Power
Not how much work, but how fast.
Lesson at a glanceShow the key points
- Power is the rate of doing work: P = dW/dt = F·v.
- SI unit: watt (1 W = 1 J/s); 1 horsepower = 746 W.
- Lifting a mass m at constant speed v needs power mgv.
- Average power over an interval = total work / time; instantaneous power can differ.
Walking up the stairs and running up them take the same work. Running is harder because you deliver that work faster: more power.
Power
The rate at which a force does work is its power. In a small time dt the work is , so
That is instantaneous power. Over an interval, average power is the total work divided by the time taken.
A loaded lift of mass 800 kg must rise at a steady 0.50 m/s. What is the minimum motor power, in watts and horsepower? (g = 9.8 m/s²)
A 3.0 kg block is pulled up a smooth 30° incline from rest with an acceleration of 2.0 m/s². Find the pulling force’s power at t = 3.0 s and its average power over the first 3.0 s. (g = 9.8 m/s²)
- 1.
- 21 W = 1 J/s; 1 hp = 746 W.
- 3Lifting at constant speed: P = mgv.
- 4Average power = total work / total time.
Check yourself
Keep exploring
Hand-picked videos, simulations and readings that explain this idea from a different angle.