Question

Find the rate of doing work by a man of 60 kg in climbing a staircase of vertical height of 10 m in half a minute. Take, g = 10 m/s².

Answer 1

Step 1: Given data

Mass of the man is, $m=60kg$

The height of the staircase is, $h=10m$

Time taken in climbing the staircase is, $t=\frac{1}{2}min=30sec$ or $30s$

Acceleration due to gravity is to be taken as, $g=10m/s^2$

Step 2: Calculating work done

When a body is lifted through a height, work done is given as,

$W=mgh$

where, $m$ is mass, $g$ is the acceleration due to gravity and $h$ is height.

Substituting the known values in the above equation, we get,

$$\begin{gathered} W=60kg\times 10m/s^2\times 10m \\ W=6000J \end{gathered}$$

Step 3: Calculating rate of doing work

The rate of doing work is termed power.

Power is given as,

$P=\frac{W}{t}$

where, $W$ is work done and $t$ is time.

Substituting the known values, we get,

$$\begin{gathered} P=\frac{6000J}{30s} \\ P=200W \end{gathered}$$

Therefore, the rate of doing work is $200W$.