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Run up the stairs in one minute or stroll up in five — the same work, but they feel completely different. That difference is power.
- Power is the rate at which work is done . Average power is the work done divided by the time taken: $$P = \dfrac{W}{t}$$
- Doing more work in the same time, or the same work in less time, needs more power.
- The SI unit of power is the watt (W) : \(1\ \text{W} = 1\ \text{J s}^{-1}\) (one joule of work per second).
- Power — the rate at which work is done; average power P = W / t.
- Watt (W) — the SI unit of power; 1 W = 1 joule of work done per second (1 J s⁻¹).
A weightlifter lifts a 75 kg mass by 2 m in 5 s. What power does she need? (g = 10 m s⁻²)
Work \(= mgh = 75 \times 10 \times 2 = 1500\ \text{J}\).
\( P = \dfrac{W}{t} = \dfrac{1500\ \text{J}}{5\ \text{s}} = 300\ \text{W} \).
A 1000 kg car reaches 72 km h⁻¹ from rest in 10 s. Find the engine power needed.
\(v = 72\ \text{km h}^{-1} = 20\ \text{m s}^{-1}\), \(u = 0\). Work \(=\) gain in KE \(= \tfrac{1}{2}\times 1000 \times 20^2 = 200000\ \text{J}\).
\( P = \dfrac{200000\ \text{J}}{10\ \text{s}} = 20000\ \text{W} \).
- The unit of power, the watt , is named in honour of James Watt , who invented an efficient steam engine that could generate rotational motion and move wheels.
- Another unit of power is horsepower (hp) , used for car engines and water pumps: \(1\ \text{hp} = 746\ \text{W}\). In the early days of engines, their power was compared with the power of actual horses that drove carriages.
NCERT Question 6 — A crane lifts a mass
A crane lifts mass m to the 10th floor, then to the 20th floor in double the time. How much more energy and power are required?
View the answer →NCERT Question 7 — Which factors determine the energy
For raising a flag by a pulley: what determines the energy needed, does slow/fast change the work, and what happens to power if the speed doubles?
View the answer →