Question

A labourer weighing 70 kg climbs 11 steps of staircase each 0.21 m high in 1.4 seconds. Find the power in watt and horsepower. (take g=9.8 m/s²)

Answer 1

1131.9 W or 1.52 horse power is required by to climb staircase.

Explanation:

1. Given data

  Mass of man (m)= 70 kg

  Gravity acceleration $\mathbf{(g)=9.8 \ \left ( \frac{m}{s^{2}} \right ))}$

  Number of steps (n) =11

  Height of each steps (h)= 0.21 m

  Time taken to climb up (t) =1.4 s

2. Total height of staircase (H) =n×h

⇒ Total height of staircase (H) =11×0.21=2.31 m

3. Work done by man (W)= m×g×H

⇒ Work done by man (W)= 70×9.8×2.31 =1584.66 (J)

4. $\mathbf{Power \ (P)=\frac{Work \ done}{Time}}$

⇒ $\mathbf{Power \ (P)=\frac{1584.66}{1.4}=1131.9 \ W}$

⇒ $\mathbf{Power \ (P)=\frac{1131.9}{746}=1.52 \ hp}$

Answer 2

Power = 1132 W or 1.52 HP

Explanation:

Mass of labourer m = 70kg

Total height of stair case = height of each step * number of steps = 0.21 * 11 = 2.31 m

Time taken to climb t = 1.4 seconds

acceleration due to gravity g = 9.8 ms-2

Work done W = mgh = 70 × 9.8 × 2.31 = 1585 J.

Power P = work done/ time = 1585 / 1.4 = 1132 W

Converting to HP:

1 HP = 746 Watts

So 1132 W in HP = 1132 / 746 = 1.52 HP