Question

A ball is dropped from rest and falls to the floor. The initial gravitational potential energy of the ball-Earth-floor system is 10 J. The ball then bounces back up to a height where the gravitational potential energy is 7 J. What was the mechanical energy of the ball-Earth-floor system the instant the ball left the floor?

Answer 1

The mechanical energy of the ball-Earth-floor system at the instant when the ball left the floor is of 7 J.

What is Mechanical Energy?

At any instant, the energy of an object by virtue of its motion or position is known as the mechanical energy of the object. In other words, mechanical energy is either the potential energy or the kinetic energy at any time instant.

Given data -

The initial gravitational potential energy is, U = 10 J.

The final gravitational potential energy is, U' = 7 J.

Now, considering the given case when the ball loses energy in the rebound due to ball deformation, heat loss from the bounce. The total mechanical energy is not conserved so mechanical energy as it bounces off the floor is equal to transformed potential energy at a maximum height of second bounce which is 7 J.

Thus, we can conclude that the mechanical energy of the ball-Earth-floor system at the instant when the ball left the floor is of 7 J.

Learn more about the gravitational potential energy here:

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