Q1. A 60 kg man runs up a 15 m high staircase in 30 seconds. What is the average power developed by him (take g = 10 m/s²)?
- (a) 300 W
- (b) 350 W
- (c) 100 W
- (d) 250 W
Answer & solution
Answer: (a) 300 W
Average power = work ÷ time = mgh ÷ t.
Work = 60 × 10 × 15 = 9,000 J, so power = 9,000 ÷ 30 = 300 W.
Revision note — Work, energy and power
• Work = force × displacement in the direction of the force; SI unit joule (J), and 1 J = 1 N m.
• Work done in climbing a height h against gravity equals the gain in potential energy, mgh.
• Power is the rate of doing work, P = W ÷ t; SI unit watt (W), and 1 W = 1 J/s.
• Power can also be written as P = F × v (force × velocity), which gives the same unit.
• 1 horsepower = 746 W. The commercial unit of energy is the kilowatt-hour, and 1 kWh = 3.6 × 10⁶ J.
• In a staircase problem only the vertical height counts — the horizontal run does no work against gravity.
Do not mix these up
• Work vs power — work is the total energy transferred (joule); power is how fast it is transferred (watt = joule per second).
• Watt vs watt-hour — the watt measures power; the watt-hour and the kilowatt-hour measure energy.
Also asked from this topic: the power of a 50 kg girl climbing a 5 m rope in 25 s (98 W, g = 9.8 m/s²); the quantity given by force × velocity (power); one kilowatt-hour in joules (3.6 × 10⁶ J).