Question

A boy of weight 40 kgf climbs up the 15 steps, each 15 cm high in 10 s and a girl of weight 20 kgf does the same in 5 s. Compare:

1. the work done, and
2. the power developed by them. Take g = 10 N kg^-1.

Answer 1

Weight of boy = 40 kgf

No. of steps = 15; Each = 15 cm; Time = 10 sec

Force of gravity on boy -

F₁ = m₁g = 40 × 10 = 400 N

Force of gravity on girl -

F₂ = m₂g = 20 × 10 = 200 N

Total height climbed (h) = 15 × 15 = 225 cm = 2.25 m

(i) Work done by boy -

W₁ = F₁ × h = 400 × 2.25 = 900 J

Work done by Girl -

W₂ = F₂ × h = 200 × 2.25 = 450 J

W₁ : W₂ = ${\displaystyle \frac{900}{450}=\frac{2}{1}}$

W₁ : W₂ = 2 : 1

(ii) Power = ${\displaystyle \frac{\text{work done}}{\text{Time taken}}}$

t₁ = 10 sec; t₂ = 5 sec

P₁ [Boy] = ${\displaystyle \frac{900\text{J}}{10\text{s}}}$ = 90 W

P₂ [Girl] = ${\displaystyle \frac{450\text{J}}{5\text{s}}}$ = 90 W

P₁ : P₂ = 90 : 90 = 1 : 1