingsdale Secondary School

119

Fig. 2 shows how the force F applied to the spring varies with extension up to an extension of
= 250 mm.

4 .0

3 .0

F / N

2 .0

1 .0

100

200

300

x / m m

400

Fig. 2

(a)

(i)

Calculate the spring constant of the spring.

spring constant = ............................ unit ................
[3]

(ii)

Calculate the strain energy in the spring when the extension is 250 mm.
strain energy = ............................ J
[2]

Kingsdale Secondary School

120

(b)

The mass M is pulled down a further 150 mm by a force F additional to its weight.
(i)

Determine the force F.

F = ............................ N
[1]

(ii)

State any assumption made.

(c)

The mass M is now released and it oscillates up and down. Fig. 3 shows the
displacement s against time t for these oscillations.
200

s / m m
100

0 .2

0 .4

0 .6

0 .8

1 .0

1 .2

1 .4

1 .6

t/s

1 .8

100

200

Fig. 3

(i)

Mark on Fig. 3 a time when the mass M has maximum downward

velocity.Label this position V.

Use the graph to determine this maximum downward velocity of the mass.
maximum velocity = ............................ m s

1
[3]

Kingsdale Secondary School

121

(ii)

Mark on Fig. 3 a time when the mass M has maximum resultant force
acting on it. Label this position with an X.

Explain your choice of position for X.

123. A student constructs a model arm to demonstrate how two particular muscles in the upper arm
control movement of the lower arm. The figure below is a simplified diagram of this model arm.

Kingsdale Secondary School

122

Use the following data for the model to calculate the tension required in string B to maintain the
arm in the position shown in the figure above.
mass of lower arm = 75 g
mass of glove = 135 g
distance of centre of mass of lower arm from pivot = 20 cm
distance of centre of mass of glove from pivot = 30 cm
string B is attached to lower arm at a distance of 2.0 cm from the pivot
string T is attached to the lower arm at a distance from the pivot of 1.0 cm
the tension in string T is zero.

tension = ..................... N
[Total 3 marks]

124. (i)

Define speed.
.........................................................................................................................
.........................................................................................................................
[1]

(ii)

Define velocity.
.........................................................................................................................
.........................................................................................................................
[1]

Kingsdale Secondary School

123

(iii)

By referring to these quantities, explain the difference between scalars and vectors.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[2]
[Total 4 marks]

125. Fig. 1 shows a long rope that is tied at one end to a high support. A woman swings forwards and
backwards across a pool using the other end of the rope.

s u p p o rt

ro p e

Fig. 1

Kingsdale Secondary School

124

Fig. 2 shows the variation with time t of the displacement x, of the woman from A to B and back
to A.

2 .5
x /m
2 .0

1 .5

1 .0

0 .5

0
0

1 .0

2 .0

3 .0

4 .0

5 .0

6 .0
t/s

Fig. 2

(i)

State what the gradient of the graph represents and explain why the graph shows both
negative and positive gradients.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[2]

Kingsdale Secondary School

125

(ii)

Mark on Fig. 2 with a cross

a position where the speed of the woman is zero (label this cross Z)

a position where the speed of the woman is a maximum

(label this cross M).
[2]

(iii)

Use Fig. 2 to calculate the maximum positive speed of the woman. Show on
Fig. 2 how you determined your answer.

maximum speed = ........................ m s

1
[3]
[Total 7 marks]

126. A child sits on a swing and is pulled by a horizontal force P so that the chains make an angle
with the vertical of 35. The diagram below shows the forces acting in this position.

c h a in
t e n s io n in c h a in s

h o r iz o n ta l fo r c e P

v e r tic a l

s w in g s e a t
w e ig h t
The combined mass of the child and swing seat is 28 kg.

