Question

An elevator lift has 12 occupants and it had to go 21 floors up 76.8 m at a constant speed. The average mass of the occupant is 62.8 kg. What is the work done by the elevator on the occupants?

Answer 1

We are given with the average mass of each occupant but we are not given with the mass of the lift. Also, it is mentioned that the lift needs to go up at constant speed. Newton’s second law, the acceleration of the lift is zero. The distance to be covered is also given.

Complete step by step answer: Mass of occupants= 62.8 kg
The only force acting on the occupants is the gravitational force which acts in the downward direction, so F=mg
$=62.8\times 9.8 \\\ =615.44N \\\$
This force acts downwards and the lift goes up with the constant velocity.
Displacement= 76.8 m
Work= $\overrightarrow{F}.\overrightarrow{d}=Fd\cos 180=-Fd=-615.44\times 76.8=47265.79J$
We can write this in kJ as 47.3 kJ. Work comes to be negative -47.3 kJ because the force and the displacement are in opposite directions.

Additional Information: Weight is the force of gravity. It acts in a downward direction and that toward the center of the Earth. No matter whether the body goes up or down the force of gravity always acts in a downward direction.

Note:
In this problem there is no clarity about the mass of the elevator and the mass of the persons inside. Because the elevator moves with constant speed it has zero acceleration and thus value of acceleration due to gravity remains same, if the lift moves up with acceleration a then net acceleration becomes (g+a) and when it moves down with acceleration a, net acceleration becomes (g-a)