chapter 2 module cg Ahmad

Calculate the velocity of trolley A and trolley B after Example 6
collision. Diagram (a) shows a bowling ball of mass 5 kg
v = L2 moves with a velocity of 6 m s-1 towards a
stationary bowling pin of mass 1.5 kg.
0.2 Diagram (b) shows the bowling pin moves with a
Calculate the total momentum before collision = m1u1 velocity of 2 m s-1 after collision.
Calculate the total momentum after collision =
(m1+ m2 )v Diagram(a)

Conclusion
From the experiment , we obtained
m1u1 = (m1+ m2 )v, the conservation of momentum
principle is obeyed in inelastic collision.

5.3.3 Elastic collision

In elastic collision , after two objects moving with
their respective velocities do collide, those two
objects will separate and move with different
velocities.

Based on The Principle Of Conservation Of Diagram(b)
Momentum, Determine
(a) the velocity of the bowling ball after the
The total momentum = The total momentum
collision.
before collision after collision (b) the direction of the bowling ball after the

m1u1 + m2u2 = m1v1 + m2v2 collision.

Example 5 Solution

A trolley of mass trolley 2 kg and moving with a 5.3.4 Experiment to investigate the conservation of
velocity 0.6 m s-1 and collides with a stationary momentum principle is obeyed in elastic collision.
trolley with a mass 1kg . After collision the trolley of
mass 2 kg and moving with a velocity 0.2 ms-1. What Aim of the experiment:
is the velocity of the trolley of mass 1 kg after
collision? Experiment to investigate the conservation of
momentum principle is obeyed in elastic collision.
Solution
List of apparatus and materials:
Trolleys with difference mass,runway,ticker
timer,ticker tape,a.c. power supply ,connecting wires.

Arrangement of the apparatus:

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Conclusion
From the experiment , we obtained
m1u1 = m1v1 + m2v2, the conservation of
momentum principle is obeyed in elastic collision.

5.3.5 Explosion

In explosion, two objects are initially at rest and after
explosion those two objects will separate and move
in opposite directions.

The procedure of the experiment Based on The Principle Of Conservation Of
Momentum,
Measure the mass of trolley A, m1 = 1 kg and mass
of trolley B, m2 = 1 kg The total momentum = The total momentum
The a.c. power supply is switched on .
Push trolley A to collides with stationary trolley B
and both trolleys not stick together after collision.

Calculation

From ticker tape makes calculation:

before explosion after explosion

m1(0) + m2(0) = m1(-v1) + m2v2

m1v1 = m2v2

Example 7

Diagram shows a bullet of mass 0.05 kg is shot out
from a gun of mass 1.5 kg.The recoil velocity of the
gun is 2 m s-1 ,

Calculate the velocity of trolley A before collision.

u1 = L1
0.2

Calculate the velocity of trolley A after collision.

v1 = L2
0.2

Calculate the velocity trolley B after collision. Calculate the velocity of the bullet after explosion?
Solution
v2 = L3
0.2

The experiment is repeated by 4 different

combinations of mass trolley A and B : m1 = 1 kg ,
m2= 1.5 kg , m1 = 1.5 kg , m2= 1 kg , m1 = 2 kg ,
m2= 1.5 kg and m1 = 1.5 kg , m2= 2 kg .
Calculate the total momentum before collision = m1u1
Calculate the total momentum after collision =

m1v1 + m2v2

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Example 8 produced out of the rocket nozzle in high speed and
hence produces downwards momentum.
A boy of mass 60 kg and a girl of mass 40 kg stand Following the principle of Conservation of
facing each other on a skating rink. The girl pushes Momentum, the rocket will propel upwards with a
the boy and he moves backwards at 2 m s-1 . What is momentum that is equal to its previous momentum
the girl’s velocity? because momentum is conserved.

Solution A jet engine uses the same principle of momentum
conservation as the rocket engine except that it takes
5.3.5 Similarities and Differences between in air to burn the fuel. So a jet engine will only work
Inelastic Collision and Elastic Collision in the atmosphere.
In the jet engine, air is sucked into the jet engine to
Similarities be compressed and is heated up in the compressor.
Total momentum is conserved The compressed air is then mixed with fuel which is
Total energy is conserved sprayed so that it starts to burn. The exhaust chamber
Total mass is conserved emits exhaust gases with a high velocity. This results
in a momentum of equal magnitude but of opposite
direction which moves the aero plane forward.

Differences Elastic collision 5.4.3 Differences between rocket engine and jet
Inelastic collision Both objects don’t stick
Both objects stick together after collision engine:Jet engine rocket engine
together after collision and move with different
and move with a velocities Rocket engine Jet engine
common velocity Total amount of kinetic
Total amount of kinetic energy is conserved The fuel is hydrogen The fuel is kerosene
energy is not conserved
@paraffin fluid

Carrying oxygen supply Uses oxygen from

alone atmospheric

Can fly in outer space Cannot fly in outer space

5.4 The Applications of the Principle of The mass reduced The mass unchanged
Conservation of Momentum in rockets or jet
engines . Need to a big thrust Less than a rocket thrust

5.4.1 Rocket Engine 5.4.4.The reason for the rocket rising is
accelerating

(1) The mass rocket decreases
(2) Air resistance is decreasing
(3) The acceleration of gravity decreases

5.4.2 Jet Engine

A rocket engine carries its fuel with it and can work
in space as well as in atmosphere.
Two fuels, such as liquid hydrogen and liquid oxygen
burn together explosively and force the gases

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TUTORIAL 5

1 Which of the following is the units of 5 Diagram shows a velocity-time graph of a car.
momentum?

A Ns B kg ms-2
C kg s-2 D kg-1s-2

2 A car of mass 800 kg is moving at a velocity of
50 ms-1 The momentum of the car is

A 0.625 kg ms-1 B 4 kg ms-1
C 16 kg ms-1 D 40000 kg ms-1

3 Which of the following has the greatest
momentum.

Which part, A, B, C or D of the graph shows
the highest magnitude of momentum
experienced by the car?

6 A ball of mass 0.5 kg hits the wall with a
velocity of 4 ms-1 and bounces back with a
velocity of 3 ms-1. What is the magnitude of

the change of momentum?