Kingsdale Secondary School

126

(a)

Calculate the combined weight of the child and swing seat.

weight = ............................ N
[2]

(b)

Use a labelled vector triangle to determine the force P required to hold the swing
stationary in the position shown in the diagram above.

force = ............................ N
[4]

Kingsdale Secondary School

127

(c)

State and explain what happens to the tension in the chains if the swing is pulled so that
the chains make a larger angle with the vertical. A numerical answer is not required.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[2]
[Total 8 marks]

127. (a)

A stone is projected horizontally from a cliff. The diagram below shows the stone at a
position A on its path.

h o r iz o n ta l c o m p o n e n t
30

c liff
v e r tic a l
com ponent

25 m s

s o ft s a n d
The velocity of the stone at position A is 25 m s

(i)

at 30 to the horizontal.

Show that the horizontal component of the velocity of the stone at A is

1
22 m s .

Kingsdale Secondary School

128

(ii)

Calculate the vertical component of the velocity of the stone at A.

vertical component ....................... m s

1
[3]

(b)

Sketch graphs on the axes below to show the horizontal and vertical displacements of the
stone from the point of horizontal projection to
the point of impact.
Ignore air resistance. Numerical values are not required.
(i)

horizontal displacement d
h
against time t

(ii)

vertical displacement fallen d

against time t
v

t
[3]

Kingsdale Secondary School

129

(c)

A second stone is released from rest from the top of the cliff. It falls vertically. Sketch
graphs on the axes below to show the velocity v and acceleration a of the stone from the
time of release to the time when the stone comes to rest in the sand below. Ignore air
resistance. Numerical values are not required.
(i)

velocity v against time t

tim e o f
r e le a s e

(ii)

im p a c t
w ith s a n d

s to n e
at
re s t

acceleration a against time t

tim e o f
r e le a s e

im p a c t
w ith s a n d

s to n e
at
re s t

[5]
[Total 11 marks]

Kingsdale Secondary School

130

128. (i)

State the principle of moments.

(ii)

State the two conditions for a system to be in equilibrium.

Kingsdale Secondary School

131

129. The diagram below shows the open bonnet of a car. The bonnet is held open at an angle of 60
to the horizontal by a vertical force V applied at one end of the bonnet (shown on the diagram).
The bonnet is 0.90 m long, has a weight of 25 N and its
centre of gravity G is 0.35 m from the hinge at O.

v e r tic a l fo r c e

car bonnet

0 .9 0 m

h o r iz o n t a l

(i)

60
h in g e O

On the diagram above, draw and label the two forces other than V acting on the bonnet.
[2]

(ii)

By taking moments about O, show that the vertical force V applied at the end of the
bonnet is 9.7 N.

[2]

Kingsdale Secondary School

132

(iii)

Calculate the magnitude of the force acting at the hinge O. Show your working.

force at hinge = ............................ N

[2]
[Total 6 marks]

130. In this question, two marks are available for the quality of written communication.
The diagram below shows stress-strain graphs up to the point of fracture for three different
materials.
s tre s s

s tre s s

s tre s s
copper

c a s t ir o n
p o ly th e n e

Kingsdale Secondary School

s t r a in

s tr a in

s t r a in

133

Use the terms plastic, elastic, brittle, and ductile, where appropriate, to describe the behaviour
of the materials represented by the graphs.
cast iron ...................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................

copper ......................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................

Kingsdale Secondary School

134

polythene .................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
[8]
Quality of Written Communication [2]
[Total 10 marks]

131. The reaction time of the driver of a car is 0.62 s.

(i)

Calculate the thinking distance when the car is travelling at a speed of 25 m s

distance = ............................ m
[2]

Kingsdale Secondary School

135

(ii)

The overall stopping distance of the car is 75 m.

Calculate
1.

the braking distance of the car

[1]

the deceleration of the car when braking. Assume the deceleration is uniform.

deceleration = .......................... unit ..............

[3]
[Total 6 marks]

132. Explain the difference between a scalar and vector quantity, including one example of each in
your explanation.
(i)

a scalar
.........................................................................................................................
.........................................................................................................................

