inelastic collision
A collision in which kinetic energy is not conserved; the missing energy goes into heat, sound, or deformation.
Definition
An inelastic collision is one in which total kinetic energy is not conserved, though total momentum (as always) is. The "lost" energy has gone into heat, sound, internal vibrations, or permanent deformation of the bodies — it is not really lost, just moved into parts of the energy ledger mechanics alone does not track.
A perfectly inelastic collision is the extreme case: the two bodies stick together and move as one. Cars in a pile-up, a lump of putty on a block, an arrow sunk into a target. For such collisions, the final common velocity is fixed by momentum conservation alone: v' = (m_A·v_A + m_B·v_B) / (m_A + m_B). The kinetic-energy fraction lost is m_A·m_B / (m_A + m_B)² of the initial KE — largest when the masses are equal and the collision is head-on.
Between elastic and perfectly inelastic, most real collisions are partially inelastic, parameterised by a coefficient of restitution e ∈ [0,1] — the ratio of post- to pre-collision relative speed. Engineering analyses of crashes, bouncing balls, and manufacturing impacts all live in this middle regime, where energy loss must be modelled explicitly rather than assumed away.