What is work?

Which one is work?

A boy pushes a loaded cart along the road. A girl sits and reads a book for an hour. Who did work?

In daily life we say that both of them worked. But in physics the word work has a narrow meaning. Let us see what it is.

The two conditions

Work is done in physics when two things happen together.

1. A force acts on an object.
2. The object moves along the force (or against it).

The boy pushed the cart, and the cart moved along his push. So he did work. The girl did no work on the book, because the book did not move.

• A student pushes against a wall with all her strength. The wall does not move: no work is done on it, however tired she gets.
• A man holds a heavy box still for five minutes. The box does not move: no work is done on it.
• A porter lifts a bag onto a shelf. A force acts up, and the bag moves up: work is done.

How much work?

When a steady force $F$ moves an object a distance $s$ along the force, the work done is

with $F$ in newtons ($\text{N}$) and $s$ in metres ($\text{m}$).

On a graph of force against distance, a steady force is a flat line. The work is the area under the line: a rectangle, force high and distance wide.

The unit of work: the joule

A newton times a metre is a joule ($\text{J}$), after James Prescott Joule.

One joule is the work done when a force of $1\ \text{N}$ moves an object $1\ \text{m}$ along the force. Lifting a small apple up by $1\ \text{m}$ takes about $1\ \text{J}$. For bigger jobs we use the kilojoule: $1\ \text{kJ} = 1000\ \text{J}$.

You should find that twice the push gives twice the work, and so does twice the distance. With no distance, there is no area, and no work.

Watch out. Put the distance in metres before you multiply. A distance of $50\ \text{cm}$ is $0.5\ \text{m}$, not $50\ \text{m}$.

A worked example

A girl pushes her cycle to the repair shop with a steady force of $40\ \text{N}$, for $125\ \text{m}$ along the road. How much work does she do?

1. The force and the distance. $F = 40\ \text{N}$ and $s = 125\ \text{m}$, along the push.
2. The work. $W = F \times s = 40\ \text{N} \times 125\ \text{m} = 5000\ \text{J}$.
3. In kilojoules. $5000\ \text{J} = 5\ \text{kJ}$.

Practise with new numbers

Try it in Python

The program finds the work for three jobs.

Remember these

• Work is done when a force moves an object along the force. No force, or no movement, means no work.
• $W = F \times s$, with the movement along the force.
• The unit of work is the joule: $1\ \text{J} = 1\ \text{N} \times 1\ \text{m}$, and $1\ \text{kJ} = 1000\ \text{J}$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A guard holds a rifle still for an hour. How much work does he do on the rifle?

2. A force of $32\ \text{N}$ moves a box $5\ \text{m}$ along the force. How much work is done?

3. What force does $72\ \text{J}$ of work over a distance of $9\ \text{m}$?

4. Write $2.5\ \text{kJ}$ in joules.