Elastic and Inelastic Collisions

Guide 9-1b. Elastic and Inelastic Collisions

It's important to understand the conditions under which particular conservation laws can be used. Here are the conditions for energy and momentum conservation.

Energy: The law W_ext = ΔE_sys applies in general. When W_ext = 0, total mechanical energy (K + U) is conserved.
Momentum: Momentum is conserved when the net, external force on the system is zero.

There are other conservation laws less general than energy and momentum. There are some situations, for example, when kinetic energy is conserved. However, it's much more likely that kinetic energy isn't conserved. Let's start with some example situations when it isn't conserved.

recoiling objects--Example 1 of the ice skaters is such a case. In the initial state, the total kinetic energy of the system is 0, since the skaters aren't moving. In the final state, both have kinetic energy. Since kinetic energy is always positive, the initial K of 0 can never equal a positive final K.

sticking collisions--See Example 2 of the coupling gliders. Let's check this situation for conservation of kinetic energy.

Kinetic energy is obviously lost in this collision. This is generally true in collisions where the objects stick or are permanently deformed. You might ask what happened to the missing energy, since it apparently didn't go into potential energy. Non-conservative forces are usually involved in these situations and that results in conversion of kinetic energy to thermal energy. Interactions in which kinetic energy isn't conserved are termed inelastic.

Whether or not a collision is elastic has nothing to do with whether momentum is conserved.

In both Examples 1 and 2, we used the law of conservation of momentum. Yet both collisions were inelastic.

There are some interactions in which both momentum and kinetic energy are conserved. An interaction in which kinetic energy is conserved is termed elastic. The only truly elastic collisions are those between elementary particles, and not all of those are elastic. In the macroscopic world, we can sometimes create situations that approximate those of elastic interactions. On an air track or air table, for example, we can arrange to eliminate as much friction as possible. Nevertheless, there will still be some thermal energy losses in the bumpers of the colliding gliders.