Both objects move independently at their respective velocities

LESSON 2.5 Momentum after the collision.

Characteristics :
• Momentum is conserved.
Definition and SI unit of momentum • Kinetic energy is conserved.
a) Momentum is defined as the product of • Total energy is conserved.
Total Momentum Before = total momentum After
P = mv
_______________and _____________
Formula : m1u1 + m2u2 = m1v1 + m2v2
b) SI unit : kg ms-1
c) vector quantity (magnitude & direction).
Example activity :
Example 1

A steel ball of mass 5.0kg rolls on the floor with a velocity of 1.2
ms-1. What is its momentum?

Solution

Steel ball moving Snooker game

Example 2 Example 3

A tennis ball of mass 1 kg moves with a velocity 2ms-1 hits a wall A truck with a mass of 1500 kg moving at a speed of 30 ms-1
and rebounds along the initial direction with a velocity 1ms-1. collides with a car of mass 1200 moving at a speed 20 ms-1 in
Calculate the same direction. After collision, the car moves with a
I. The initial momentum velocity of 25 ms-1 in the same direction. Calculate the velocity
II. The final momentum of the truck after collision.
Solution
Solution

Principle of Conservation of Momentum

a) The total momentum in a closed system of object is

constant. Example 4
b) The total momentum before the collision is equal to the total
momentum after the collision if no external force acts on
the system.

Types of collision
R S
There are two types of collision, that is
i. Elastic collision ii Inelastic collision Car R of mass 1000 kg moving at 20 ms-1 collides with car S of
mass 1200 kg moving at 15 ms-1.
i) Elastic Collision If the collision reduces the speed of car R to 8 ms-1, what is the
speed of car S after the impact?

Solution

Before collision After collision

ii) Inelastic Collision iii) Explosion

Before collision After collision

The two objects combine and move together with a common

velocity after the collision.
Characteristics :
• Momentum is conserved.
• Kinetic energy is not conserved. Before explosion both objects stick together and at rest. After
• Total energy is conserved. collision, both objects will move in opposite directions.

Total Momentum Before = total momentum After Total momentum Total momentum
before explosion is after explosion :
Formula : m1u1 + m2u2 = (m1+ m2) v zero m1v1 = - m2v2

Example activity : From the law of conservation of momentum:

Total Momentum Before = total momentum After

Formula : 0 = m1v1 + m2v2

m1v1 = - m2v2

-ve sign means opposite direction

Example activity :

Example 5

Diagram above shows a car of mass 1000 kg moving at 20

ms-1 hits the back of a lorry of mass 5000 kg which is packed by
the road side. If the car sticks to the lorry after the collision, what
is their common velocity?

Solution
1) When a rifle is fired, the bullet of mass m, moves with a high Example 9
velocity, v.
2) This creates a momentum in the forward direction. The diagram shows tow identical trolleys touching each other
3) From the principle of conservation of momentum, an equal on a smooth horizontal surface. (crk)
but opposite momentum is produced to recoil the riffle
backward.

Example 6

A bullet of mass 5 g with velocity of 150 ms-1 hits a 1.5 kg of What is the total momentum of the trolleys after separation?
stationary ice cube on a smooth surface. The bullet passes
through the ice cube and travels with velocity of 70ms-1. What is Solution
the resulting velocity of the ice cube?

Example 10

A car travels with velocity 32ms-1 collides head on with moving

Solution at velocity 17ms-1. If the masses of the car and the lorry are
1200 kg and 5500 kg respectively, calculate
(a) The momentum of the car before collision
(b) The total momentum
(c) The final velocity of the two vehicles after collision is the
collision is inelastic.

Example 7

A trolley of mass 3kg is moving with velocity 2 ms-1 and collides

with another stationary trolley B. After the collision, trolley A
moves with velocity 0.4 ms-1. If the collision is elastic, calculate
the momentum of trolley B after collision. Solution

Example 11
Solution
A trolley P of mass 2 kg travels at a speed of 3ms-1 towards
another trolley q of mass 1 kg traveling at a speed of 1 ms-1 in
opposite direction as shown in the diagram. (crk)

Example 8

A bullet of mass 10 g is fired from a gun of mass 490 g. The

bullet leaves the gun with a speed of 120 ms-1. Find the initial a) Find the velocity of Q if the velocity of P is 1 ms-1 after
speed of recoil of the gun. collision.
b) If the trolleys collide and move with the same velocity after
Solution collision, find the magnitude of the velocity of trolley P
after collision.

