Gordon Young

2023-02-21

How to calculate the coefficient of restitution?

Brisa Fitzgerald

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, ${V}_{A}-{V}_{B}\alpha {U}_{A}-{U}_{B}$
$\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}{V}_{B}-{V}_{A}\alpha {U}_{B}-{U}_{A}$
For a system of colliding bodies $\text{A}$ and $\text{B}$
The constant of proportionality is $-e$
Thus we have,
${V}_{A}-{V}_{B}=-e\left({U}_{A}-{U}_{B}\right)$
$⇒e=-\frac{{V}_{A}-{V}_{B}}{{U}_{A}-{U}_{B}}$
The initial and final velocities of the two bodies colliding are all that are required to calculate e.

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