Question

In a one-dimensional collision between two identical particles $A$ and $B$. $B$ is stationary and $A$ has momentum $p$ before impact. During impact, $B$ gives an impulse $J$ to $A$. Find the coefficient of restitution between $A$ and $B$?

Answer 1

Given that,

Momenta of $A=p_1$

Momenta of $B=p_2$

Now, applying impulse

For A,

$J=p_1$

For B,

$J=p-p_2$

$p_2=p-J$

Now, the coefficient of restitution is

$e=\frac{p_1-p_2}{p}$

$e=\frac{2J-p}{p}$

$e=\frac{2J}{p}-1$

Hence, the coefficient of restitution is $\frac{2J}{p}-1$