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Manipal MET2021PhysicsCenter of Mass, Momentum and Collision

A ball falls vertically on to a floor, with momentum p , and then bounces repeatedly, the coefficient of restitution is e . The total momentum imparted by the ball to the floor is

Options

  1. Ap(1+e)
  2. Bp (1-e)
  3. Cp ( 1+e 1-e )
  4. Dp (1- 1 e )

Correct answer

C. p ( 1+e 1-e )

Step-by-step solution

When a particle undergoes normal collision with a floor or a wall, with coefficient of restitution e , the speed after collision is e times the speed before collision. Therefore, change in momentum after Ist impact is e p-(-p)=p(1+e) After the second impact, change in momentum would be e(e p)-(-e p)=e p(1+e) and soon. Therefore, total change in momentum of ball aligned & =p(1+e) [1+e+e^2+ ] & =p ( 1+e 1-e ) aligned

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