(ii)

a vector
.........................................................................................................................
.........................................................................................................................
[Total 4 marks]

Kingsdale Secondary School

136

133. The diagram below shows the path of a car as it travels around a right-angled bend.

25 m s

B
25 m s

The car travels from point A to point B in 7.6 s at a constant speed of 25 m s

(i)

Calculate the distance the car travels in 7.6 s.

distance = ............................ m
[2]

(ii)

Draw a line on the diagram above to show the displacement of the car having travelled
from A to B.
[1]

(iii)

Explain why the velocity of the car changes as it travels from A to B although the speed
remains constant.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[2]

Kingsdale Secondary School

137

(iv)

Using a labelled vector triangle, calculate the magnitude of the change in velocity of the
car (velocity at B velocity at A).

magnitude of velocity change = ....................... m s

1
[4]

(v)

State and explain whether the car is accelerating as it travels around the bend from A to
B.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[2]
[Total 11 marks]

Kingsdale Secondary School

138

134. Explain the quantities

(i)

gravitational potential energy

(ii)

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

(iii)

power.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[1]
[Total 5 marks]

135. Water leaves a reservoir and falls through a vertical height of 130 m and causes a water wheel
to rotate. The rotating wheel is then used to produce 110 kW of electrical power.
(i)

Calculate the velocity of the water as it reaches the wheel, assuming that all the
gravitational potential energy is converted to kinetic energy.

velocity = ...................................... m s

1
[3]

(ii)

Calculate the mass of water flowing through the wheel per second, assuming that the
production of electrical energy is 100% efficient.

Kingsdale Secondary School

139

mass of water per second = .......................... unit ..............

[3]

(iii)

State and explain two reasons why the mass of water flowing per second needs to be
greater than the value in (ii) in order to produce this amount of electrical power.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[2]
[Total 8 marks]

Kingsdale Secondary School

140

136. Fig. 1 shows a helicopter that has a cable hanging from it to the sea below.

c a b le

sea
Fig. 1
A girl of mass 55 kg is rescued by a man of mass 75 kg. The two are attached to the cable and
are lifted from the sea to the helicopter. The lifting process consists of an initial acceleration
followed by a period of constant velocity and completed by a final deceleration.

(a)

Name the two main forces acting on the two people being lifted.
.........................................................................................................................
.........................................................................................................................
[2]

(b)

Calculate the combined weight of the man and girl.

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

Kingsdale Secondary School

141

(c)

Calculate the tension in the cable during

(i)

the initial acceleration of 0.55 m s

tension = ............................ N
[2]

(ii)

the period of constant velocity.

tension = ............................ N
[2]

(d)

Calculate the final deceleration if the tension in the cable is 1240 N.

deceleration = ....................... m s

2
[2]

Kingsdale Secondary School

142

(e)

Sketch on Fig. 2 a graph of velocity v against time t for the complete lifting process.
Numerical values are not required.

Fig. 2
[3]
[Total 12 marks]

137. Define the Young modulus.

Kingsdale Secondary School

143

138. (a)

The wire used in a piano string is made from steel. The original length of wire used was
0.75 m. Fixing one end and applying a force to the other stretches the wire. The
extension produced is 4.2 mm.
(i)

Calculate the strain produced in the wire.

strain = ................................
[2]

(ii)

11
The Young modulus of the steel is 2.0 x 10 Pa and the cross-sectional area of
7 2
the wire is 4.5 10 m . Calculate the force required to produce the strain in the
wire calculated in (i).

force = ............................ N
[3]

(b)

A different material is used for one of the other strings in the piano. It has the same
length, cross-sectional area and force applied. Calculate the extension produced in this
wire if the Young modulus of this material is half that of steel.

extension = ......................... mm
[2]
[Total 7 marks]

Kingsdale Secondary School

144

139. (i)

Define density.
.........................................................................................................................
.........................................................................................................................
[1]

(ii)

State and explain what happens to the density of the material of a wire when it is
stretched. Assume that when the wire stretches the cross-sectional area remains
constant.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
[1]
[Total 2 marks]

Kingsdale Secondary School

145

140. Explain why friction is important in accelerating and decelerating a car.

In your answer

discuss factors affecting the magnitude of the acceleration

state the direction in which friction acts for both acceleration and deceleration.

..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
[4]
Quality of Written Communication [2]
[Total 6 marks]

Kingsdale Secondary School

146

As OCR Mechanics Questions
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