Work and Its Measurement: Quick Revision

A brief note on Work and Its Measurement. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• Work is done when a force moves an object along (or against) the force. No movement, no work.
• $W = F \times s$, in joules: $1\ \text{J} = 1\ \text{N} \times 1\ \text{m}$, and $1\ \text{kJ} = 1000\ \text{J}$.
• On a graph of force against distance, the work is the area under the line.
• The work is positive when the force is along the motion, negative when it is against it, and zero at right angles.
• Lifting at a steady speed: $W = mgh$. Only the height counts, not the path.
• Pulling along level ground at a steady speed: $W = f \times s$, with $f$ the friction.

The facts at a glance

A worked example

A girl pushes a $9\ \text{kg}$ suitcase up a smooth ramp $3\ \text{m}$ long onto a stage $0.6\ \text{m}$ high, then slides it $4\ \text{m}$ across the stage against a friction force of $20\ \text{N}$.

1. Up the ramp. Against gravity only the height counts: $9\ \text{kg} \times 9.8\ \text{m/s}^2 \times 0.6\ \text{m} = 52.9\ \text{J}$.
2. Across the stage. $20\ \text{N} \times 4\ \text{m} = 80\ \text{J}$.
3. In all. $52.9\ \text{J} + 80\ \text{J} = 132.9\ \text{J}$.

Practice with new numbers

A program to try

The program adds up the work of a day's jobs.

Mistakes to avoid

• Using the mass as the force. Change kilograms to newtons with $mg$ first.
• Counting sideways walking as work on a load you carry. Your force on it is up; the motion is sideways.
• Forgetting the sign. Friction and brakes do negative work.
• Using the length of a ramp as the height. Use the vertical height for $mgh$.

Check yourself

1. A man pushes a wall for ten minutes, and it does not move. How much work does he do on the wall?

2. A force of $18\ \text{N}$ moves a box $5\ \text{m}$ along the force. Find the work.

3. What is the sign of the work done by gravity on a ball that rises?

4. How much work is done in lifting a $2.5\ \text{kg}$ bag onto a shelf $2\ \text{m}$ high?