Question

A ball of mass `m` moving at speed `v` makes a head on collision with an identical ball at rest. The kinetic energy of the balls after the collision is `3//4th` of the original. Find the coefficient of restitution.

Answer 1

As we have seen in the above discussion that under the given conditions:

`v_(1)=((1+e)/2)v` and `v_(2)=((1-e)/2)v`
given that `K_(f)=3/4K_(i)`
or `1/2mv_(1)^(2)+1/2mv_(2)^(2)=3/4(1/2mv^(2))`
Substituting the values we get
`((1+e)/2)^(2)+((1-e)/2)^(2)=3/4`
or `(1+e)^(2)+(1+e)^(2)=3` or `2+2e^(2)=3`
or `e^(2)=1/2 ` or `e=1/(sqrt(2))`