1. Aim: How do we use conservation of momentum to analyze collisions?

2. Conservation of Momentum
If momentum is conserved in a collision, this means that the total momentum of the system before the collision is equal to the total momentum of the system after the collision. Pbefore = pafter

3. Proving that Momentum is Conserved
How can we use the Impulse-Momentum Theorem to prove that Momentum is Conserved?

4. Problem 1: Momentum of a system
An 1875 kg car going 23 m/s rear ends a kg compact car going 17 m/s on ice in the same direction. What is the total momentum of the system before the collision occurs? After the collision occurs?
pbefore=pafter=m1v1+m2v2=1875kg(23 m/s)+(1025kg)(17 m/s)
= =60,550 kg m/s

5. Problem 2: Momentum of the System
A 0.50 kg ball is traveling at 6.0 m/s and collides head on with a 1.00 kg ball moving in the opposite direction at 12.0 m/s. What is the total momentum of the system? psystem=m1v1+m2v2=0.5kg(6m/s)+1kg(-12m/s) psystem =-9kg m/s

6. Elastic Collision
A collision in which the two objects do not stick together.

7. Inelastic Collision
A collision in which objects stick together

8. Identifying collisions
A skater is using very low friction rollerblades. A friend throws a frisbee at her, along the the straight line along which she is skating. Describe each of the following events as elastic or inelastic. -She catches the Frisbee and holds it. Inelastic -She catches the Frisbee and immediately throws it back with the same speed (relative to the ground) to her friend. Elastic

9. One Dimensional Collisions
An 1800 kg car stopped at a traffic light is struck from the rear by a 900 kg car and the two become entangled. If the smaller car was moving at 20 m/s before the collision, what is the speed of the entangled cars after the collision?
pbefore = pafter
m1v1i +m2v2i=(m1+m2)vf
900kg(20 m/s) kg(0m/s)=(900kg kg)vf
Vf = 6.7m/s

10. One Dimensional collisions
2. A railroad car of mass 2.50 x 104 kg is moving with a speed of 4.00 m/s. It collides head on and couples with another railroad moving at 2 m/s in the opposite direction.
With what speed will the two cars move together after the collision?
pbefore=pafter
m1v1i+m2v2i=(m1+m2)vf
(2.5x104 kg)(4m/s)+(2.5x104kg)(-2m/s)=(2.5 x 104 kg x 104 kg)vf
Vf = 1 m/s

11. Explain this
Since the total momentum is conserved, when the dropped block falls on the cart the mass increases so the velocity must decrease.