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Power and the watt

Energy and power · level 4, lesson 2 of 6

A question to start

You and a friend each carry a heavy box up the same stairs. You walk; your friend runs. Did you use the same energy? What is different?

The idea

You both lifted the same box to the same height, so you used the same energy. But your friend used it faster. How fast energy is used, or passed on, is called power:

\[\text{power} = \frac{\text{energy}}{\text{time}}.\]

Power is measured in watts, W, after James Watt, who improved the steam engine. One watt is one joule every second. A kilowatt (kW) is 1,000 watts.

Thing Power
A phone charging 5 to 20 W
An LED lamp about 8 W
A person resting about 100 W
A laptop 30 to 60 W
A kettle about 2,000 to 3,000 W
A car's engine, flat out about 100,000 W
walking: 20 ssame energy, less powerrunning: 5 ssame energy, 4 × the power

On Mars, power matters a lot, because a rover or a habitat has only so many watts to spare at any moment. Running many machines at once can use up more power than the panels or power unit can give.

Worked examples

1. The boxes. Lifting a box takes 600 J. Walking up in 20 s: \(600 \div 20 = 30\) W. Running up in 5 s: \(600 \div 5 = 120\) W.

2. A kettle. 2,000 W for 2 minutes (120 s): energy \(= 2000 \times 120 = 240{,}000\) J, or 240 kJ.

3. Energy from power. Rearranged: energy \(=\) power \(\times\) time. An 8 W lamp on for an hour (3,600 s) uses \(8 \times 3600 = 28{,}800\) J.

Try it

  1. What does power measure?
  2. A motor uses 1,500 J in 30 s. What is its power?
  3. A 60 W bulb is on for 10 minutes. How much energy does it use?
  4. Two rovers climb the same hill. One takes twice as long. Which uses more power?
Answers
  1. How fast energy is used or passed on.
  2. \(1500 \div 30 = 50\) W.
  3. \(60 \times 600 = 36{,}000\) J.
  4. The faster one: same energy in less time.

Common mistake

"A more powerful machine always uses more energy." It uses energy faster. A 2,000 W kettle on for a minute uses less energy than a 100 W lamp on for an hour.

Where it leads