First slide

Coefficient of restitution

Question

Two spheres moving in opposite directions with velocities $u_{1}$ and $u_{2}$ collide will each other. If e is the coefficient of restitution, their distance of separation at time ‘t’ after collision is

Easy

A

$(u_{1} - u_{2}) e t$
B

$(u_{2} - u_{1}) e t$
C

$(u_{1} + u_{2}) e t$
D

$(\frac{u_{1}}{u_{2}}) e t$

Solution

$\frac{v_{2} - v_{1}}{u_{1} - u_{2}} = e \frac{v e l . o f s e p a r a t i o n}{v e l . o f a p p r o a c h}$ along the line of impact
$(v_{2} - v_{1}) = e (u_{1} - u_{2})$
Separation after time t, $(v_{2} - v_{1}) t = e (v_{1} - v_{2}) t$
As $v_{1} a n d v_{2}$ are opposite direction

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