Positive, negative and zero work

The direction matters

A force and a movement both have a direction. So far they pointed the same way. What if they do not?

Positive work

The force acts along the movement. A girl pushes a cart forward and it moves forward: she does positive work. Gravity does positive work on a falling stone: the pull is down, and the stone moves down. Positive work gives the object energy, and it speeds up.

Negative work

The force acts against the movement. A box slides to the right while friction pulls it to the left: friction does negative work,

The minus sign says the force takes energy away, and the box slows down. Gravity does negative work on a stone thrown up, and a brake does negative work on a moving cycle.

Zero work

The force acts at right angles to the movement. A man carries a bag along a level road. His hand pushes the bag up, but the bag moves forward. Up is at right angles to forward, so he does no work on the bag.

A satellite goes round the Earth on a circle. Gravity pulls it towards the centre, at right angles to its path. So gravity does no work on it, and its speed stays the same.

You should find that the work of gravity is negative all the way up, and grows back to zero on the way down. When the ball is back in your hand, gravity has done no work in all.

Watch out. The sign belongs to one force. Friction can do negative work on a box while your push does positive work on it, at the same time.

A worked example

A ball of $0.25\ \text{kg}$ is thrown up and rises $8\ \text{m}$. Find the work done by gravity on the way up, on the way down, and in all.

1. The force. The weight is $0.25\ \text{kg} \times 9.8\ \text{m/s}^2 = 2.45\ \text{N}$, pointing down.
2. Up. The ball moves up, against the weight: $W = -2.45\ \text{N} \times 8\ \text{m} = -19.6\ \text{J}$.
3. Down. The ball moves down, along the weight: $W = +19.6\ \text{J}$.
4. In all. $-19.6\ \text{J} + 19.6\ \text{J} = 0\ \text{J}$.

Practise with new numbers

Try it in Python

The program gives each force its sign.

Remember these

• Positive work: the force is along the movement. Negative work: the force is against it.
• Zero work: the force is at right angles to the movement, or nothing moves.
• Negative work takes energy away, so the object slows down.

Check yourself

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

1. An apple falls from a tree. Is the work done on it by gravity positive, negative or zero?

2. A stone on a string is whirled round in a circle at a steady speed. What work does the string's pull do on it?

3. A friction force of $10\ \text{N}$ acts on a sledge while it slides $3\ \text{m}$. What is the work done by friction?

4. Why does a ball thrown up slow down as it rises?