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Hello I really need help with this question please!! Explain the energy conversations that occur as a basketball falls, hits the ground, and bounces up ignore frictional forces. ???

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We know that, if we ignore frictional forces, the mechanical energy of the system is conserved, this means that all point of time we have that:


K_i+U_i=K_f+U_f

This means that as the ball is falling the potential energy is being converted to kinetic energy until all the potential energy becomes zero (when the ball hits the ground); at this point all the energy is kinetic. After this point all the kinetic energy of the ball is being converted to potential energy while the ball rises until it reaches the maximum height (which has to be the same from where the ball started); at this point all the energy is potential energy since the ball stops for a fraction of time. Then the process begins again and the potential energy is being converted into kinetic energy as we explained earlier and the process goes on.

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