Perfectly Inelastic Collision

A PERFECTLY INELASTIC collision is the special, extreme case of an inelastic collision in which the colliding bodies join together (stick) and move off with one COMMON final velocity after impact. Since it is still a type of inelastic collision, kinetic energy is necessarily lost -- and in fact the loss of kinetic energy is the MAXIMUM possible of any collision type, for given initial conditions.

Illustrations: (i) a bullet fired into a stationary block on a smooth surface -- if the bullet rebounds at exactly its original speed and the block stays stationary, the collision is elastic; if the bullet becomes embedded and the two move off together, it is PERFECTLY inelastic; if the bullet rebounds slower, or passes through and exits with reduced speed, it is inelastic but not perfectly so (there is no such thing as 'partially elastic' -- elastic collisions are always perfectly elastic, whereas inelastic collisions can be either partial or perfect). (ii) a ball dropped on a hard surface in vacuum -- if it rebounds to exactly the same height, the collision is elastic (never achieved i …