Question

A girl of mass 50 kg, climbs a flight of 100 stairs each measuring 0.25 m in height, in 20 s. Find

1. Force acting on the girl
2. Work done by the girl
3. Gain in potential energy
4. Power in (i) Watts (ii) Horse power.

[Take g = 10 ms⁻²; 1 HP = 750 W]

Answer 1

Given: Mass = 50 kg

Height of each stair = 0.25 m

Number of stairs = 100

Time = 20 s

g = 10 ms⁻²

1 HP = 750 W

Total height climbed = 100 × 0.25 = 25 m

(a) Force acting on the girl (her weight) = mg

= 50 × 10

= 500 N

(b) Work done = force × vertical distance

= 500 × 25

= 12,500 J

(c) Gain in potential energy = mgh

= 50 × 10 × 25

= 12,500 J

This equals the work done in climbing.

(d) (i) Power = `"work"/"time"`

= `12500/20`

= 625 W

(ii) Power in horsepower = `625/750`

≈ 0.83 HP