Elastic and Inelastic Collisions

A collision is a brief, forceful interaction between objects, and two quantities are at stake. Momentum is conserved in every collision of an isolated system, because the objects push on each other with equal and opposite forces. Kinetic energy is different: it survives only when the collision is elastic. The topic comes down to keeping those two ledgers apart, classifying a collision by its energy rather than by how it looks, and in a plane tracking the x and y components separately.

Two ideas separate the collisions that look alike: what happens to the kinetic energy, and how the components behave in a plane. The trap is calling a collision elastic just because the objects bounced, when bouncing can still lose energy; calling it inelastic only when they stick, when sticking is merely the extreme case; reaching for energy conservation in a collision that does not conserve energy; and conserving a single speed in two dimensions instead of each momentum component on its own. Get those straight and collisions turn into bookkeeping.