Question

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.

Answer 1

Hint: By using Newton’s third law of motion and the second law of Newton’s law of motion we can find the work performed on you by the elevator


Formula used:
\[W{\text{ }} = {\text{ }}\Delta {\text{ }}P.E{\text{ }} + {\text{ }}\Delta {\text{ }}K.E\]

Complete step by step solution:
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 energy.
That is, \[W{\text{ }} = {\text{ }}\Delta {\text{ }}P.E{\text{ }} + {\text{ }}\Delta {\text{ }}K.E\]
Here \[{\text{ }}P.E{\text{ }}\]is the potential energy and \[{\text{ }}K.E\]is the kinetic energy
But the elevator moves in the constant speed, so \[K.E{\text{ }} = 0.\]
\[W{\text{ }} = {\text{ }}\Delta {\text{ }}P.E{\text{ }}\]
The work performed on you by the elevator is force times displacement \[ = - MgH\]
Negative sign shows it is moving upwards, that is against g.

Note: The work done on an object by a net force equals the change in kinetic energy of the object. Essentially kinetic energy is the energy used for motion. ... Interestingly, as work is done on an object, potential energy can be stored in that object.