Question

A crane can lift a box of 600kg mass to a height of 20m in 2 minutes. Calculate the power at which the crane is operating?
A. 1000 watts
B. 6000 watts
C. 60,000 watts
D. 240,000 watts
E. 1,440,000 watts

Answer 1

Hint: We can define the work done by the crane in lifting the box as the change in potential energy of the box. Obtain the expression for power in terms of work done and time. Put the values on the equation to find the required solution.

Complete answer:
Given, the mass of the box is $m=600kg$
The crane lifts the box by a height of $h=20m$
The time taken by the crane to lift the box is, $t=2\min =120\sec $
Now, since the box is simply lifted from the ground, we can find the work done by the crane in lifting the box with the help of the potential energy of the lifted box.

So, the work done in lifting the box will be,

$W=mgh$

Where, m is the mass of the box, g is the acceleration due to gravity and h is the height of the lifted box.
So, we can write,
$W=600\times 10\times 20=120000J$
Now, power can be defined as the rate of work done per unit time. Mathematically we can write it as,
$P=\dfrac{W}{t}$
So, the power required by the crane to lift the box will be,

$P=\dfrac{120000}{120}=1000\text{watts}$
So, the correct answer is “Option A”.

Note:
The potential energy of an object can be defined as the work done on the object to move it from a reference point where the potential energy is zero to another position. So, we can write the work done on an object equal to the potential energy stored in the object.