### Collisions and Elasticity

During a collision the objects involved generally apply equal-and-opposite forces on one another for a short time. There are usually no external forces, so the momentum of the system of objects is conserved.

Generally, momentum is conserved in all types of collisions.

There are four classes of collisions based on what happens during the collision and, in particular, what happens to the total kinetic energy of the system.

The elasticity of the collision is related to the ratio of the relative velocities of the two colliding objects after and before the collision:
k = |
 v2f - v1f v1i - v2i
|

The elasticity is related to the type of collision as follows:

Type of CollisionDescriptionElasticity
Super-elasticKinetic energy is larger after the collision (e.g., an explosion) k > 1
ElasticKinetic energy is conserved k = 1
InelasticKinetic energy is smaller after the collision k < 1
Completely inelasticKinetic energy is smaller, and the objects stick together, after the collision. k = 0

Consider one of the collisions involving the moving 5m cart colliding with the stationary cart of mass m. Which of the two carts experiences the largest average force during the collision? Consider the magnitude of the forces only.

1. The cart of mass m experiences a larger magnitude force
2. The cart of mass 5m experiences a larger magnitude force
3. The carts experience forces of equal magnitude

Consider now all three of the collisions where the cart in motion before the collision has a mass of 5m and the stationary cart has a mass of m.
The elastic collision (k=1) is collision A.
The inelastic collision (k = 0.5 in this case) is collision B.
The completely inelastic collision (k = 0) is collision C.

Assuming the time the carts are in contact with one another is the same in each case, rank the collisions based on the average force experienced by the cart of mass m during the collision.

1. A=B=C
2. A>B=C
3. A=B>C
4. A>B>C
5. C>B>A
6. C>B=A
7. C=B>A