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Coefficient of restitution
Intermediate
Ratio of separation speed to approach speed.
e = (v₂−v₁)/(u₁−u₂)e = relative speed of separation ÷ relative speed of approach. e = 1 is elastic, e = 0 perfectly inelastic.
A ball dropped from 1 m bouncing to 0.64 m has e = 0.8.
e depends on materials and speed.
In more detail
The coefficient of restitution, e, is the ratio of relative speed after a collision to relative speed before. It is 1 for elastic collisions and 0 for perfectly inelastic ones.
Real-world uses
- Sports balls are rated by their coefficient of restitution, which affects bounce height.
- Car safety tests measure how much energy is returned in collisions.
- A tennis ball dropped onto a hard floor bounces back to a fraction of its height, which the restitution coefficient describes.
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Frequently asked questions
What values can e take?
Between 0 and 1 for ordinary collisions.
Does e depend on speed?
Real materials show some dependence on impact speed, but e is often treated as a constant.
What is a coefficient of restitution of zero?
A perfectly inelastic collision, where the bodies stay together after impact.
Related topics in Momentum & Collisions
Elastic collision · Inelastic collision · Perfectly inelastic collision · Elastic head-on collision velocities · Equal masses collide elastically · Light hits heavy object