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A ball is dropped on a floor from a heig...

A ball is dropped on a floor from a height `h`. If the coefficient of restitution is `e`, find the height to which the ball will rise after touching the floor and the time it will take to come to rest again.

Text Solution

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The ball reaches the floor with velocity `u=sqrt(2gh)`
if collision on the floor is elastic, the ball will rebound with the same vellcity `u` and it will reach the same height. But if the coefficient of restitution between the ball and the floor is `e`, the ball will rebound with a lesser vellocity `v`, given as
`v=eu`.......i
where `v` is the velolcity of spearation and `u` is th velocty of approach
in this case the ball will rebound to a height `h_(1)`: from equations it is given that
`h_(1)=v^(2)/(2g)=e^(2)s`............ii
In downward and upward motion the accelertion of the particle is `g` only, thus total time of motion is the time of downward motion plus the time of upward motion as
`t=sqrt((2h)/g)+sqrt((2e^(2)h)/g)=sqrt((2h)/g)+esqrt((2h)/g)`
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Knowledge Check

  • A ball is dropped on the ground from a height of 1m . The coefficient of restitution is 0.6 . The height to which the ball will rebound is

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