Question

A steel ball with a mass of 50.0 g is dropped from a height of 2.40 m onto a horizontal steel slab. The ball rebounds to a height of 1.40 m. Use coordinates with y directed downward. How much mechanical energy was lost in the impact with the steel slab? Express your answer in joules.

Answer 1

The amount of mechanical energy lost in the impact is 0.49 J.

Step-by-step explanation:

In this problem, we can use the principle of conservation of mechanical energy to determine the amount of energy lost during the impact. The mechanical energy of the ball before the impact is equal to its potential energy, which is given by the formula PE = mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height from which the ball is dropped. Substituting the given values, we have PE = (0.05 kg)(9.8 m/s^2)(2.4 m) = 1.176 J.

After the impact, the mechanical energy of the ball is equal to its potential energy at the rebound height given by the formula PE = mgh. Substituting the given values, we have PE = (0.05 kg)(9.8 m/s^2)(1.4 m) = 0.686 J. Therefore, the amount of mechanical energy lost in the impact is the difference between the initial and final mechanical energies, which is equal to 1.176 J - 0.686 J = 0.49 J.