First slide

Coefficient of restitution

Question

A body 'x' with a momentum 'p' collides with another identical stationary body 'y' one dimensionally. During the collision 'y' gives an impulse 'J' to the body 'x'. Then the coefficient of restitution is

Easy

A

$\large \frac {2J}{p}-1$
B

$\large \frac {J}{p}+1$
C

$\large \frac {J}{p}-1$
D

$\large \frac {J}{2p}-1$

Solution

Initial momentum of body - 1 = p. As the impulse transeferred by y to x is in a direction opposite to the direction of initial motion of x, its final momentum mv₂ = p + (-J). Also, since impulse transferred by x to y is in the direction of motion of y , we can write, mv₂ = J
$\large \therefore e=\frac {v_2-v_1}{u_1-u_2}=\frac {mv_2-mv_1}{mu_1}=\frac {J-(p-J)}{p}\\\therefore e=\frac {2J}{p}-1$

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