# 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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