A basketball of mass 0.40 kg is dropped from rest from a height of 1.22 m. It re

Question

A basketball of mass 0.40 kg is dropped from rest from a height of 1.22 m. It rebounds to a height of 0.52 m.
(a) How much mechanical energy was lost during the collision with the floor?
1 J

(b) A basketball player dribbles the ball from a height of 1.22 m by exerting a constant downward force on it for a distance of 0.13 m. In dribbling, the player compensates for the mechanical energy lost during each bounce. If the ball now returns to a height of 1.22 m, what is the magnitude of the force?
2 N

Explanation / Answer

The mass of the ball m = 0.7kg the heigth of the ball h1 = 1.22m the rebound heigth h2 = 0.64m (a) The initial potential enregy                 U1 = mgh1 = (0.7)(9.8)(1.22) = 8.4J the rebound energy                 U2 = mgh2 = (0.7)(9.8)(0.64) = 4.4 J therefore the energy lost = 8.4 - 4.4 = 4.0J (b) The force exert on ball for a disatnce d = 0.13m      and the mechanical lose = 4J Workdone W = F*d therefore the force F = W/d = 4/0.13 = 30.76 N

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