Solution
 The Applications of the Principle of Conservation of
Momentum.
Example 12
Rocket Engine
The diagram shows a strip of ticker-tape before and after the
collision of trolley A and B which was initially at rest. Trolley A
and B sticks together after collision.

a) Calculate the
(i)velocity of trolley A before collision,
(ii)
velocity of trolley A and B after collision.
b) The momentum of the trolleys after collision is 12 kg ms-1.
What is the total mass of the trolleys?
c) Find the mass of trolley A and trolley B
1. Mixture of hydrogen and oxygen fuels burn in the
combustion chamber.
Solution 2. Hot gases are expelled through the exhausts at very high
speed .
3. The high-speed hot gas produce a high momentum
backwards.
4. By conservation of momentum, an equal and opposite
momentum is produced and acted on the rocket, pushing
the rocket upwards.

Jet engine
Example 13

As shown in the diagram, a bullet of mass 50 g is fired

horizontally from a gun of mass 2 kg.

a) If the gun recoils at a velocity of 5 ms-1 after the bullet is fired,

find the velocity of the bullet.
1. In the jet engine, air is sucked into the jet engine to be
b) The bullet then travels horizontally into a target of mass 4 kg.
compressed and is heated up in the compressor.
It sticks in the target and moves together with a velocity, v.
2. The compressed air is then mixed with fuel which is
Find the magnitude of velocity, v.
sprayed so that it starts to burn.
3. The exhaust chamber emits exhaust gases with a high
Solution
velocity.
4. This high-velocity hot gases are ejected from the
back with high momentum.
5. This produces an equal and opposite momentum to propel
the jet plane forward.
 TUTORIAL 2.5
What is the recoil velocity of the leaf?
1. Diagram shows two trolleys, P and Q, on a frictionless A 0.05 ms-1 B 0.2 ms-1
plane. Trolley P moves and collides with the stationary C 5.00 ms-1 D 20.00 ms-1
trolley, Q.
4. The diagram describes the motion of two bodies
before and after collision.

Which of the following statements is true?

What is the value of v ?
A The collision is an elastic collision
B Both trolleys do not undergo changes in momentum A 1.3 ms-1 B 2.6 ms-1
C The total momentum before and after the collision C 4.0 ms-1 D 5.0 ms-1
is the same
D The total kinetic energy before and after the 5. Diagram shows two trolleys each of mass 1 kg
collision is conserved. before and after collision. The initial velocity of
trolley A and trolley B are 6 m s-1 and 4 m s-1
2. Diagram shows two identical balls, P and Q, moving respectively. After collision, both trolleys move
towards each other with a velocity of v and 2v together in the direction of their initial velocity.
respectively. The collision between the two balls is an
elastic collision

Which statement is correct about the elastic collision? What is the velocity of both trolleys after collision?
A The momentum of the ball P before the collision is A 1.0 ms-1 B 2.0 ms-1
equal to the momentum of ball Q before the C 5.0 ms-1 D 10.0 ms-1
collision.
B The total momentum before the collision is equal to
6. A man of mass 50 kg stands on a stationary boat of
the total momentum after the collision.
C The kinetic energy of ball P before the collision is mass 25 kg. Figure shows him jumping out of the
equal to the kinetic energy of ball Q before collision. boat on to a jetty at a velocity 4 ms-1
D The total kinetic energy before the collision is not
equal to the total kinetic energy after the collision.

3. Diagram (a) shows a frog of mass 200 g on a

leaf of mass 50 g on the surface of a pond.
Diagram (b) shows the frog leaping away from
the leaf with a velocity of 5 m s-1.
7. The diagram shows a velocity-time graph for the motion
of an object.
 The momentum of the object is constant from Which physical quantity becomes smaller after the
A 0 s to 3 s B 3 s to 6 s collision?
C 6 s to 8 s D 0 s to 8 s A Mass B Velocity
C Momentum D Acceleration
8. Diagram below shows 5 steel balls of the same mass: A,
B, C, D, and E 11 Diagram 3 shows three identical coins, P, Q and R, at
rest on a horizontal surface.

What will happen when P collides with Q?

What will happen if ball A is pulled aside and let go P Q R

with a velocity of v? A Moves Stationary Moves
A Velocity of ball A decreases while the velocity B Stationary Stationary Moves
of ball E increases. C Moves Moves Stationary
B Balls B, C, D and E moves with the same velocity, D Moves Stationary Moves
v.
C Ball A becomes stationary while ball E moves
with the same velocity, v. 12 Figure below shows a pile driver at a velocity of
D All balls move with the same velocity, v. 20 ms-1 driving a foundation pile into the ground.
The pile driver and the foundation pile move
9. The diagram below shows a ticker tape produced in together after hitting it.
a non-elastic collision between a trolley P which is
moving and a trolley Q which is stationary.

