Q. 274.1( 16 Votes )
A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with a uniform speed of 7 m s–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?
Mass of the bolt, m = 0.3 kg
The speed of the bolt, v = 7 m s-1
Length of the elevator, h = 3 m
The relative velocity of the bolt with respect to the elevator is zero. So, the potential energy gets converted into heat energy upon impact according to law of conservation of energy.
Heat produced, H = Loss of potential energy
⇒ H = mgh
m is the mass of the bolt
g is the acceleration due to gravity
h is the height of the elevator
⇒ H = 0.3 kg × 9.8 m s-2 × 3 m
⇒ H = 8.82 J
The answer will not change because of the fact that the relative velocity of the bolt with reference to the elevator is 0.
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