Collisions

In every collision the total linear momentum of the colliding bodies is conserved, because the forces between them are internal and equal and opposite.

In an elastic collision total kinetic energy is also conserved; in an inelastic collision part of it becomes heat, sound or deformation.

In a completely inelastic collision the bodies stick together after impact and the loss of kinetic energy is the largest possible.

Kinetic energy is not conserved during the brief contact itself, even in an elastic collision; the statement applies to the energy before and after.

For one-dimensional elastic collision of m₁ (speed v₁ᵢ) with m₂ at rest: v₁f = (m₁ − m₂)v₁ᵢ/(m₁ + m₂) and v₂f = 2m₁v₁ᵢ/(m₁ + m₂).

Equal masses in a one-dimensional elastic collision exchange velocities: the moving body stops and the struck one moves off with its speed.

A light body striking a very heavy body at rest rebounds with nearly the same speed, while the heavy body barely moves; a heavy body hitting a light one at rest carries on almost unchanged and the light one moves off at nearly twice its speed.

For a completely inelastic collision with m₂ initially at rest, the common velocity is v = m₁v₁ᵢ/(m₁ + m₂) and the kinetic energy lost is ½[m₁m₂/(m₁ + m₂)]v₁ᵢ².

Each body's own kinetic energy changes in an elastic collision; it is only the total that is conserved.