Elastic vs Inelastic Collisions — What's the Difference?

Elastic collision

An elastic collision is one in which the total kinetic energy of the system is the same after the collision as before. The objects deform briefly and spring back, returning the stored energy.

∑KEbefore=∑KEafter\sum KE_{before} = \sum KE_{after}

Unit: joule (J) for the energies

Example: Two billiard balls colliding are nearly elastic: they bounce apart with almost all their kinetic energy intact — only a click of sound energy is lost.

Inelastic collision

An inelastic collision is one in which some kinetic energy is converted into other forms — heat, sound, or permanent deformation. Momentum is still conserved, but kinetic energy is not.

KElost=KEbefore−KEafterKE_{lost} = KE_{before} - KE_{after}

Unit: joule (J) for the energies

Example: A car crash is highly inelastic: the crumpling metal converts kinetic energy into heat and deformation, which is exactly what crumple zones are designed to do.

Key differences

AspectElastic collisionInelastic collision
Kinetic energyYes — kinetic energy is conservedNo — some becomes heat, sound and deformation
MomentumAlways conservedAlways conserved (for an isolated system)
Everyday exampleBilliard balls clicking togetherA car crash — metal crumples, kinetic energy becomes heat
OutcomeObjects bounce apartObjects may stick together (perfectly inelastic)
Coefficient of restitutione = 1e < 1 (e = 0 when objects stick)
Why students confuse them

'Elastic' here has nothing to do with stretchy rubber — it means kinetic energy is preserved. A collision can look violent yet be nearly elastic (two billiard balls), or look gentle yet be perfectly inelastic (a lump of clay hitting a wall). Always check the energy, not the drama.