A 2.0 Ns B 1.5 Ns
C 0.5 Ns D 3.5 Ns

7 The diagram shows two objects A and B of
masses 3 kg and 2 kg respectively moving
towards each other.

4 The diagram shows a velocity-time graph for
the motion of an object.

The momentum of the object is constant from Which of the following is not true?
[ The positive sign if moves to the right and
A 0 s to 3 s B 3 s to 6 s negative sign if moves to the left ]
C 6 s to 8 s D 0 s to 8 s
A The total of momentum before collision
+ 3 kg ms-1

B The total of momentum after collision
+ 3 kg ms-1

C The momentum of object A before
collision is + 15 kg ms-1

D The momentum of object B before
collision is + 12 kg ms-1

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8 Diagram shows two trolleys before and after 11 Diagram shows two trolleys of equal mass , m .
collision. After collision they stick together

What is the common velocity of the trolleys?

v v

A B

4 2

Cv D 2v

What is the velocity of both trolleys after 12 Diagram shows two trolleys of equal mass
collision? ? before and after collision.

A 0.60 ms-1 B 0.83 ms-1
C l.20 ms-1 D 2.00 ms-1

9 Diagram shows two metal balls move toward
each other. After collision the balls stick
together.

Which is the following is true to relate x and y

A x=y B x <y
C x=½y D x = 2y

Which of the following about the balls after 13 A bullet of mass 10 g is shot horizontally with
collision? a velocity of 200 ms-1 so that it hits an initially

A The balls move to the left with speed of stationary block of wood. The bullet enters the
3 m s-1
block of wood and they move together with a
B The balls move to the right with speed of common velocity of 2.0 ms-1 What is the mass
3 m s-1
of the block of wood.
C The balls move to the left with speed of
5 m s-1 A 860 g B 990 g
C 1000 g D 1020 g
D The balls move to the right with speed of
5 m s-1 14 Diagram shows a ticker tape from an
experiment by pushing of trolley A of mass
10 Two trolleys of masses 2 kg and 3 kg
respectively moving towards each other. Both 2kg to collide with a stationary trolley B.
of the trolleys are moving at same velocity of
2ms-1. After collision they stick together with a After collision both trolleys move together.
common velocity. What is the common velocity
of the trolleys ? Mass of trolley B is B 1.0 kg
D 2.0 kg
A 2 ms-1 in the original direction of the A 0.5 kg
trolley of mass 2kg C 1.5 kg

B 2 ms-1 in the original direction of the
trolley of mass 3kg

C 0.4 ms-1 in the opposite direction of the
trolley 2 kg

D 0.4 ms-1 in the opposite direction of the
trolley 3 kg

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15 Diagram shows a collision between two balls. 18 A bullet of mass 0.01 kg is fired from a rifle

of mass 2 kg. The recoil velocity of the rifle is
1.25 ms-1,what is the velocity of the bullet ?

A 100 ms-1 B 150 ms-1
C 200 ms-1 D 250 ms-1

Based on the diagram above , what is the value 19 Diagram shows a cannon before and after
of v ? collision.The total mass of a cannon ball and a
cannon is 300 kg. The cannon ball of mass 10
kg is fired from the cannon , the recoil velocity
of the cannon is 1.5 ms-1

A 2.0 ms-1 B 2.5 ms-1
C 3.0 ms-1 D 3.5 ms-1

16 Diagram shows two objects P and Q of . What is the velocity of the bullet when the
masses 0.8 kg and 0.6 kg respectively moving bullet is fired.
towards each other before collision. After
collision object P bounces back with a velocity
of 1.6 ms-1.

A 43.5 ms-1 B 45.0 ms-1
C 50.0 ms-1 D 65.0 ms-1

What is the velocity and the direction of motion 20 A man of mass 50 kg stands on a stationary boat
of object Q after collision ? of mass 25 kg. When he jumps out of the boat
onto a jetty at a velocity 4 ms-1, calculate the
A 0.8 ms-1 moves to left velocity of the boat as the man jumps.
B 0.8 ms-1 moves to right
C 2.2 ms-1 moves to left A 2 ms-1 B 4 ms-1
D 2.2 ms-1 moves to right C 6 ms-1 D 8ms-1

17 Two objects M and N of masses 4 kg and 21 Diagram shows the trolleys A and B of masses
2 kg respectively. Both the objects travel 2 kg and 4 kg respectively are placed together
towards each other with velocities of 6 ms-1 with the plunger of trolley B pressed and in
and 1 ms-1 respectively. After collision object N contact with trolley A initially .
moves in the opposite direction as its original When the plunger is released by hitting the pin
direction with the velocity of 5 ms-1. What is by a hammer ,the two trolleys move apart in
the velocity and the direction of motion of opposite directions and collide with the wooden
object M after collision ? blocks at the same time.

A 3 ms-1 is the same direction as the object What is the value of d ?
M
A 2.0 m B 3.0 m
B 3 ms-1 is the opposite direction as the C 4.0 m D 6.0 m
object M

C 6 ms-1 is same direction as the
object M

D 6 ms-1 is the opposite direction as the
object M

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22 In which situation can the principle of 26 Diagram shows two trolley of same mass moves
conservation of momentum be applied? towards each other.

When the elastic collision occur , which
diagram true to show the motion of both trolleys
after collision.

23 Which of the following is not obeys the 27 Diagram shows two balls, M and N, moving
principle of conservation of momentum ? towards each other with a same speed v.
The collision between the two balls is an elastic
A The inelastic collision collision.
B The elastic collision
C The explosion Which statement is correct about the elastic
D The linear motion collision?

24 In an inelastic collision , which of the following A The momentum of ball M before the
is not conserved? collision is equal to the momentum of ball
N before the collision
A Total amount of mass
B Total amount of energy B The total momentum before the collision is
C Total amount of momentum equal to the total momentum after the
D Total amount of mass kinetic energy collision

25 The diagram shows two trolleys A and B C The kinetic energy of ball M before the
moving towards each other. collision is equal to the kinetic energy of
ball N before the collision
Which of the following is true.
D The total kinetic energy before the
A An elastic collision will occur collision is not equal to the total kinetic
B The total momentum of the system is energy after the collision

conserved
C The total kinetic energy of the system is

conserved
D After collision the two trolleys will

separate and move with different
velocities.

