How fast is the work done

The idea

Power is the rate of doing work: average power P = W/t, W being the work done in time t; doing more work in the same time, or the same work in less time, needs more power.

Stairs, fast and slow

You carry your bag up a flight of stairs. One day you run up in one minute. Another day you walk up in five minutes.

The same work is done both days. Why does running feel so different?

• The work is done in a shorter time
• More work is done by running
• The bag becomes heavier

Work and time

Set the work done and the time taken.

Work per second

The same 600 J took 6 s in one case and 3 s in the other, and the shorter time needed twice the power. More work in the same time also needed more power. Power measures how fast the work is done.

Power is the rate at which work is done. The average power is P = W / t, where W is the work done in time t. Doing more work in the same time, or the same work in less time, needs more power.

Notes

Power = the rate of doing work: P = W / t. More work in the same time, or the same work in less time, needs more power.

Check yourself

A weightlifter does 1500 J of work in 5 s. What is her average power, in J s⁻¹?

Answer: 300 J s⁻¹

P = 1500 J ÷ 5 s = 300 J s⁻¹.

400 J of work is done in 8 s. What is the average power, in J s⁻¹?

Answer: 50 J s⁻¹

P = 400 J ÷ 8 s = 50 J s⁻¹.

Two students do the same work. One takes 1 minute and the other takes 5 minutes. Which one uses more power?

Power is defined as…

• The one who takes 5 minutes. The same work in a longer time means less power.
• The one who takes 1 minute — correct. Yes!
• Both use the same power. The work is the same, but the times differ, so the powers differ.
• the force applied to an object. Force is a push or a pull. Power is the work done per unit time.
• the energy an object has due to its motion. That is kinetic energy. Power is the rate of doing work.
• the rate at which work is done — correct. Yes!