Determine the velocity of the foundation pile

immediately after being hit by the pile driver.
The frequency of the ticker timer used is 50 Hz and A 0.4 ms-1 B 0.43 ms-1
the mass of trolley P is 2.0 kg, calculate the mass of C 4.28 ms -1 D 14 ms-1
trolley Q. E 30.0 ms -1

A 0.5 kg B 1.5 kg
C 2.0 kg C 2.5 kg 13. A bullet of mass 10 g fired from a riffle of mass 1.5 kg.
E 3.0 kg The velocity of the bullet and the riffle are 250 m s–1 and
1.67 m s–1. Calculate the momentum of the bullet and
Diagram shows block L moving towards a stationary the riffle.
block M on a smooth surface. After collision the two
blocks move together.
 Solution :

14 A lorry of mass 1 000 kg is moving with a velocity 5 ms-1 collides with a car of mass 800 kg and moves with 2 ms-1. After the
collision, the car moves with velocity 3 ms-1. What is the velocity of the lorry after the collision?
Solution :

15 Solution :

Calculate the velocity of ball B after collision.

16 Solution :

Calculate the common velocity, v, of the fishes after collision.

17 Solution :

The diagram shows a man jumps out from a boat. Calculate

the velocity of the boat.
18 Figure shows a truck colliding with a stationary’ car. After the collision, the truck and car moved in the same
direction. (3M)
 a) What is the meaning of momentum?

___________________________________________________________________________________

b) Calculate the momentum of truck before collision.

c) Calculate the velocity, v2 of the car after the collision.

d) Name the principle used in calculation at 18(c).

___________________________________________________________________________________
e) If the time of collision, t = 0.08 s, calculate the impulsive force applied by the truck to the car.

f) Name one application in space exploration using the principle in 18 (d).

___________________________________________________________________________________

19 Diagram shows a cannon of mass,M, 1200 kg fires a

cannonball of mass,m, 4 kg. The speed of the
cannonball as it leaves the cannon is 60 ms-1.
a) What is meant by mass?

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b) Base on Diagram above

i) What is the relation between the backward momentum and the forward momentum?

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ii) Write the equation to show the relationship in (b)(i) ?

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c) Calculate the initial velocity of the recoil cannon when the cannonball is fired.

20 Diagram shows the motion of a bowling ball and a bowling pin before and after the collision.
Table 5 shows the momentum of the bowling ball and
bowling pin before and after the collision.
Momentum before Momentum after
collision (kgms-1) collision (kgms-1)
Bowling Bowling Pin Bowling Bowling Pin
Ball Ball
2.5 0.0 2.5 0.0
 a) What is the meaning of momentum?

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b) Based on Diagram above and table 5, determine the total momentum of the bowling ball and the bowling pin
(i) before the collision

(ii) after the collision

c) Compare the answer in 20(b)(i) and 20(b)(ii).

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d) (i) Based on the answer in 5(b) and 5(c), state a conclusion about the total momentum.

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(ii) Name the physics principle involved in 20(d)(i).
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(iii) State one condition needed in order to apply the physics principle stated in 20(d)(ii)

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21 Diagram 7.1 shows a rocket which is used to launch a spacecraft that carries supplies to the International Space
Station. The rocket engine works on the principle of conservation of momentum. （sarawak）

a) Based on the principle stated, explain how the rocket produces a

thrust to move upwards.

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b) Diagram 7.2 shows the apparatus to launch a water rocket at a competition in school. The water rocket
moves vertically upwards with an initial velocity of 15 m s–1. Calculate the maximum height of the water rocket.
Solution :
 c) Suggest modifications that can be made to the water rocket in 7(b) so that it is more stable and can fly higher
based on the following aspects:
(i) Shape of the water rocket

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Reason

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(ii) Pressure of air inside the water rocket

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Reason

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(iii) Additional structure

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Reason

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22 Diagram 22.1 shows the structure of a rocket.

a) (i) What are the principles of physics applied to rocket?

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b) (ii) Explain in term of the principle of conservation of momentum, how the rocket
is launched.

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b) Study the specification of all four jet engines. Explain the suitability of each design and specifications.
Determine the most suitable jet engine to be used in the aircraft. Give reasons for your choice.
Design Reason