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28 Diagram shows trolley P and Q with the same
masses.

Which of the following comparison is true Diagram 32.2

about momentum of trolley P and trolley Q after (a) Based on Diagram 32.1 and 32.2 name the
Physics principle involved in the above
collision occured. …………………………………………….
[1 mark]
Trolley P Trolley Q
(b) Calculate the value of velocity, v.
A Increase Increase
B Decrease Decrease [2 marks]
C Increase Decrease (c) State the type of collision involved.
D Decrease Increase
……………………………………............
29 Which of the following is true? [1 mark]

A The launching of a rocket can be explained (d) What happen to the total kinetic energy
by the Newton’s second law of motion after collision.
…………………………………………….
B The fuel normally used in rocket engine is [1 mark]
liquid hydrogen
(e) State one condition needed in order
C The air from atmosphere is sucked into to apply the physics principle stated in (a)
the rocket engine ....................................................................
[ 1 mark]
D The total weight of the rocket is constant
33 Diagram 33.1 shows two metal balls of mass 2.0
30 A rocket can works in outer space as well as in kg and 2.5 kg respectively before collision.
atmosphere because Diagram 33.2 shows the metal balls after collision
occur.
A the mass of the rocket is less
B the velocity of the rocket is high Diagram 33.1
C the rocket experiences acceleration
D the rocket carries oxygen tank with it Diagram 33.2

31 The higher the rocket moves vertically upwards (a) What is meant by momentum
, the higher ……………………………………………
[ 1 mark]
A the air resistance
B the mass of the rocket (b) State the type of collision involved
C the acceleration of the rocket …………………………………………....
D the acceleration due to gravity [ 1 mark]

32 Diagram 32.1 shows a cat chasing a mouse.

The mass and velocity of the cat and the mouse
are 5.0 kg , 14 m s-1 and 0.04 kg , 4 m s-1
respectively.
Diagram 32.2 shows the cat successfully

catches the mouse both of them are moving with
a same velocity of v m s-1.

Diagram 32.1

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(c) Calculate (c) Calculate the mass of trolley B.
(i) the total momentum before collision
[ 2 marks]
[ 2 marks]
(ii) the total momentum after collision. 35 Diagram 35 shows two trolleys A and B of
masses 1 kg and 2 kg respectively. The velocity
[ 2 marks] of trolley A is 5 ms-1 and trolley B at the rest.
(d) Relate your answer in (c)(i) and (c)(ii) and After collision trolley A moves with a velocity
2.5 ms-1 in same direction as before.
state the physics principle involved.
………………………………………………… Diagram 35
…………………………….…………………… (a) What is the type of the collision which will
…………………………………………………
occur between two trolleys ?
[ 2 marks] ……………………....................................
(e) State one physical quantity is conserved.
………………………………………………… [ 1 mark]
(b) (i) Calculate the velocity of the trolley
[ 1 mark]
B after collision.
34 Diagram 34.1 shows a trolley A of mass 1 kg is
attached to a ticker tape and a stationary trolley [ 2 marks]
B on a friction-compensated runway. (ii) Based on your answer in (b)(i), what

Diagram 34.1 is the direction of motion of the
trolley B after collision.
When they collide, a pin fixed to one trolley ............................................................
sticks into a cork fixed to the other ,keeping
them both together. Diagram 34.2 shows the [ 1 mark]
ticker tape produced by the motion of trolley A (c) Calculate the change of momentum of

(i) trolley A

[ 2 marks]

(ii) trolley B

Diagram 34.2 [ 2 marks]
(a) State the type of collision.
36 Diagram 36.1 shows a boy of mass 60 kg
……………………………………………. standing on a stationary skateboard of mass 2.5
[ 1 mark] kg. The boy then jumped off from the skateboard
with a velocity of 4 m s-1 and caused the
(b) Before collision , what is skateboard to move left as shown in Diagram
(i) the velocity of the trolley A 36.2.

[ 2 marks]

(ii) total of momentum.

[ 2 marks]

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Diagram 36.1 Diagram 36.2 (ii) Explain in terms of the principle of
conservation of momentum, how the
(a) Name the physics principle involved . water rocket is launched.
……………………………………………. [4 marks]
[1 mark]
(b) You are required to give some suggestions
(b) Explain why the skateboard moves to the to improve the design of the water rocket
left. so that it travels at a higher speed.
…………………………………………… Explain the suggestions based on the
………………………………………….... following
………………………………………….... - material of the bottle
[2 marks] - mass of water filled
- extra component that can be
(c) Calculate the velocity of the skateboard used to increase stability
after the boy jumped off from the - method used to make the rocket
skateboard . in soft landing
- angle of launching
.
[10 marks]
[2 marks]
(d) Name one application of the physics 38 (a) Diagram 38.1 shows a frog in stationary
situation on top of a leaf in a pond.
principle stated in (a) in an exploration of
outer space. Diagram 38.1
………………………………………… Explain what happens to the leaf when the
frog jumped out of the leaf?
[1 mark]
37 Diagram 37 shows a water rocket bottle is [4 marks]
(b) Diagram 38.2 shows the design of a jet
connected to a bicycle pump at to launch it.
The rocket works according to the principle of engine.
conservation of momentum.
Diagram 38.2
Diagram 37
(a) (i) State the principle of conservation of (i) Explain why a jet cannot fly in outer
space?
momentum. [2 marks]
[ 1 mark]
(ii) Based on Diagram 38.2 study the
design of the jet engine. Give your
suggestions to make the jet engine
work effectively.
Your suggestions based on the
following:
-Air intake opening
-Blade
-Combustion chamber
-Exhaust gases opening
[10 marks]

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39 Diagram 39.1 shows a car moving at a speed of
100 km j-1 hitting an obstacle in a test lab at a
car factory.
Diagram 39.2 shows the car's velocity increased
to 150 km j-1.

