Collisions: Elastic and Inelastic

Although the momentum of individual objects may change during a collision, the total momentum of all the objects in an isolated system remains constant.
An isolated system is one on which the net force from external sources is zero. For example, a hockey puck sliding along the ice is an isolated system: there is a gravitational force down on it, but also a normal force from the ice up on it; the two external forces add up to zero.
Collisions may be separated into several categories, some of which are easier to solve than others:
- Completely inelastic collisions involve objects which stick together afterwards. Kinetic energy is not conserved, but the result is easy to calculate via conservation of momentum.
- Partially inelastic collisions involve objects which separate after they collide, but which are deformed in some way by the interaction. Kinetic energy is not conserved. It's not easy to figure out what happens afterwards, because there are many possible solutions which satisfy conservation of momentum.
- Elastic collisions involve objects which separate after they collide, and which are not changed at all by the interaction. Billiard balls, ping-pong balls, and other hard objects may collide elastically. Kinetic energy is conserved in elastic collisions. One must use both conservation of energy and conservation of momentum to figure out the motions of the objects afterwards. This usually involves solving 2 equations for 2 unknowns.

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