1. Chapter 9 - Collisions Momentum and force Conservation of momentum
Impulse
Inelastic collisions
Perfectly inelastic
Elastic collisions in one dimension
moving target
stationary target
Elastic collisions in two dimensions
Center of mass

2. Momentum Linear momentum
quantity of motion
Product of mass times velocity
The time rate of change of the momentum of an object is equal to the resulting net external force acting on the object.

3. Conservation of momentum
If there are no external forces
We say momentum is conserved
For two particles we write:

4. Problem 1 Inelastic Collision
Car 1 with a mass of 1000 kg and a velocity of 20 m/s runs into the rear end of a larger car with mass of 2000 kg initially at rest. The two cars stick together.
Find the final velocity
Find the energy lost in the collision

5. Applications of conservation of momentum

6. Impulse

7. Average force during a collision

8. Problem 2
A ball (mass = 0.1 kg) is released from 2 meters and rebounds to 1.5 meters. What is the Impulse of the floor on the ball

9. The ballistic pendulum
If you can measure M, m, and h,
how fast was the bullet traveling?

10. Elastic vs. inelastic Momentum is conserved in all collisions.
Elastic collision – Kinetic energy is also conserved.
Inelastic collision – Kinetic energy is not conserved.
Perfectly Inelastic – Objects stick together after the collision.

11. Elastic collisions
Momentum:
Energy:

12. Elastic collisions

13. Elastic collisions – equal mass

14. Elastic collision – mass at restv1 m1 m2

15. Elastic collision – general casev1 v2 m1 m2

16. Problem 3 Elastic Collision
A 3 kg mass moving at 8 m/s in the x direction collides with a 5 kg mass initially at rest
Find the final velocity of each mass.
Find the final kinetic energy of each mass m1 m2

17. Elastic collision in two dimensions
m2 is at rest

18. Problem 4
Two shuffleboard disks of equal mass are involved in a elastic glancing collision. One disk is initially at rest and is struck by the other which is moving with a speed of 4 m/s. After the collision, the incident disk moves along a direction that makes an angle of 30o with its initial direction of motion. The originally stationary disk moves in a direction perpendicular to the final direction of motion of the other disk. Find the final speeds.
30o
4 m/s
60o