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? (A) 0J (B) 3J (C) 7J (D) 10J

Answer 1

The mechanical energy of the ball-Earth-floor system after bouncing would be equivalent to the gravitational potential energy at the maximum height reached after the bounce, which is 7J.

Step-by-step explanation:

The question we are addressing revolves around the mechanical energy of a ball-Earth-floor system when a ball is dropped, allowed to hit the floor, and then bounce back up to a certain height. Initially, the ball has a gravitational potential energy of 10 Joules. When it bounces back up to a point where its potential energy is 7 Joules, we can deduce that since energy is conserved in a closed system without losses, initially the mechanical energy must have been the sum of potential and kinetic energy. Considering that all the initial potential energy would have converted to kinetic energy just before the bounce, and knowing that some of that energy would be lost during the bounce (to sound, heat, etc.), the mechanical energy when the ball leaves the floor would be the same as the gravitational potential energy at the peak of its bounce, 7 Joules. Therefore, the correct answer is (C) 7J.

Answer 2

C is the right option

Step-by-step explanation:

The ball looses energy in the rebound due to ball deformation, heat loss from bounce. Total mechanical energy is not conserved so mechanical energy as it bounces of the floor is equal to transformed potential energy at maximum height of second bounce which is 7j.