8.01SC | Fall 2016 | Undergraduate

Classical Mechanics

Week 5: Momentum and Impulse

15.3 Worked Example - Bouncing Ball

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Definition of Average Force:

The time average of a force \(\vec{F}(t)\) between times \(t_1\) and \(t_2\) is defined as:

\[\displaystyle \vec{F}_{ave} = \frac{\int_{t_1}^{t_2}\vec{F}(t)dt}{t_2-t_1}\]

A ball of mass \(\displaystyle m\) is released from rest from a height \(\displaystyle h_ i\) above a horizontal surface. It hits the surface and bounces off vertically to reach a maximum height \(\displaystyle h_ f\). The ball is in contact with the table for a time \(\displaystyle T\). Calculate \(\displaystyle N_{ave}\), the magnitude of the time average normal force exerted by the table on the ball. Express your answer in terms of \(\displaystyle m\), \(\displaystyle g\), \(\displaystyle T\), \(\displaystyle h_ i\), and \(\displaystyle h_ f\).

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