Work and Energy - Bouncing ball

Problem Statement:

A tennis ball of mass m = 50 g is dropped from a height h = 8 m without initial speed. The tennis ball reaches 75% of its initial height after bouncing on the floor, determine the energy it has lost in the rebound.

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Solution:

As the ball loses energy in the rebound, its mechanical energy is not conserved. We must then use this equation:

Where the initial energy is the potential energy before dropping the tennis ball and the final energy is the potential energy in the final state (when the tennis ball reaches its maximum height after bouncing off the ground). There is no kinetic energy because the tennis ball is at rest in both states.

The work that appears in the second member of the previous equation includes the mechanical energy that is lost during the rebound for various reasons: heat dissipation during the impact with the ground, deformation of the tennis ball, etc.

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By developing the previous expression we get:

And after substituting the givens of the problem statement we obtain:

In the problem we have used g = 10 m/s2

Do not forget to convert givens to the SI and to include the units in the results of the problems.

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