Coefficient of Restitution

Coefficient of restitution e is the ratio of relative speed AFTER collision to relative speed BEFORE: e = |v_2 − v_1|/|u_1 − u_2|.

Range: 0 ≤ e ≤ 1. e = 1: perfectly elastic. e = 0: perfectly inelastic (objects stick together). 0 < e < 1: partially elastic.

Property of MATERIALS — not just objects. Different surface pairs have different e.

Typical values: glass-glass ~0.95, steel-steel ~0.7-0.9, basketball-floor ~0.75, clay-clay ~0.1-0.2.

Determines bounce height: h_n = e^(2n) × h₀ for n bounces.

Ratio of bounce heights: h_after/h_before = e². Direct experimental method.

In oblique collisions: e applies only to NORMAL component of velocity; tangential component (if smooth) is unchanged.

e depends slightly on relative speed and surface conditions — not a constant in all situations.