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A ball of mass m moving with a speed v makes a head on collision with an identical ball at the kinetic energy of the boss after the collision is 3/4 of the original kinetic energy calculate the coefficient of restitution.
Conservation of momentum,mv = mv1+ mv2v = v1 + v2........................(1)Given Kinetic Energy,K’ = 0.75K0.5mv1^2 = 0.75mv^2v1^2 = 1.5v2^2v1 = v root(1.5)................(2)Put (2) in (1) eqn. we get,v = vroot(1.5) + v2v2 = v(1 – root(1.5)).....................(3)coeff. of Restitution=>e = (v2 – v1)/v = [v(1 – root(1.5)) – vroot(1.5)]/v = 1 – 2root(1.5).
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