3.6.1—Coefficient of restitution

For a direct impact, the coefficient of restitution e is relative speed of separation divided by relative speed of approach, measured along the line of impact. For ordinary passive impacts 0≤e≤1.

Choose one positive direction and write velocities immediately before and after impact. Combine the restitution equation with conservation of momentum when external impulse is negligible.

If two particles approach at 5 m s⁻¹ relative speed and separate at 2 m s⁻¹, e=2/5=0.4. The individual velocities still depend on their masses and momentum.

Restitution does not conserve kinetic energy except in the elastic case e=1; it also does not mean each particle reverses direction.