Gordon Young

2023-02-21

How to calculate the coefficient of restitution?

Brisa Fitzgerald

Beginner2023-02-22Added 5 answers

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,

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

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

The initial and final velocities of the two bodies colliding are all that are required to calculate e.

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,

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

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

The initial and final velocities of the two bodies colliding are all that are required to calculate e.