Energy, work & power
Power
Power
| Symbol | Quantity | Unit |
|---|---|---|
| \( P \) | Power | watt, W |
| \( W \) | Work done (energy transferred) | joule, J |
| \( E \) | Energy transferred | joule, J |
| \( t \) | Time taken | second, s |
- 1 kW (kilowatt) = 1000 W
- 1 MW (megawatt) = 1 000 000 W
- Typical human walking: ~100 W
- Typical car engine: ~60–120 kW
- Large power station: ~1–3 GW
Power and velocity (Extended)
Extended (Supplement)This is useful when the force and speed are known but time and distance are not.
Worked examples
Example 1 — calculate power
A motor transfers 15 000 J of energy in 25 s. Calculate the power of the motor.
\( P = \dfrac{E}{t} = \dfrac{15\,000}{25} = 600\,\text{W} \)
Example 2 — find time from power and energy
A 2.0 kW electric kettle transfers 360 000 J of thermal energy. How long does it take?
\( t = \dfrac{E}{P} = \dfrac{360\,000}{2000} = 180\,\text{s} = 3.0\,\text{min} \)
Example 3 — stair-climbing power
A student of mass 60 kg climbs stairs of vertical height 4.0 m in 6.0 s. Calculate the power output. (g = 10 N/kg)
Work done against gravity: \( W = mgh = 60 \times 10 \times 4.0 = 2400\,\text{J} \)
\( P = \dfrac{W}{t} = \dfrac{2400}{6.0} = 400\,\text{W} \)
Example 4 — P = Fv (Extended)
A car's engine exerts a driving force of 2500 N when travelling at a constant speed of 30 m/s. Calculate the power output of the engine.
\( P = Fv = 2500 \times 30 = 75\,000\,\text{W} = 75\,\text{kW} \)
Note: at constant speed, driving force = friction + air resistance, so all power goes to overcoming drag.