Power
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 4 practice questions.
Power is how fast energy is transferred: P = W ÷ Δt. A force pushing along the motion delivers power P = Fv. Power is measured in watts: 1 W = 1 J/s.
1. Same work, different power
2. Power vs. energy
Energy is how much; power is how fast. Two students who climb the same stairs do the same work. The one who climbs faster has more power.
A 100 W bulb uses 100 joules every second.
P = Fv comes from P = W/t = (Fd)/t = F(d/t). It works when the force points along the velocity.
To keep a car at constant speed against air resistance, the engine’s power must equal (drag force)(speed).
3. Example, then try it
A 600 N student climbs 3.0 m of stairs in 6.0 s. What is her average power?
Work against gravity: W = mgΔh = (600 N)(3.0 m) = 1800 J.
P = W ÷ Δt = 1800 ÷ 6.0 = 300 W. Walking up in 12 s would take only 150 W.
A 1000 kg car speeds up from 0 to 20 m/s in 8.0 s on a level road. (a) What average power goes into kinetic energy? (b) At 20 m/s, air resistance is 500 N. What power keeps it moving at that speed?
(a) Energy gained: ΔK = ½(1000)(20)² = 200,000 J.
Average power: P = 200,000 ÷ 8.0 = 25,000 W (25 kW).
(b) Constant speed: the engine’s forward push must equal the 500 N drag.
Power: P = Fv = (500)(20) = 10,000 W (10 kW).
Answer: (a) 25 kW; (b) 10 kW.
4. Common mistakes
A 40 W bulb and a 100 W bulb are each on for 10 s. Which one transfers more energy?
Energy = power × time. The 100 W bulb transfers (100)(10) = 1000 J; the 40 W bulb only (40)(10) = 400 J.
Ready to practice?
4 questions on Power, each with a hint and an explanation for every wrong answer.