Work, Power and Energy

Question : 27

Total: 30

A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7ms–1. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact? Would your answer be different if the elevator were stationary?

Solution:

Here, m=0.3kg,v=7m∕s, h = length of elevator = 3 m
As relative velocity of the ball w.r.t. elevator is zero, therefore, in the impact, only potential energy of the ball is converted into heat energy.
Amount of heat produced = P.E. lost by the bolt =mgh=0.3×9.8×3=8.82J.
The answer shall not be different, if the elevator were stationary as the bolt too in that case would start from stationary position, i.e. relative velocity of the ball w.r.t. elevator would continue to be zero.

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