1. Lesson 10: Conservation of Momentum
Objective:
S4P Solve problems using the impulse-momentum equation and the Law of Conservation of Momentum.

2. The Law of Conservation of Momentum
In the 17th century, Newton and others had measured the momentum of colliding objects before and after collision, and had discovered a strange phenomenon: the total momentum of the colliding objects was the same after the collision as it was before. Newton expressed this relationship as the Law of Conservation of Momentum:
The total momentum of a closed, isolated system does not change.

3. The Law of Conservation of Momentum
A group of objects involved in a collision is called a system. A system:
May contain any number of objects
Is considered closed provided that no object leaves or enters the system
Is considered isolated if no net external force acts on it

4. The Law of Conservation of Momentum
To picture the difference between an external force and an internal force, consider the difference between:
Sitting inside a car pushing on the dashboard (internal)
Standing outside the car pushing against the bumper (external).
Only the external force can produce a change in the momentum of the car.

5. Conservation of Momentum in One Dimension: Collisions
When analyzing the momentum in collisions, we say that:
Total initial momentum = total final momentum
There are 3 types of collisions:
Elastic Collisions
Inelastic Collisions
Explosions

6. Conservation of Momentum in One Dimension: Elastic Collisions
When two objects collide and then move along on their separate ways after the collision.
An example would be two billiard balls colliding.
Video

7. Conservation of Momentum in One Dimension: Inelastic Collisions
Two objects collide and stick together.
For example, train cars coupling
Video

8. Conservation of Momentum in One Dimension: Explosions
Two objects are initially stuck together and then separate in an “explosion”.

9. Example 1:
A mass of 40.0 kg is initially at rest. This mass now explodes into two pieces so that one piece of mass 10.9 kg moves to the right at m/s. What is the final velocity of the second piece?

10. Conservation of Momentum in Two Dimensions: Glancing Collisions
Conservation of momentum in two dimensions occurs in situations called glancing collisions.
This is when the objects are deflected in more than one dimension.
An example would be a curling shot. The stones that collide are moved at various angles because the collision is not head on.

11. Example 2:
During a curling math, a curler throws a rock with a mass of 20.0 kg, with a speed of 2.00 m/s. This rock collides head-on with the stationary target stone, which also has a mass of 20 kg. After the collision, which lasted s, the first rock is stationary.
a) What is the final velocity of the target stone
b) What is the change in momentum of the target stone?
c) What impulse was applied to the target stone?
d) What was the force of interaction between these two rocks?

12. Example 3:
A train car of mass 1250 kg is travelling at 14.0 m/s [W]. It collides head-on with a train car of mass 5680 kg travelling at 10.0 m/s [E]. After the collision, the two vehicles proceed, stuck together, sliding along the icy tracks.
a) What is the final velocity of these two cars locked together?
b) What is the change in momentum of the second car?
c) What is the change in momentum of the first car?
d) What impulse is applied to the second car during the collision?
e) What impulse is applied to the first car during the collision?
Let east be the positive direction. Let the first car be mass 1 and let the second car be mass 2.