Aball 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?

The mechanical energy of the ball-Earth-floor system the instant the ball left the floor is 7 Joules.

Explanation:

It is given that,

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.

Let U is the mechanical energy of the ball-Earth-floor system the instant the ball left the floor. Due to the conservation of energy, the mechanical energy is equal to difference between initial gravitational potential energy and the after bouncing back up to a height.

Initial mechanical energy is 10 + 0 = 10 J

Mechanical energy just before the collision is 0 + 10 = 10 J

Final mechanical energy, 7 + 0 = 7 J

Hence, the mechanical energy of the ball-Earth-floor system the instant the ball left the floor is 7 Joules.

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