Question

A car of 2000 kg is lifted up a distance of 30 m by a crane in 1 min. A second crane does the same job in 2 min. Do the cranes consume the same or different amount of fuel? What is the power supplied by each crane? Neglect power dissipation.

Answer 1

Hint: In order to solve this question, you must be aware about the relationship between work done and power. When a force acts on an object over a distance, it is said to have done work on the object. Power is the rate at which work is done.

Complete step by step answer:
Given, $m = 2000$kg $s = 30$m
${t_1} = 1\min = 60\sec $ , ${t_2} = 2\min = 120\sec $
$W = Fs = mgs$
$W = 5.88 \times {10^5}$J
As both cranes do the same amount of work, therefore, both the cranes consume the same amount of fuel.
${P_1} = \dfrac{W}{{{t_1}}}$ and ${P_2} = \dfrac{W}{{t_2^{}}}$
${P_1} = 9800W$ and ${P_2} = 4900W$

Note: There are three types of work done:
Positive work- when the force and the displacement are in the same direction.
Negative work- When the force and the displacement are in the opposite direction.
Zero work- When the applied force does not cause displacement.