Diagram 39.1

Rajah 39.2
Based on the above information and
observation:

(a) State one suitable inference.
[ 1 mark]

(b) State one suitable hypothesis.
[ 1 mark]

(c) With the use of apparatus such as ball
bearing, wooden block,curtain rail, and
folded thin cardboard other apparatus,
describe an experiment framework to
investigate the
hypothesis stated in (b).
In your description state clearly the
following.
(i) Aim of the experiment
(ii) Variables in the experiment.
(iii) List of apparatus and materials
(iv) Arrangement of the apparatus
(v) The procedure of the experiment
which include the method of
controlling the manipulated variable
and the method of measuring the
responding variable.
(vi) The way you would tabulate the data
(vii) The way you would analysis the data
[ 10 marks ]

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LESSON 6 : FORCE 6.5 Relationship a, F and m.
a is directly proportional to F ,
6.1 Meaning of force
a αF
Force is defined as anything that changes the state of
rest or motion of an object moving in a straight line. a is inversely proportional to m
aα 1
Force is a vector quantity which has both direction m
and magnitude
6.6 Solving problems involves the formula F = ma
The S.I. unit for force is N or kg m s-2 Example 1
Diagram shows a force of 8 N act horizontally to a
Force is measured by using a Spring Balance wooden block of mass 4 kg in a smooth surface

6.2 Definition of force Calculate the acceleration of the block.
Solution
Force is the rate of change of momentum

F = m(v - u) = ma
t

6.3 The effects of a force

A force can
• move a stationary object
• stop a moving object
• accelerate a moving object
• decelerate a moving object
• change the direction of a moving object
• alters the size of the object
• alters the shape of the object

6.4 Force is related to the Newton‘s second laws
of motion

Newton’s Second Law of motion state ,” The rate of
change of momentum is directly proportional to the
force and acts to the direction of the force.

F α m(v - u)
t

F = k m(v - u)
t

F = kma and k = 1

Hence F = ma

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Example 2 6.7 Experiment to investigate the relationship
between the force and acceleration
A car has a mass of 1000 kg, determine the engine
thrust of the car needs to apply when it is to Aim of the experiment :
accelerate at 5.0 ms-2. To investigate the relationship between the
acceleration and the force.
Solution Variables in the experiment:
Manipulated variable: Force
Responding variable: Acceleration
Constant variable: Mass
List of apparatus and materials:
A Trolley, ticker timer, ticker tape, 6 elastic cords, a
wooden runway, 12 V a.c power supply.
Arrangement of the apparatus:

Example 3 The procedure of the experiment which include
A bus of mass 2 000 kg travels with a uniform the method of controlling the manipulated
velocity 40 ms-1 for a distance 2500 m before it variable and the method of measuring the
comes to rest. Calculate responding variable.
(a) the average deceleration of the bus Use an elastic cord to present one unit of force = F
(b) the average force applied by the brakes to bring The ticker-timer is switched on and a trolley is pulled
using a rubber band. The extension of the rubber
the bus to a standstill band is ensured to be of the same length
Solution Acceleration of the trolley is calculated using the
ticker-tape. by using the formula a = v − u
Example 4
Diagram shows a trolley of mass 2 kg mass moves t
with velocity 6 m s-1 enters the rough surface by 2.8 The experiment is repeated 5 times by increasing the
m and finally stops. number of the elastic cords.
Tabulate the data:
F
a

Analysis the data:
Plot the graph a against F

Determine the magniude of frictional force found on
the rough surface

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6.8 Experiment to investigate the relationship
between the mass and acceleration

Hypothesis:
When the mass increased, the acceleration will be
decreased
Aim of the experiment :
To investigate the relationship between the
acceleration and the mass
Variables in the experiment:
Manipulated variable: Mass
Responding variable: Acceleration
Constant variable: Force
List of apparatus and materials:
Trolley, ticker timer, ticker tape, elastic cord, a
wooden runway, 12 V a.c power supply and balance

Arrangement of the apparatus:

The procedure of the experiment which include
the method of controlling the manipulated
variable and the method of measuring the
responding variable.

Measure the mass of a trolley by using a balance = m
Use an elastic cord to present one unit of force = F
The ticker-timer is switched on and a trolley is pulled
using a rubber band. The extension of the rubber
band is ensured to be of the same length
Acceleration of the trolley is calculated using the
ticker-tape. by using the formula a = v − u

t
The experiment is repeated 5 times by increasing the
number of the trolleys.
Tabulate the data:
m
a
Analysis the data:
Plot the graph a against m

64

TUTORIAL 6 7 The diagram shows the graph of motion for two
objects M and N is acted on by a same force.
1 1 N is equivalent to B 1 kg ms-2
D 1 kg s m-1 Which comparison is correct about the mass of
A 1 kg ms-1 M and N?
C 1 ms kg-1 A Mass of M = Mass of N
B Mass of M < Mass of N
2 Which of following is not effects of a force C Mass of M > Mass of N
acts on a moving toy car? D Mass of M ≤ Mass of N
8 Diagram shows how a force, F initially acting
A The velocity of the car is increased on stationary body varies with time.
B The velocity of the car is reduced
C The direction of the car is changed Which of the following graph shows the
D The mass of the car is reduced variation of velocity, v of the body with time, t.

3 Which of following is not effects of a constant
force?

A Change the direction of motion
B Change the shape of an object
C Change the velocity of a moving object
D Change the acceleration of a moving

object

4 The equation F = ma is obtained based on

A Newton's first law of motion
B Newton's second law of motion
C Newton's third law of motion
D Newton’s universal law of gravitation

5 Which of the following graph is true to show
the relationship between the acceleration a , the
mass , m and the force ,F

6 An object of mass 0.2 kg pulled by 8 N of force
on a smooth surface.
What is the acceleration of the object?

A 20 ms-2 B 40 ms-2 9 Diagram shows a toy car of mass 4 kg. The car
C 60 ms-2 D 80 ms-2 is pushed forward by a force of 10 N. The

65

frictional force between the toy car and the floor A 5N B 240 N
is neglected. C 2 400 N D 6 000 N

13 A particle of mass 0.02 kg is moving with a
velocity 10 ms-1 on a smooth surface . A force

5 N acts on the particle such that its velocity
increases to 15 m s-1. For how long will the

force act on the particle?

