# How do you calculate the coefficient of restitution?

Apr 19, 2015

The coefficient of restitution often denoted $e$ can be found with some notion of Newton's Experimental Law.

This law states that: "in a system of colliding bodies(usually 2 bodies) the relative velocity of separation is directly proportional to the relative velocity of approach".

Mathematically expressed, ${V}_{A} - {V}_{B} \alpha {U}_{A} - {U}_{B}$
$\mathmr{and} {V}_{B} - {V}_{A} \alpha {U}_{B} - {U}_{A}$
For a system of colliding bodies $\text{A}$ and $\text{B}$

The constant of proportionality is $- e$
Thus we have,

${V}_{A} - {V}_{B} = - e \left({U}_{A} - {U}_{B}\right)$

$\implies e = - \frac{{V}_{A} - {V}_{B}}{{U}_{A} - {U}_{B}}$

Thus, all you need to calculate e are the respective initial and final velocities of the two bodies involved in collision.