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)?
Show answer & explanation
Correct answer: A
Explanation
Solution: The correct answer is 300 W.
Explanation:
☛ Power is defined as the rate of doing work or the rate at which energy is transferred over time: Power (P) = Work done (W) / Time (t).
☛ When a person climbs stairs, the work done is against gravity and equals the increase in gravitational potential energy: W = m × g × h.
☛ Given data:
Mass (m) = 60 kg
Height (h) = 15 m
Acceleration due to gravity (g) = 10 m/s²
Time taken (t) = 30 s
☛ Total work done: W = 60 × 10 × 15 = 9000 Joules (J).
☛ Average power developed: P = 9000 J / 30 s = 300 Watts (W).
Extra Exam-Relevant Facts:
☛ Watt (W): The SI unit of power, named after James Watt, where 1 Watt = 1 Joule per second (1 J/s).
☛ Horsepower (hp): A commercial unit of power commonly used in engines and motors, where 1 hp = 746 Watts.
☛ Kilowatt-hour (kWh): It is a commercial unit of electrical energy, not power, where 1 kWh = 3.6 × 10⁶ Joules.
☛ Scalar Quantity: Both work and power are scalar quantities possessing only magnitude and no direction.
Important One-Liners for Upcoming Exams:
☛ What is the dimensional formula of power? → [M¹ L² T⁻³]
☛ How many watts are equal to one horsepower (hp)? → 746 W
☛ Which physical quantity has the SI unit Joule per second? → Power
☛ What is the work done by a centripetal force on an object moving in a circle? → Zero
☛ What is the relation between power, force, and velocity? → Power = Force × Velocity (P = F · v)