You are in a lift moving from the 3rd floor to the 12th floor, through a height H. If the elevator moves at a constant speed without stopping, what is the work performed on you by the elevator? Take your body mass as M.

According to newton’s third law of motion, the force exerted on the floor by the person is equal and opposite the force exerted on the person by the floor.

According to the second law of newton’s law of motion, the net force exerted on the person is equal to the person’s mass times the person’s acceleration.

The net force exerted on the person = Force exerted by the floor+ Force exerted by gravity.

If the elevator goes up with acceleration g, the same is the person inside the elevator.
The work done on the man by the floor is the sum of the change in potential energy and kinetic
i.e W = Δ P.E + Δ K.E
But the elevator moves in the constant speed, so K.E =0.
W = Δ P.E

The work performed on you by the elevator is force times displacement = -MgH

Negative sign shows it is moving upwards, i.e., against g.


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