Work & power

You haul a crate of water up to the third floor. At the top you are out of breath, but your neighbour with the same crate is not, because he took his time. Did you still achieve the same thing? Physics has a surprisingly clear answer, and it lives in two words: work and power.

Work = force times distance

In physics you do work when you move something over a distance with a force: W = F · s. The formula is this simple as long as the force pulls or pushes along the direction of motion. The unit is the joule, J for short, and 1 J is 1 N times 1 m. If you lift a bar of chocolate (about 1 N of weight) one metre up, you have done roughly 1 J. For the crate going to the third floor, only force and height count, not how exhausted you feel.

Power = work per time

Power says how fast work is done: P = W/t, measured in watts, W for short, where 1 W equals 1 J per second. If you run up the stairs, you do the same work as when climbing slowly, but in less time, so with more power. That's exactly why you're out of breath at the top: your body had to deliver the energy faster.

Metric horsepower, watts and your own power

For cars you often read PS, the old German unit of metric horsepower: 1 PS is about 735 W. A 100 PS car therefore delivers around 73500 W, which is just over 73 kW, since one kilowatt is 1000 watts. And you? If you weigh 50 kg, the Earth pulls on you with about 500 N. Climbing a 3 m staircase means 1500 J. If you manage that in 5 seconds, you deliver 300 W, so briefly about 0.4 PS!