Inelastic Collision

Inelastic collision: momentum is conserved, but KE is NOT — some converts to heat, sound, deformation.

PERFECTLY inelastic: objects STICK TOGETHER. Maximum KE loss.

Common cases: cars colliding (crumple), bullet embedding in a block, clay balls sticking, two trains coupling.

Perfectly inelastic 1D: m₁u₁ + m₂u₂ = (m₁ + m₂)·v_common.

KE loss in perfectly inelastic: ΔK = ½·(m₁m₂/(m₁+m₂))·(u₁−u₂)² — reduced-mass times relative speed squared.

Real-world collisions are MOSTLY inelastic — perfectly elastic is rare in macroscopic objects.

Coefficient of restitution e: e = 1 for elastic, e = 0 for perfectly inelastic, 0 < e < 1 for partially inelastic.

Used in: crash-test physics, billiards (partial inelasticity), bullets, ballistics pendulum.