If a ball is initially dropped from height h and has coefficient of restitution 0.9 .How many bounced will the ball make before comping to rest? Please help...

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Answer 1 · 2018-06-05T21:00:13

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If the ball was dropped from a height $h$ , then it originally had gravitational potential energy relative to ground, of:

So, just before it's first collision with ground, the ball will have kinetic energy $T$ , such that:

The Coefficient of Restitution, $e$ , as it applies between 2 bodies [here, ground and ball], is related to kinetic energy, as:

$e= sqrt ( {sum T_("post-collision"))/{sum T_("pre-collision")} )$

In the reference frame of ground, only the ball has Kinetic Energy.

$implies e= sqrt ( (T')/T ) = 0.9$

$implies T' = T * 0.9^2$

$implies mg h' = mgh * 0.9^2$

$implies h' = 0.81 h$

And so $h'$ is the height to which the ball will rise after the first collision with ground

So:

Follows that:

In this highly idealised model, the ball will never come to rest, ie $h_n = 0$ requires that $n to oo$ .