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

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.