What is the acceleration of the toy car? A 0.01 s B 0.02 s
C 0.1 s D 0.2 s

A 20 m s-2 B 12 m s-2 14 A force of 120 N acts on an object in a
C 5 m s-2 D 2.5 m s-2
stationary.After 5 s the force is applied the
10 Diagram shows the forces 550 N acts on a velocity of the object is 40 m s-1.What is the
bicycle. The mass of the bicycle and the cyclist mass of the object?
are 9.5 kg and 70 kg respectively.
A 0.6 kg B 1.7 kg
C 15 kg D 960 kg

15 Diagram 15 shows two identical boats, R
and S with the same mass. Boat R is paddled by
one person while boat S ia paddled by two
persons. In 10 minutes, the distance travelled by
boat R is 200 m and the distance travelled by
boat S is 400 m.

What is the acceleration of the cyclist?

[ Frictional force is negligible]

A 57.9 m s-2 B 9.1 m s-2

C 7.9 m s-2 D 6.9 m s-2

11 Diagram (a) shows two identical wooden Diagram 15
(a) Based on Diagram 15, compare
blocks are pulled by a force experience
acceleration of 4 m s-2 on a smooth surface.. (i) the distance travelled by the boat
...........................................................
Diagram (a) Diagram (b) [ 1 mark ]

What is the acceleration of the wooden block in (ii) the force applied by the person to the
Diagram (b), when the same force, F exerted on boat.
it. ...........................................................
[ 1 mark ]
A 4 m s-2 C 8 m s-2
B 6 m s-2 D 10 m s-2 (iii) the acceleration of the boat
...........................................................
12 A car of mass 1 200 kg travelling at 20 ms-1 is [ 1 mark ]
brought to rest over a distance 40 m. Find the
average braking force. (b) Based on your answer in (a) , state the
relationship

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(i) the distance travelled by the [2 marks]
boat and the force applied (c) What happen to the box when the pushing
...................................................
[ 1 mark ] force is doubled. Give the reason for your
answer.
(ii) the force applied and the ...................................................................
acceleration of the boat ...................................................................
...................................................
[ 1 mark ] [2 marks]
(d) Sketch a displacement-time graph motion
(c) Name the physics law involved in (b)(ii).
…………………………………………… of the box in Diagram 16.2.
[ 1 mark ]
Diagram 16.2
(d) The mass of each boat is 200 kg and start [1 mark]
from rest. The total mass of two persons is
120 kg. 17 Diagram 17.1 a trolley is pulled with a constant
Calculate force F N.
[ Water resistance is negligible ] Diagram 17.2 shows another trolley is placed on
the first trolley and is pulled with the same force
(i) the acceleration of the boat R FN

[2 marks]
(ii) the average forward force to move

boat R.

[2 marks]

16 Diagram 16.1 shows a 50 kg box is pushed by a
man with a force of 300 N.The box moved on a
smooth horizontal surface.

Diagram 17.1

Diagram 16.1 Diagram 17.2
(a) What is the meaning of force? Diagram 17.3 shows the motion graph of the 1
trolley and the 2 trolleys.
……………………………………………
[1 mark]

(b) Calculate the acceleration of the box.

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Diagram 17.3 (i) the acceleration of the wooden block
(a) What is meant by velocity ? P.

……..…………………………………… [2 marks]
[1 mark] (ii) the mass of the wooden block P.

(b) Using Diagram 17.1 and Diagram 17.2 [2 marks]
compare the mass of the arrangement of (b) When the wooden block is moves from
the trolleys.
……………………………………………. rest again ,it is pulled by a 18 N force
[1 mark] ,calculate
(i) the acceleration of the wooden block?
(c) Using diagram 17.3 ,
(i) compare the gradient of the graph P [2 marks]
and Q (ii) the velocity of the wooden block
.……………………………………
[1 mark] after 4 s.
(ii) name the physical quantity is
represented by the gradient of the [2 marks]
graph. (c) Diagram 18.2 shows two identical wooden
………………………………………
[1 mark] blocks Q and R have the same mass as
(iii) state the unit of the gradient of the wooden block P.
graph
……………………………………… Diagram 18.2
[1 mark] Calculate the force is needed to move the
wooden blocks with an acceleration is
(d) Based on your answer in (b) and (c) , state same as the acceleration in (b)(i).
the relationship between the mass and the
physical quantity in (c)(ii). [2 marks]
…………………………………………… 19 A physics law state that “The rate of change of
[1 mark]
momentum is directly proportional to theforce
(e) Suggest one method how the gradient of and acts to the direction of the force”
the graphs can be increased? (a) Name the law.
……………………………………………
…………………………………………… [1 mark]
(b) From the statement of the law derive
18 Diagram 18.1 shows a spring balance which is
pulling a wooden block P from rest with a the equation F = ma
force of magnitude 10 N on a smooth surface. [4 marks]
After 2.5 s the block moves with a velocity of
5 ms-1.

Diagram 18.1
(a) Calculate

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20 Diagram 20.1 shows a car and a truck at the (v) The procedure of the experiment
traffic light when the red light turns on. which should include one method of
Diagram 20.2 the car and the truck start to move controlling the manipulated variable
when .the green light is turns on and one method of measuring the
responding variable.

(vi) The way to tabulate the data
(vii) The way to analyse the data.

[10 marks ]

Diagram 20.1

Diagram 20.2

Based on the information and observation :

(a) State one suitable inference.
[I mark ]

(b) State one suitable hypothesis.
[I mark ]

(c) With the use of apparatus such as a trolley
, ticker timer, runway and other apparatus
, describe one experiment to investigate
the hypothesis stated in (b).
In your description, state clearly the
following.
(i) The aim of the experiment.
(ii) The variables in the experiment.
(iii) The list of apparatus and material.
(iv) The arrangement of apparatus.

69

LESSON 7 : IMPULSE AND
IMPULSIVE FORCE

7.1 Impulse

7.1.1 Definition and S.I. unit for Impulse Example 1
Impulse is defined as the change in momentum An object of mass 0.4 kg falls from a building. Its
velocity is 6 ms-1 before it touches the ground. How
I= m(v-u) much is the impulse on the object once it hits the
ground.
m = mass Solution
v = final velocity
u = initial velocity Example 2
Diagram shows a trolley of mass 1.5 kg hits the wall
Unit of impulse = kg ms -1 or N s magnitude of the with a velocity 5 ms-1 and bounces back with a
impulse velocity of 4 ms-1.
Impulse is a vector quantity.
Calculate the magnitude of the impulse during
From Newton’s second law of motion, collision.
F = m(v - u) = = I Solution

tt

Ft = m( v – u ) = change in momentum

I = Ft

F = Impulsive force
t = time impact

Impulse = area under graph F – t Example 3
(because I = Ft)
A box of mass 2 kg is pulled with a force of 40 N for
7.1.2 “ Follow -through” in sport 5s. How much is the impulse upon the object.

