Types of Collisions

In any collision, the total linear momentum and the total energy of the system are always conserved, but the total kinetic energy need not be -- because the impact and any deformation of the bodies can convert some of it into heat, sound, light, or permanent deformation. This distinction is used to classify every collision into one of two types.

1. Elastic collision: a collision in which the total kinetic energy of the bodies before the collision exactly equals the total kinetic energy after the collision --

   $\text{Total KE before collision} = \text{Total KE after collision}$

2. Inelastic collision: a collision in which the total kinetic energy before does not equal the total kinetic energy after --

   $\text{Total KE before collision} \ne \text{Total KE after collision}$

   For an inelastic collision, the shortfall is written as $\Delta Q$, the energy lost during the collision: $\text{KE}_{\text{after}} = \text{KE}_{\text{before}} - \Delta Q$. Even though kinetic energy alone is not conserved, the total energy (including whatever form $\Delta Q$ takes) still is -- consistent with the overall law of conservation of energy. …