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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.

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.

Grade:12th pass

1 Answers

Vikas TU
14149 Points
7 years ago
Conservation of momentum,
mv = mv1+ mv2
v = v1 + v2........................(1)
Given Kinetic Energy,
K’ = 0.75K
0.5mv1^2 = 0.75mv^2
v1^2 = 1.5v2^2
v1 = v root(1.5)................(2)
Put (2) in (1) eqn. we get,
v = vroot(1.5) + v2
v2 = 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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