Solution

The follow-through in sport increases the time of
collision and subsequently contributes to an increase
in the velocity change and also increase the impulse ,
because I= Ft

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7.2 Impulsive force Example 5

7.2.1 Definition and S.I. unit for Impulsive Force A boy of mass 50 kg falls a high place to the ground.
The velocity of the boy when he just touches the
The impulsive force is a large force which acts over ground is 4 ms-1.
a very short time interval. What is the impulsive force acting on the boy if
(a) he bends his knees upon landing on the ground
Impulsive force is defined as the rate of change of
momentum in a collision and take a short timew. and takes 0.5 s to stop
(b) he lands on the ground with stiff legs and takes
Impulsive force , , F = Change of momentum
Time 0.02 s to stop

F = m(v-u) Solution
t

where , m = mas , v = final velocity
u = initial velocity and t = time impact

Unit of impulsive force = kg ms -2 or N
Impulse force is a vector quantity.

Impulsive force also defined as the rate of impulse
F = Impulse = I

Time t

Impulsive force = gradient of the graph 7.2.1 Effect of time interval of impact on size of
Impulse – Time impulsive force

(Because F = Impulse ) From the formula for impulsive force,
Time F = m(v - u)
t
Example 4
we can see that when the stopping time ,t , is small, F
A tennis ball of mass 0.1 kg is moving at a velocity is big ; and when t is big , F is small.
of 40 m s-1 .A player hits the ball and moves in the The impulsive force is inversely proportional to the
opposite direction with a velocity of 10 m s-1. How time of impact.
much is the impulsive force experienced by the ball
if the time of collision is 0.02 s. 7.2.2 Impulsive force and Newton’s third law of
motion
Solution
Newton’s third law of motion state “For every action,
there is an equal and opposite reaction.

For example : When a collision between a truck and a
car occurs, the car is more damaged than the truck.
The impulse power acting on the lorry to the car is
the same as the magnitude of the impulse force acting
by the car to the lorry, but the direction of action is
opposite.
The car is more damaged because mass of the car
smaller than the truck.

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7.2.3Reducing impulsive forces 7.3 Safety features in vehicles

1. A gymnast bends her knees as he lands, the 1. Crumple zone.
momentum change occurs over a longer period In a collision, the bonnet and boot of a car are
of time, and so the impulsive force will be lower designed to be easily crushed to lengthen the
and to avoid breaks her leg. impact time and thus reduce the impulsive force
to the passengers
2. In games like baseball, cricket and softball, the
catcher always pulls his hand backward when 2. Strong steel struts or framework of the car
catching the ball to lengthen the collision time The strong steel struts prevents the collapse of
and hence reduces the impact of the impulsive the front and back of the car into the passenger
force. compartment. Also gives good protection from
a side-on collision.
3. Thick mattresses with a soft surface are used in
events such as the high jump so that the time 3. Padded dashboard , seat and headrest. .
interval of impact on landing is increased, thus To reduce the risk of injury , the interior of the
reducing the impulsive force. car must be made to absorb the impact. The car
can have padded dashboards. The seat is padded
4. Items that are fragile, such as eggs, glass and and the headrest reduces the risk of the
electrical appliances must be packed in passenger’s neck being damaged in near-end
materials that are stiff but compressible. These collision.
materials are able to absorb and reduce
impulsive forces by extending the time interval 4. Collapsible steering wheels
of the change in momentum during an impact Steering wheel of a car is made of material soft
enough to lighten the collision time and to
7.2.4When impulsive forces are beneficial cushion the momentum impact of the driver’s
head during an accident.
1. Hammer and nail are made of metal. When a
hammer hits at a nail , the collision time is 5. Shatterproof windscreen glass .
small and hence the impulsive force is great. So Usage of shatterproof windscreen to prevent
the nail penetrates a wooden material easily. the passengers from being injured by glass
pieces during accident because the glass pieces
2. In the field of construction, a heavy metal pile will not scattered easily .
falls on an iron post. When the metal pile hits
the iron post , the high rate of change of 6. Automatic air bag.
momentum will cause the big impulsive force to Become cushioned to the head and body of the
force the iron post into the ground. passenger during the collision.

3. A pounder and a mortar made from hard stone 7. Seat belts
are used to crush the foodstuffs such as chilli Prevents the passengers from humping forward
and pepper into small pieces by a big impulsive and longer the time for the passenger to hit the
force. dashboard

4. An exponent of karate has the capability to split .
a thick wooden sleb by bringing his hand down 8. Tyre design
hard onto the surface of the wood. The
momentary contact produces a great impulsive The tyre of a car should be broad and with
force which splits the wooden slab. friction grooves so as to control better the
stability and change of momentum of the car.

9. Brake ABS (Antilock brake system)
Avoiding tire rotation stops suddenly when
brakes are applied so that the car is not

skidding.

72

7.4 Newton’s third law of motion
Newton’s third law of motion state ,
‘For every action, there is an reaction which has
same magnitude but acts in opposite direction”
For example, when you skateboard and push
backward, the opposite reaction is to drive the
skateboard forward. A jet moves forward when the
exhaust moves backward. Other examples include
paddling a boat etc.
Example 6
Diagram shows two trolleys M and N has mass of
2 kg and 5 kg respectively.
The velocity of trolley M before hits a stationary
trolley N is 5 m s-1. The time collision is 0.2 s before
the trolley M stops.

(a) Calculate the force exerted by trolley N to
trolley M.

(b) Determine the force exerted by trolley M to
trolley N.

