9 min readConcept sheetSection A MCQ (1 mark) and fill in the blanks (2 marks, two parts); Section B very short answer (2 marks) or short answer numerical (3 marks)

Power and its units

Power is the rate of doing work: P = W/t. Its SI unit is the watt; 1 kW = 1000 W and 1 horse power = 746 W.

PowerP = W/t (W = work done in J, t = time taken in s)

Watt1 W = 1 J of work done in 1 s; 1 W = 1 J s⁻¹

Larger units1 kilowatt (kW) = 1000 W; 1 horse power (hp) = 746 W

kW and kWhThe kilowatt is a unit of power; the kilowatt hour (kWh) is a unit of energy

How fast work is done

Two people of the same weight climb the same stairs. They do the same work. The one who runs up gets more tired, because she does the work faster. The rate of doing work is called power. Power = work done ÷ time taken, or P = W/t. A machine's power rating tells how fast it can do work.

Activity: climb stairs slowly, then run up

You need a staircase, a stopwatch or phone timer, a ruler and a friend to time you.

1
Count the steps and measure the height of one step. Multiply them to get the total height h in metres.
2
Walk up slowly while your friend times you. Note the time t₁.
3
Rest, then run up the same stairs carefully, holding the railing. Note the time t₂.
4
The work done against gravity is mgh both times. Use your mass m and g = 9.8 m s⁻².
5★
Find the power each time: P = mgh/t. Running gives a larger power, because t₂ is smaller.
6
Record: the work was the same, but running felt harder because you did it in less time.

★ key step

Worked example: power of a stair climber

Problem

A girl of mass 40 kg runs up a staircase 4.5 m high in 6 s. Find her power. (g = 9.8 m s⁻²)

Working

Work done = mgh = 40 × 9.8 × 4.5 = 1764 J.
Power = W/t = 1764 J ÷ 6 s = 294 W.

Answer

294 W

Worked example: a water pump

Problem

A 1 hp pump lifts water. How much work can it do in 1 minute? How much water can it lift through 10 m in that time? (1 hp = 746 W; g = 9.8 m s⁻²)

Working

P = 746 W and t = 1 min = 60 s.
W = P × t = 746 W × 60 s = 44 760 J.
Mass lifted = W ÷ (gh) = 44 760 ÷ (9.8 × 10) ≈ 457 kg.

Answer

About 44 760 J (44.8 kJ) of work, enough to lift about 457 kg (about 457 litres) of water through 10 m

Units of power

SI unit: the watt (W), named after James Watt. 1 W = 1 J s⁻¹.
1 kilowatt (kW) = 1000 W. Geysers and air conditioners are rated in kW.
1 horse power (hp) = 746 W. Water pumps and motors are often rated in hp.
Do not confuse kW (power) with kWh (energy): 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J.
A 1 hp motor works twice as fast as a ½ hp motor, so it fills a tank in half the time.

In real life

An electric kettle marked 1500 W turns 1500 J of electrical energy into heat every second. A farmer choosing between a 1 hp and a 2 hp pump set is choosing how fast water is lifted.

Exam angle

2 marks: “Define power and give its SI unit. Express 2 hp in watts.” Power is the rate of doing work: P = W/t. Its SI unit is the watt (1 W = 1 J s⁻¹). 2 hp = 2 × 746 = 1492 W.

1 marks: “Which is the unit of power: kW or kWh?” The kW. The kilowatt hour is a unit of energy.

3 marks: “A motor lifts a 200 kg load through 15 m in 20 s. Find its power in watts and in kilowatts. (g = 9.8 m s⁻²)” W = mgh = 200 × 9.8 × 15 = 29 400 J. P = W/t = 29 400 ÷ 20 = 1470 W = 1.47 kW.

Remember it

Same work in less time means more power: P = W/t.