Question

What is the power output of a machine that lifts a 600 kg weight through a height of 20 m in 1 min?
(A) $1.96$kW
(B) $0.98$kW
(C) 12 kW
(D) $3.92$kW

Answer 1

Hint:
The power output of any machine is generally referred to as the rate of doing any work. It is calculated as the time derivative of work done by the machine.
Formula used : $P = \dfrac{W}{t}$, where P is the power output, W is the work done and t is the time period for which the power is being calculated. The SI unit of power is given by Watt (W).

Complete step by step answer:
In this question, we are provided with a machine that does work for some amount of time, and we are required to find its power output. Let us first see the information that is given to us:
Weight lifted $M = 600$kg
Height $h = 20$m
Time $t = 1{\text{ min}} = 60$sec
We remember to keep all the units in the standard form for ease of calculation. Now, we can see that the amount of work done by the machine is not explicitly provided to us. To calculate this parameter from the given values, we know that the work done is given as:
$\Rightarrow W = Mgh$
Where g is the gravitational acceleration.
To calculate this energy or work done, we input the values provided to us:
$\Rightarrow W = 600 \times 9.8 \times 20$
$\Rightarrow W = 12000 \times 9.8 = 117600$J
We know, the power output can be calculated by using the work done W as:
$\Rightarrow P = \dfrac{W}{t}$
Substituting the known values in this equation gives us:
$\Rightarrow P = \dfrac{{117600}}{{60}} = 1960$W
This can also be written as $P = 1.96$kW.
Comparing all the given options, we see that the correct answer is option (A).

Note:
We saw that the work done calculated by us was the same as the potential energy of a body. This is because the mass in consideration was lifted through some height, and we are aware that the potential energy is equivalent to the work done against gravity.