Solution

73

TUTORIAL 7 6 Which of the following statement is true about
impulse and impulsive force except
1 Which one of the following physical quantities
has the same unit as the unit of impulse? A Impulse has the same unit as momentum
B Impulse increases as impact time
A Force B Momentum
C Energy D Power increases
C Impulsive force is change of momentum
2 A trolley of mass 0.4 kg hits a stone wall with D Impulsive force increases as impact time
a velocity 4 ms-1 and bounces back with a
velocity of 3 ms-1. What is the magnitude of the decreases

impulse during collision. 7 Two plasticine balls are dropped into two
surfaces with different hardness. Which of the
A 4.0 kg ms-1 B 0.4 kg ms-1 following physical quantity is same relate to the
C 1.6 kg ms-1 D 2.8 kg ms-1 two surfaces?

3 Diagram shows a ball of mass 0.40 kg A Impulse
hitting a concrete wall with a velocity 15 m s-1 B Impulsive force
C Impact time and impulse
The ball bounces back with a velocity of D Impact time and impulsive force
10 m s-1
8 Which diagram produces the longest time of
impact ?

What is the impulse acting on the ball?

A - 10 kg ms-1 B - 2 kg ms-1
C 2 kg ms-1 D 10 kg ms-1

4 An acrobat weighing 40 kg jumps from a height
place . Before his feet land on the ground , his
velocity is 5 m s-1. What is the impulse on his
legs when he lands on the ground?

A - 200 Ns B - 1 Ns 9 Diagram shows a tennis player ready to hit a
C 1 Ns D 200 N s tennis ball.

5 Diagram shows a graph force against time for
the motion of a car during collision.

What is the impulse acts on the car.

A 100 Ns B 200 Ns
C 500 Ns D 1000 Ns

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Impulsive force is produced when

A the racket is swung at high velocity 14 An athlete of mass 60 kg falling on a mattress in
B the racket is swung backward a high jump competition. He hits the mattress
C the racket hits the tennis ball at a velocity of 10 ms-1 and stop after 0.5 s.
D the racket is gripped strongly What is the magnitude of impulsive force?

10 Which of following action does not show the A 1200N B 300 N
impulsive force used in a useful way? C 3N D 0N

A hitting a nail into a piece of board 15 A boy kicks a stationary ball of mass 0.15 kg. If
B colliding between two vehicles the ball moves forward at a velocity of 60 ms-1
C hitting a ball with a racket and the time interval of contact of the boy’s
D kicking a ball in a game foot on the ball is 5 ms, what is the impulsive
force of the ball?

11 Which of the following is not related to A 300 N B 600 N
impulsive force? C 1800 N D 6000 N

A High jumper's leg is injured when landing 16 A golf ball of mass 0.05 kg is hit with a force
without used mattress 4500 N. The time interval of interaction
between the golf ball and the club is 0.3 ms.
B Hockey ball is hit by a player with a What is the velocity of the golf ball immediately
hockey stick after it was hit.

C A bicyclist descends a steep hill
D Wood pieces broken by a karate expert

12 An object of mass 0.4 kg is pulled with a force A 5 ms-1 B 10 ms-1
of 20 N for 10 s . How much is the impulse C 27 ms-1 D 33 ms-1
upon the object?
17 The following graph shows the impulse – time
graph for a tennis ball is hit by a racket.

A 8 Ns B 80 Ns
C 200 Ns D 250 Ns

13 Diagram shows a camera being pulled off and What is the impulsive force experienced by the
dropped from a drone while a man controlled it. ball?
The mass of the camera is 0.02 kg and moves
with a velocity 15 m s-1 at the moment before
touching the ground. The camera stops 0.05 s
after touching the ground.

A 100 N B 250 N
C 500 N D 750 N

18 The diagram shows an athlete performing the
high jump.

What is the magnitude of the impulse force

acted on the camera?

A 0.015 N B 0.05 N

C 6.0 N D 37.5 N What is the function of the mattress?

75

A To reduce the collision time between the 22 The advantage of using the bumpers fitted with
athlete and the mattress and incraese shock absorbers in a car is
impulsive force
A to ensure that the car will decelerate in an
B To reduce the collision time between the accident
athlete and the mattress and reduce
impulsive force B to minimised the impulsive force during an
accident
C To increase the collision time between the
athlete and the mattress and incraese C to ensure that the car is not smashed in an
impulsive force accident

D To increase the collision time between the D to minimized the time of impact
athlete and the mattress and reduce
impulsive force 23 Which of the following is not a safety feature
installed in a vehicle ?
19 A football goalkeeper catching a fast - moving
ball by moving his hand backwards while A Engine capacity
another goalkeeper catching a fast - moving ball B Automatic air bag
without moves his hand backwards C Collapsible steering wheels
Which of the following explains the magnitude D Shatterproof windscreen glass
of the impulsive force on the hands when
catching the ball? 24 The use of antilock brake systems (ABS) is to

moves his hand without moves A avoid the tyre stop rotating immediately
when the brake is applied and avoid the
backwards his hand vehicle skidding

backwards B reduce time of impact of the car while the
brake is applied and avoid the car skidding
A Small Small
C reduce impulsive force while the car
B Small Big brought to rest

C Big Small D prevent the collapse of the front and back
of the car
D Big Big
25 Which one the following safety features in cars
20 Diagram shows a parachutist landing with his is not true regarding the impulsive force?
legs bent.
A Air bag
Why does the parachutist bend his legs? ? B Seatbelt
C Headrest
A To lengthen the time of impact of his feet D Shatter-proof windscreen
with the ground
26 Diagram 26 shows a watermelon being dropped
B To shorten the time of impact of his feet from rest onto a brick and the watermelon
with the ground cracks after an impact .

