A hard rubber ball, released at chest height, falls to thepavement and bounces b

Question

A hard rubber ball, released at chest height, falls to thepavement and bounces back to nearly the same height. When the ballis in contact with the pavement, its lower side is temorarilyflatened. Before the dent in the ball pops out, suppose that itsmaximum depth is on the order of 1cm. Compute an order-of-magnitudeestimate for the maximum acceleration of the ball. State yourassumptions, the quantiies you estimate, and the values youestimate for them. I have used 26.4cm for the displacement and -9.8m/s forthe acceleration from chest to gound. What else do I need to answer this problem? thanks, Tony Holmes A hard rubber ball, released at chest height, falls to thepavement and bounces back to nearly the same height. When the ballis in contact with the pavement, its lower side is temorarilyflatened. Before the dent in the ball pops out, suppose that itsmaximum depth is on the order of 1cm. Compute an order-of-magnitudeestimate for the maximum acceleration of the ball. State yourassumptions, the quantiies you estimate, and the values youestimate for them. I have used 26.4cm for the displacement and -9.8m/s forthe acceleration from chest to gound. What else do I need to answer this problem? thanks, Tony Holmes

Explanation / Answer

In this problem, the gravitaional acc is not veryimportant. If you notice when the ball hit the ground, it suddenly changeits speed direction, i.e. in a short time, the velocity vary from vto -v. Since the time is two short, the acceleration during thisinterval is much bigger than the gravitational acceleration. Hencethe maximum acceleration is the one that the ballexperenced during it hit the ground. To solve this problem, you need to assume the ball as a springof elastic constant k, then find out how much it was compressed, calculate theelastic force, then divide by the mass to get the maximumacceleration

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