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Mechanics
Mechanics

Coefficient of Restitution

e=v2′−v1′v1−v2e = \frac{v_2' - v_1'}{v_1 - v_2}

Ratio of relative speeds after and before collision. e=1 for elastic, e=0 for perfectly inelastic.

Variables

e
Coefficient of restitution
Measure of elasticity (0 to 1)
unitless
v₂'
Final velocity of object 2
After collision
m/s
v₁'
Final velocity of object 1
After collision
m/s
v₁
Initial velocity of object 1
Before collision
m/s
v₂
Initial velocity of object 2
Before collision
m/s

Derivation

e = (relative speed of separation)/(relative speed of approach). Measures energy loss in collision.

Your notes

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Common questions

What is the Coefficient of Restitution formula?

Coefficient of Restitution is written e = v₂' - v₁'/v₁ - v₂. Ratio of relative speeds after and before collision. e=1 for elastic, e=0 for perfectly inelastic. It belongs to Mechanics, under Momentum.

What are the units in e = v₂' - v₁'/v₁ - v₂?

In SI units, e is coefficient of restitution (dimensionless); v₂' is final velocity of object 2, measured in m/s; v₁' is final velocity of object 1, measured in m/s; v₁ is initial velocity of object 1, measured in m/s; v₂ is initial velocity of object 2, measured in m/s.

How is the Coefficient of Restitution formula derived?

e = (relative speed of separation)/(relative speed of approach). Measures energy loss in collision. The result is e = v₂' - v₁'/v₁ - v₂.