Building up the joule

The unit of work is not defined by a formula but by a situation: one particular force moving one particular distance. Everything else is measured against it.

One newton through one metre

An object rests on a horizontal surface. A steady force of 1 N is applied to it and it moves 1 m in the direction of that force.

Figure to be added

Figure 18.1 — a block on a horizontal table, a force of 1 N acting on it horizontally, and the block shown again in dashed outline 1 m further along, with the 1 m marked by a double-headed arrow.

The joule

The amount of work done when a force of 1 N moves an object 1 m in the direction of the force is called one joule.

1 J

The joule — the unit in which work is measured.

Doubling and trebling the force

Now repeat the same 1 m journey with a bigger force. The distance is unchanged; only the force is different.

Figure to be added

Figure 18.2 — the same block and table, now with a force of 2 N acting on it, moved through the same 1 m.

Figure to be added

Figure 18.3 — the same block and table again, with a force of 3 N, moved through the same 1 m.

Force applied	Distance moved	Work done
1 N	1 m	1 J
2 N	1 m	2 J
3 N	1 m	3 J

The pattern is a multiplication

Treble the force over the same distance and the work trebles. Work is not something that merely grows with the force — it is exactly proportional to it, which is why the next page can write it as a product rather than a graph.