# Work, power and efficiency

## Energy and work

When a causes a body to move, work is being done on the object by the force. Work is the measure of energy transfer when a force (F) moves an object through a distance (d).

So when work is done, has been transferred from one energy store to another, and so:

energy transferred = work done

Energy transferred and work done are both measured in joules (J).

### Calculating work done

The amount of work done when a force acts on a body depends on two things:

• the size of the force acting on the object
• the through which the force causes the body to move in the direction of the force

The equation used to calculate the work done is:

work done = force × distance

$W=F\times d$

This is when:

• work done (W) is measured in joules (J)
• force (F) is measured in newtons (N)
• distance (d) is in the same direction as the force and is measured in metres (m)

### Example

In this example, a force of 10 N causes the box to move a horizontal distance of 2 m, so:

$W=F \times d$

$W=10 \times 2$

$W=20~J$

One joule of work is done (or one joule of energy is transferred) when a force of one newton causes a body to move through a distance of one metre.
Question

A horizontal force of 50 N causes a trolley to move a horizontal distance of 30 m. How much work is done on the trolley by the force?

$W=F \times d$

$W=50 \times 30$

$W=1,500~J$

Question

12,000 J of energy is supplied to move a small truck a distance of 80 m. What is the size of the force applied?

$W=F \times d$

$F= \frac{W}{d}$

$F = \frac{12,000}{80}$

$F = 150~N$