Consider a perfectly elastic ball of mass m bouncingup and down on a horizontal

Question

Consider a perfectly elastic ball of mass m bouncingup and down on a horizontal surface under the action of a downwardgravitational acceleration, g. Prove that in thetime average over an integral number of bounces, the downward forceexerted by the ball upon the surface is equal to the weight of theball. [Hint: The downward force is equal to thedownward momentum imparted to the surface with each bounce dividedby the time interval between successive bounces.] Does this result suggest anything about the "weight" of anatmosphere comprised of gas molecules? Consider a perfectly elastic ball of mass m bouncingup and down on a horizontal surface under the action of a downwardgravitational acceleration, g. Prove that in thetime average over an integral number of bounces, the downward forceexerted by the ball upon the surface is equal to the weight of theball. [Hint: The downward force is equal to thedownward momentum imparted to the surface with each bounce dividedby the time interval between successive bounces.] Does this result suggest anything about the "weight" of anatmosphere comprised of gas molecules?

Explanation / Answer

Since it is a perfectly elastic ball, so there is no energy lost.Its maximum velocity is constant ( right before it get to thesurface, and right after it get off the surface). Using the momentum equation, we have P=2mv . and time for oneloop t=2v/g The average force F is equal to P/t = mg.

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