Energy and work

When a force 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, energy 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 by a force

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 distance 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 \ x \

This is when:

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

Example

A man pushes a box with a force of 10 newtons to move it a distance of 2 metres

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

\ W \ = \ F \ x \

\ W = 10 \times 2 \

\ W = 20 \ J \

curriculum-key-fact
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 \ x \

\ 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 \ x \

\ F \ = \frac{W}{x} \

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

\ F = 150 \ N \

Calculating work done when a current flows in a circuit

A current will flow in a circuit when there is a potential difference applied to the circuit. The power supply (or cell or battery) gives an amount of energy to each coulomb of charge flowing.

A 6 volt cell, for example, gives 6 joules of energy to each coulomb. We can also use the word 'work' instead of the word 'energy' because:

work done = energy transferred

so

\ V = \frac{E}{Q} \

which can be rearranged to

energy = voltage × charge

\ E = \ VQ \

can be called energy transferred or work done by the power supply.

Question

How much energy is transferred (or work done) when 3 C of charge moves through a potential difference of 6 V across a resistor?

\ V = \frac{E}{Q} \

\ E = \ VQ \

\ E = \ 6 \times 3 \

\ E = \ 18 \ J \

Question

If the 3 C of charge flows in 6 seconds, how big is the current in the resistor?

\ I \ = \ \frac{Q}{t} \

\ I \ = \ \frac{3}{6} \

\ I \ = \ 0.5 \ A \

Question

What is the total energy dissipated in the resistor?

\ E \ = \ Pt \

\ E \ = \ 3 \times 6 \

\ E \ = \ 18 \ J \

Note that the first answer and the last answer agree.