C To lengthen the time of falling to the Diagram 26
ground

D To shorten the time of of falling to the
ground

21 Why are the front and rear sections of a car
designed to crumple easily?

A To reduce impact time
B To increase momentum
C To reduce impulsive force
D To increase friction

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(a) Name the force involved during the (a) What is meant by impulsive force?
impact. …………………………………………………
…………………………………………..... [1 mark]
[1 mark]
(b) Based on Diagram 27.1 and Diagram 27.2,
(b) Give one reason why the watermelon
cracked after the impact. (i) Compare the impulsive force produced by
…………………………………………… the two surfaces.
[1 mark] ……………………………………………
[1 mark]
(c) The mass of the water melon is 2.5 kg and
it takes 0.6 s to reach the brick and the (ii) Compare the time of collision between the
impact time is 0.02 s. glass cup and the two surfaces
Calculate ………….…………………………………
(i) the velocity of the watermelon just [1 mark]
before the impact .
(iii) State the relationship between the
[2 marks] impulsive force and the time of collision.
(ii) the force that you named in (a) ……………………………………………
………………………................................
[2 marks] [1 mark]
(d) Give one suggestion how you would avoid
(c) Mark with (√ ) for the correct statement about
the watermelon from cracking when the impulse of the glass cup in the both
dropped from the same height. situations
……………………………………………
The impulse in Diagram 27.1 < 27.2
[1 mark]
27 Diagram 27.1 and 27.2 show two glass cups being The impulse in Diagram 27.1 > 27.2

dropped from rest onto a carpet surface and a The impulse in Diagram 27.1 = 27.2
marble tile surface. The quantity physics involved [1 mark]
when the glass cups hit the surfaces are impulse
impulsive force. (d) Diagram 27.3 shows a pile hammer used in
driving a pile into the ground at aconstruction
site.

Diagram 27.1 Diagram 27.3
Diagram 27.2 Explain how a large force is produced by the
pile hammer in driving the pile into the ground
without change the mass of the pile and the pile
hammer.
…………………………………………………
…………………………………………………
…………………………………………………
…………………………………………………

[2 marks ]

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28 Diagram 28.1 shows a car of mass 800 kg 29 (a) Diagram 29.1 shows a softball player
moving at 20 m s-1 collides with a truck of continues his throwing after the ball
mass 1200 kg which is traveling in the same moves forward. This action is called
direction at 10 m s-1. ‘follow through’ .
Diagram 28.2 shows , the two vehicles become
interlocked and move together with a common
velocity , v , after the collision and the time
collision is 0.4 s

Diagram 28.1 Diagram 29.1

Diagram 28.2 Explain why the ‘follow through’ technique is
used.
(a) Calculate the velocity , v , of both vehicles
immediately after collision. [ 4 marks]

[2 marks] (b) A sprinter pressing on a pair of starting
(b) Calculate block to start running. Mass of the
sprinter is 70 kg.
(i) the force exerted on the car by the The sprinter exerting a force of 550 N on
truck. the starting block for 300 ms.
Calculate the speed of the sprinter when he
[2 marks] starts to run.
(ii) the force exerted on the truck by the [ 3 marks]

car. (c) Diagram 29.2 show a log truck.

[2 marks] Diagram 29.2
(c) Compare the answer in b(i) and b(ii) and
You are required to give some suggestions
state the law involved. about design of the truk to deliver log
……………………………………………. safely.
…………………………………………… Your sugestions should be based on the
…………………………………………… following aspects:
………………………................................. - The design of bumper
- The type of brakes
[2 marks] - The number of tyres
(d) Explain why the collision causes serious - The chains used
- The distance between the trailer and
damage to the car compare to the truck..
……………………………………………… the tractor
……………………………………………… [ 10 marks]
………………………………………………

[2 marks]

78

Solution

LESSON 8 : WEIGHT The difference between mass and weight

Gravitational field strength , g Mass Weight
Is the quantity of matter Is the gravitational
The gravitational field strength , g is defined as in an object force
force per unit m. The S.I units is Kilogram The S.I. units is
Newton
g=F A base quantity and A derived quantity
m scalar quantity and vector quantity
Is fixed at all places Varies from place
The unit of the gravitational field strength , g to place
is N kg-1 Measured with an inertia Measured with a
The gravitational field strength , g of the Earth is 9.81 balance or a chemical spring balance
N kg-1 or ≈ 10 N kg-1 balance
The gravitational field strength , g of the Moon is
only 1.6 N kg-1 or 1 of the gravitational strength of

6
Earth.

Mass and weight

Mass is the quantity of matter in an object

Weight is the gravitational force exerted on it .

From F = ma , a = g

Hence W = mg

The S.I. units of weight is Newton (N)

Example 1

An astronaut took back a moon rock and found that
the weight of the rock when weighed on the earth
was 50 N
[ The acceleration due to gravity on the moon = 1 on

6
the Earth ]

Calculate ,
(a) the mass of the rock on Earth
(b) weight of the rock on the Moon

79

TUTORIAL 8 6 Which of the following is true about weight?

1 The gravitational field strength is A is a scalar quantity
B is measured in unit of kilogram
A Force per acceleration C is a based quantity and also is a vector
B Force per volume
C Force per weight quantity
D Force per mass D is depends on the gravitational field

2 Which of the following phsical quantity has strength
the same unit with the gravitational field
strength? 7 Which comparison is true about weight of an
object at Equator , at North Pole and on the
A Gravity Moon’s surface?
B Gravity field
C Gravitational force A Equator > North Pole > Moon’s surface
D Gravitational acceleration B North Pole> Equator > Moon’s surface
C Moon’s surface> Equator > North Pole
3 Which statement is correct about the D North Pole > Moon’s surface >Equator
earth gravitational force?
8 Karim’s weight on Earth is 800 N
A Not all objects on the earth are influenced by What will happen to his weight on the
the earth gravitational force moon?

B The earth gravitational force is stronger A Increased B Deccreased
when an object is further away from the C Unchanged D Becomes zero
centre of the earth
9 Weight of an object at position P is W.
C The acceleration of all falling objects is
influenced by the earth gravitational force Weight the object at position Q is W .
4
D The earth gravitational force not depends on
the mass of an object What is the ratio of the gravitational
acceleratioan at P to at Q.
4 Which of the measurement measure weight
of an object. A 1:1 B 2:1
C 1:4 D 4: 1
5 Which the following is true about mass.
10 Weight of an object at the moon surface is
A Mass is a vector quantity 50 N. What is the mass of the object at the
B Mass is weight of an object surface of Earth.
C Direction of mass always to the centre of [ The acceleration due to gravity on the moon =

Earth 1 on the Earth ]
D Mass an object at any places on the Earth 6

always same A 300 kg B 30 kg
C 8.33 kg C 0.83 kg

11 An astronaut’s boots weight 100 N on Earth
where the acceleration of the free fall is 10 ms-2.

How much will they weight on Mars where the
acceleration of free fall is 4 ms-2 ?

A 25 N B 40 N
C 100 N D 200 N

80

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