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Converted document IMPACT

IMPACT

When two bodies collide, they are said to impact. The duration of impact is usually quite short. As an example, consider two billiard balls a moment before collision. Both balls have some component of their velocity vector pointed into the other. An instant later, the balls have already struck eachother and are now traveling in seperate directions. The impact is what occurs for the duration between just before and after the collision.
In general, the process of impact entails several steps:
  • Two (or more) bodies meet with non-zero kinetic energy.
  • This energy is transformed from kinetic to work done on the bodies by restitution forces.
  • The bodies deform under the work performed on them, storing the energy as elastic potential energy.
  • The potential energy is released as the bodies restore their shape (perhaps to their original shape, for purely elastic collisions).
  • The potential energy is converted back into kinetic energy, as the bodies travel in separete directions.
As coefficient of restitution may be defined to describe this process. It is a handy tool used to describe impact, as it only requires knowledge of initial and final velocities and does not require any information about the deformation.
e = (v2, final − v1, final)/(v2, initial − v1, initial)
There are two very important cases to examine. These represent limiting cases, one where e = 1 and the other is when e = 0.

ELASTIC COLLISIONS
Elastic collisions occur when the coefficient of restitution, e, is equal to 1. When this occurs, no energy is lost to heat in the process of the collision. Of course, this is never perfectly true (all real collisions convert some kinetic energy into heat), however it is a great model for some bodies such as billiard balls.

INELASTIC/PLASTIC COLLISIONS
When the coefficient of restitution, e, is equal to 0, a collision is said to be inelastic, or plastic. When this occurs, the maximum possible energy has been converted into heat such that no potential energy is recovered from the work done by deforming the body. Without any energy left to restore the bodies shapes, the two bodies stick together and move with the same velocity.