You are in a lift moving from the $3^{rd}$ floor to the $12^{th}$ 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.

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Solution

Step 1: Given parameters
Mass of the body is $M$ .
The elevated height is $H$ .
Step 2: Concept used:
Work is the force applied to an object to displace it from its original position.
Newton's second law of motion states that the net force exerted on the person is equal to the person’s mass times the person’s acceleration.
Newton's third law of motion states that the force exerted on the floor by the person is equal and opposite to the force exerted on the person by the floor.
Step 3: Calculating the work done by the elevator
According to the work-energy theorem,
$Work done by all the forces = Change in kinetic Energy W = ∆ K$
$The total force exerted on the person = Force exerted by the floor + Force exerted by the elevator$ .
Work done by the elevator is the sum of the change in potential energy and change in kinetic energy,
$W = ΔP . E + ΔK . E$
As the elevator is moving at a constant speed,
Then, $ΔK . E = 0$
$W = ΔP . E + 0$
Hence, $W = ΔP . E$
The work performed by the elevator on the person = $- MgH$ , where $g$ is the acceleration due to gravity.
The negative sign indicates the force acting against $g$ .

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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.

You are in a lift moving from the $3^{rd}$ floor to the $12^{th}$ 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.