Definition
- Power is the rate at which work is done, or equivalently the rate at which energy is transferred
- The SI unit is the watt (W), where 1 W = 1 J/s (one joule transferred per second)
- Common multiples: 1 kW = 1000 W; 1 MW = 1 000 000 W
Why time matters
- Two machines that do the same total work over different times have different powers. A weightlifter and a forklift may both lift a 200 kg crate onto a shelf, but if the forklift does it in 1 s while the weightlifter takes 30 s, the forklift's power is 30 times larger
- High-power devices either deliver large amounts of useful work very quickly (a rocket engine) or low amounts of useful work continuously over long periods (a wall-mounted clock running for years)
The power equation
P = W / t
- where:
- P = power (W)
- W = work done, or energy transferred (J)
- t = time taken for the transfer (s)
- Useful rearrangements:
- W = P × t (the energy a device transfers in a given time)
- t = W / P (how long a device of fixed power needs to deliver a target amount of energy)
Typical power ratings
| Device | Approximate power |
|---|
| Pocket torch | ~1 W |
| Incandescent light bulb | ~60–100 W |
| Hair dryer | ~1500 W |
| Electric oven | ~3 kW |
| Family car at cruise | ~25 kW |
| Saturn V rocket at launch | ~100 MW |
| Large coal-fired power station | ~2 GW (2000 MW) |
Example — a hair dryer rated at 1500 W is used continuously for 90 seconds. Calculate the total energy it transfers.
- Rearrange P = W / t to W = P × t
- W = 1500 × 90 = 135 000 J (or 135 kJ)
Example — an electric motor lifts a 60 kg load to a height of 5.0 m in 4.0 s. Take g = 10 N/kg and ignore friction. Calculate the useful output power of the motor.
- Work done against gravity = m × g × h = 60 × 10 × 5.0 = 3000 J
- Useful power = W / t = 3000 / 4.0 = 750 W