Conservation of Linear Momentum

1. CONSERVATION
OF LINEAR
MOMENTUM
Quarter 4: Lesson 3

2. WHAT IS
CONSERVATION?

3. THE BILLIARD BALL

4. THE BILLIARD BALL
What do you think will happen to the momentum of a billiard ball if it collides with
another billiard ball?

5. MOMENTUM IS CONSERVED
How do we know if there is conservation of momentum?

6. If the value of mass and the
velocity remain the same, the
momentum value will be
constant.
The momentum of an object or
set of objects (system)
remain the same if it is left
alone.

7. LAW OF CONSERVATION OF
MOMENTUM
In a closed and isolated system, the total momentum of the objects
before and after the collision are equal.

8. • The law of conservation of
momentum states that the total
momentum of a system remains
constant if no external forces
(such as: air resistance, friction,
gravity, and applied force) act on
the system.
• Thus, momentum is always
conserved in all types of collisions
as long as the system is isolated
from external forces.

9. NEWTON’S 3RD
LAW OF
MOTION
“For every action, there is an equal yet opposite reaction.”

10. THE TWO TYPES OF
COLLISION
COLLISION- Is an encounter between two objects resulting in
exchange of impulse and momentum.
“In any collision there must be conservation of linear momentum.”
Kinetic energy may be lost during collisions when:
• It is converted to heat or other forms like binding energy, sound,
light, etc.
• It is spent in producing deformation or damage such as when
two cars collide.

11. 1. ELASTIC COLLISION
One in which the total kinetic energy of the system does not
change, and colliding objects bounce off after collision.
Both momentum and kinetic energy are conserved.

12. 2. INELASTIC COLLISION
• One in which the total kinetic
energy of the system
changes (i.e. converted to
some other form of energy.)
• Objects that stick together
after collision is said to be
perfectly inelastic.
Momentum is conserved, but kinetic energy is not conserved (some energy is
transformed into other forms, like heat or deformation).

13. SAMPLE PROBLEM
Two ice skaters stand together. They “push off” and travel directly away from each
other, the boy with a velocity of 1.50 m/s. If the boy weights 75 kg and the girl, 50kg,
what is the girl’s velocity after they push off?
-m1v1= m2v2
-(75kg)(1.50m/s)=(50kg)vgirl
-112.5 kg.m/s=(50kg) vgirl
=
vgirl= -
2.25m/s
Given:
m1=75 kg
v1=1.50 m/s
m2=50 kg
v2=?

14. SAMPLE PROBLEM
A 0.2-kg billiard ball traveling at 1.5 m/s on a table undergoes a collision with another
0.15-kg billiard ball travelling at 2.0 m/s. The two cue balls stick together after
collision. What is the velocity of the combined balls after the collision?
m1v1+ m2v2=( m1m2)v′
(0.2 kg)(1.5 m/s)+(0.10 kg)(3.0 m/s) = (0.30
kg) v′
0.30 kg.m/s+0.3 kg.m/s=(0.30 kg) v′
=
v′= 2.0m/s
Given:
m1=0.2 kg
v1=1.5 m/s
m2=0.15 kg
v2=2.0 m/s
v’=?

15. TRY THIS!
1. A 10 kg billiard ball traveling at 3.5 m/s on a table undergoes a collision with
another 10 kg billiard ball travelling at 2.0 m/s. The two cue balls stick together
after collision. What is the velocity of the combined balls after the collision?
2. Two friends are playing with their skateboards. They “push off” and travel
directly away from each other, the boy with a velocity of 3.6 m/s. If the boy
weights 40 kg and the girl, 30kg, what is the girl’s velocity after they push off?