Question

A ball of mass m moving at a speed v make a head on collision with an identical ball at rest. The kinetic energy after the collision is 3/4 of the original kinetic energy . calculate the cofficient of restitution

Answer 1

initial vel. of I ball = u

final vel. of I ball = v1

final vel. of II ball =v2

coeff. of restitution = e

now, e = vel. of separaion / vel. of approach

e = v2 -v1 / u => v2-v1 = eu ....(1)

momentum conservation => mu = mv1 +mv2 => u = v1 + v2 ...(2)

energy eqn

3/4((mu^2)/2)= 1/2*m (v1^2 + v2^2)

3/4*(u^2) = (v1^2 + v2^2) 2*(v1^2 + v2^2)=(v1 + v2)^2 + (v2 -v1)^2 = u^2 + (eu)^2

{FROM 1& 2 } => 3/2 (u^2) = u^2 + (eu)^2

=> 1/2 (u^2) = (eu)^2 => e = root(1/2)