Define work and power, and use work = force times distance and power = work divided by time

What this dot point is asking

SEAB wants you to define work done and power, to use work $=$ force $\times$ distance and power $=$ work $\div$ time, and to tell the difference between how much work is done and how quickly it is done. The big idea is that work is energy transferred by a force, and power is how fast that energy is transferred.

The answer

Work done

In physics, work is done when a force moves an object in the direction of the force. Work done equals the energy transferred:

In symbols, $W = Fd$. The unit is the joule ($\text{J}$), the same unit as energy, because doing work transfers energy. One joule is the work done when a force of one newton moves an object one metre.

If you push on a wall that does not move, no work is done in the physics sense, because the distance moved is zero, even though you feel tired.

Work and energy

Doing work always transfers energy from one store to another. Lifting a box does work against gravity and gives it gravitational potential energy. Pushing a trolley does work that becomes kinetic energy. Rubbing your hands does work against friction that becomes heat. The work done equals the energy transferred.

Power

Power tells you how fast work is done, or how fast energy is transferred:

In symbols, $P = \dfrac{W}{t}$. The unit is the watt ($\text{W}$), where one watt is one joule per second ($1\ \text{W} = 1\ \text{J s}^{-1}$).

A more powerful machine does the same work in less time, or more work in the same time. Two cranes might lift the same load to the same height (the same work), but the more powerful one does it faster.

Work and power compared

Work (in joules) is the total energy transferred. Power (in watts) is the rate of transfer. A small motor can do a large amount of work if you give it enough time; a powerful motor does it quickly.

Examples in context

Example 1. Climbing stairs. Two students of the same weight climb the same staircase. They both do the same work against gravity, because the force (weight) and height are the same. But the one who runs up does it in less time, so they develop more power. This is the idea behind a simple "power up the stairs" experiment.

Example 2. Electric kettles. A $2000\ \text{W}$ kettle transfers energy twice as fast as a $1000\ \text{W}$ one, so it boils the same water in about half the time. The total energy needed to boil the water is the same; the higher-power kettle just delivers it more quickly.

Try this

• Cue. A force of $25\ \text{N}$ moves a box $4.0\ \text{m}$ in the direction of the force. Find the work done. [2 marks] $W = Fd = 25 \times 4.0 = 100\ \text{J}$.

• Cue. A machine does $900\ \text{J}$ of work in $15\ \text{s}$. Find its power. [2 marks] $P = \dfrac{W}{t} = \dfrac{900}{15} = 60\ \text{W}$.

• Cue. Explain why no work is done when you hold a heavy bag still. [2 marks] Work is force times distance moved; the bag does not move, so the distance is zero and no work is done.