Equations · equation
Coefficient of Restitution
Mechanics · 1687
- Equation
- e = v_separation / v_approach; energy of the relative motion kept = e²
- Field
- Mechanics
- Named After
- Isaac Newton
- Year
- 1687
Symbols
e a number between 0 (perfectly inelastic — they stick) and 1 (perfectly elastic — none lost) · v_approach, v_separation the relative speeds along the line of centres before and after
Significance
Newton's experimental law of 1687: how much of the closing speed survives a collision. What e² measures is the energy in the relative motion — the collision's own energy, seen from the centre of mass — and not the total, because the momentum the pair carries between them cannot be lost. For equal balls, one at rest, the fraction of the original kinetic energy still there afterwards is (1 + e²)/2. Phenolic pool balls run about 0.92: the object ball leaves with 96 % of the cue ball's speed and 92 % of its energy, the cue ball creeps forward carrying under a fifth of a percent, and about 8 % of the energy has gone into sound and deformation. A cushion returns roughly 0.75 of the energy, so the ball comes off at 87 % of its speed. Steel on steel is 0.9-ish, a superball 0.9, a lump of clay near 0. It is why the ninety-degree rule is really eighty-eight, and why a stop shot needs a touch of draw.
Open on the Equations shelf — the interactive card, the filters, and everything alongside it.