Question

A boy weighing $40kgf$climbs up a stair of $30$ steps each $20cm$ high $4min$ and a girl weighing $30kgf$ does the same in $3min$. Compare

(i) the work done by them.

(ii) the power developed by them.

Answer 1

Step 1: Given data:

Weight of the boy, $F_b=40kgf$

$$\begin{gathered} =40\times 10 \\ =400N \end{gathered}$$ (Assumption; $g=10m/s^2$).

Time taken by the boy, $t_b=4min$

$$\begin{gathered} t_b=4\times 60seconds(1min=60seconds) \\ {t}_b=240s \end{gathered}$$

Weight of the girl, $F_g=30kgf$

$$\begin{gathered} =30\times 10 \\ =300N \end{gathered}$$

Time taken by the girl, $t_g=3min$

$$\begin{gathered} =3\times 60seconds \\ =180s \end{gathered}$$

Number of steps = 30

Height of each step = 20 cm

Displacement covered(D) by them, $D=Numberofsteps\times Heightofeachstep$

$D=30\times 20$

$$\begin{gathered} =600cm \\ =6m(1m=100cm) \end{gathered}$$

Step 2: Finding the work done by them.

We know, $Workdone=Force\times Displacement$

Work done by the boy in climbing the stairs, $W_b=F_b\times D$

$=400\times 6$

$=2400J$

Work done by the girl in climbing the stairs, $W_g=F_g\times D$

$=300\times 6$

$=1800J$

Step 3: Comparing the work done by them:

On comparing the work done by them, we get

$\frac{W_b}{W_g}=\frac{2400J}{1800J}$

$=\frac{4}{3}$

Thus, the ratio of the work done by the boy : girl is $4:3$.

Step 4 : Finding the power developed by them.

We know, $Power=\frac{Workdone}{Timetaken}$

Thus, the power developed by boy, $p_b=\frac{2400J}{240s}$

$=10\text{W}$

The power developed by girl, $p_g=\frac{1800J}{180s}$

$=10\text{W}$

Step 5: Comparing the power developed by them:

On comparing power developed by them, we get

$\frac{p_b}{p_g}=\frac{10}{10}$

Therefore, the power developed by the boy : girl is $1:1$ and the ratio of the work done by the boy : girl is $4:3$.