Question

A man weighing \[60{\text{ }}kg\] climbs up a staircase carrying a load of \[20{\text{ }}kg\] on his head. The staircase has \[20\] steps each of height \[0.2{\text{ }}m\]. If he takes \[10{\text{ }}s\] to climb. Find his power.

Answer 1

Hint: Power can be defined as the rate of change at which work is done. Work is the energy transferred into or out of the system through the action of the force. Work is said to be done whenever a force moves something over a distance. So first we need to calculate the work done by the man. And then we need to substitute this work done in the formula to get the answer.

Complete step by step solution:
Let the mass of the man be \[M\]. Given the mass of the man \[M = 60kg\]
He carries a load that weighs about \[m = 20kg\]
Therefore the total weight mass\[{M_{total}} = 80{\text{ }}kg\]
The height in between each step in the staircase is \[0.2{\text{ }}m\]
Therefore the total height of the staircase is \[h = 20 \times 0.2 = 4m\]
Let the acceleration due to gravity be, \[g = 10m/{s^2}\]
We know that work equals force times height. That is,
\[W = F \times h\]
Also, \[F = mg\].
Therefore substituting in the above equation,
\[W = mgh\]
Now substituting all the values,
\[W = 80 \times 10 \times 4 = 3200joules\]
Given that he takes \[10{\text{ }}s\]to climb. Therefore \[t = 10s\]
Now we have the formula for power which is given below.
\[Power = \dfrac{{work}}{{time}}\]
\[Power = \dfrac{W}{t}\]
Substituting the values for work and time we get,
\[Power = \dfrac{{3200}}{{10}}\]\[ = 320watt\]

Therefore the power of the man is found to be \[320watt\].

Note:
Power can also be defined as the rate of change of energy gained or lost. Power can be divided into two types based on time interval. One is the average power which can be defined as the power delivered at a particular time interval. And the other is the instantaneous power that can be defined as the power delivered at a particular instant.