Question

An elevator is designed to lift a load of 1000 kg through 6 floors of a building averaging 3.5 m per floor in 6 sec. Power of the elevator neglecting other losses will be
A) $ 3.43\times 10^4 $ watt
B) $ 4.33\times 10^4 $ watt
C) $ 2.21\times 10^4 $ watt
D) $ 5.65\times 10^5 $watt

Answer 1

Hint: Height will be 6 times 3.5 m since there are 6 floors of the building averaging 3.5m per floor.

Formula used:
Work done = $mgh$ where m = mass, g = acceleration due to gravity and h = height,
P=$\dfrac{w}{t}$ where p = power, w = work done and t = time

Complete step by step solution:
Given,
Mass= 1000kg,
$ Time = 6 $ sec, $ Height = 6 \times 3.5 $ m = $ 21 $ m
Work done = $mgh =1000\times6\times21=205800 $ J
Power is a rate at which work is done.
Power = $\dfrac{w}{t}$=$\dfrac{{205800}}{6} = 3.43\times{10^4}watt$
Therefore, Option (A), $ 3.43\times 10^4 $ watt is the correct answer.

Note: It is work done against the gravitational force so the formula is work done = $mgh$ and Power is a rate at which work is done.
An elevator is simply a device that increases or decreases a person's potential energy without them needing to supply that energy themselves.