Calculating Work Done Revision Notes | GCSE AQA Higher Physics

1. Why Work Done Matters

When you lift your school bag, push a door open, or drag a box across the floor — you're doing work. But in physics, 'work' has a very specific meaning that's different from everyday language.

Here's the key insight: work is only done when a force actually moves something. You can push against a brick wall all day with enormous force, but if the wall doesn't budge, you've done zero work in physics terms. The energy you feel you're using? That's your muscles working inefficiently, not physics work.

This concept appears in every GCSE physics exam because it connects forces, energy, and motion. Master this, and you'll understand how engines transfer energy, why ramps make lifting easier, and how to calculate the energy cost of any movement.

2. The Work Done Equation

The work done equation is beautifully simple: work done equals force times distance. But there's a crucial detail that catches students out — the distance must be in the same direction as the force.

Notice that distance uses the symbol $s$, not $d$. This is standard physics notation — $s$ represents displacement or distance moved. The force and distance must be in the same direction for the equation to work.

Here's the key relationship that examiners love to test: 1 joule = 1 newton-metre. This isn't just a conversion — it's the fundamental definition of the joule. When you see 'N⋅m' in an answer, you can immediately write it as 'J' instead.

3. Worked Examples and Calculations

Let's tackle some exam-style calculations. The key is to identify the force, find the distance moved in the direction of that force, then multiply. Watch out for unit conversions — distances might be given in centimetres or kilometres.

Worked example: Basic Work Done Calculation

A weightlifter applies a force of 800 N to lift a barbell 1.5 m vertically upwards. Calculate the work done. [3 marks]

1. $W = F \times s$ — [M1] Correct formula stated
2. $F = 800 \text{ N}$, $s = 1.5 \text{ m}$ — Force and distance are in the same direction (upwards)
3. $W = 800 \times 1.5 = 1200 \text{ J}$ — [M1] Correct substitution [A1] Correct answer with units

Answer: 1200 J (or 1200 N⋅m)

Notice how we included units at every step and showed our working clearly. Examiners award method marks for the correct approach, even if your final answer is wrong due to a calculation error.

Worked example: Work Done with Unit Conversion

A car engine provides a driving force of 2500 N. The car travels 800 m. Calculate the work done by the engine in kilojoules. [4 marks]

1. $W = F \times s$ — [M1] Correct formula
2. $W = 2500 \times 800$ — [M1] Correct substitution
3. $W = 2,000,000 \text{ J}$ — [A1] Correct calculation
4. $W = 2,000,000 \div 1000 = 2000 \text{ kJ}$ — [A1] Correct unit conversion (1 kJ = 1000 J)

Answer: 2000 kJ

4. When No Work is Done

This is where students often get confused. You can apply a huge force and feel exhausted, but still do zero work in physics terms. The key is understanding when force and movement are connected.

Work is only done when the force causes movement in the direction of the force. If you carry a heavy suitcase horizontally across a room, the upward force from your arm does no work because the movement is horizontal, not vertical.

Similarly, when you hold a heavy object stationary, you're applying force but there's no movement, so no work is done. The force from a table supporting a book does no work because the book isn't moving.

5. Real-World Applications

Understanding work done helps explain how machines transfer energy efficiently. When you use a ramp to load heavy boxes into a van, you're doing the same amount of work as lifting them directly — but the ramp lets you use less force over a greater distance.

Car engines do work by applying force to move the car forward. The faster the car goes or the steeper the hill, the more work the engine must do per second. This is why cars use more fuel when accelerating or climbing hills.

In sports, athletes do work when they accelerate their bodies or equipment. A shot-putter does work accelerating the shot from rest to release speed. The work done equals the kinetic energy gained by the shot.

6. Exam Technique and Common Mistakes

Examiners set predictable traps in work done questions. The most common mistake is forgetting to check that force and distance are in the same direction. Always ask yourself: 'Is the object moving in the direction of the applied force?'

Unit errors can result in lost marks. Remember that work is always measured in joules, and 1 J = 1 N⋅m. If your calculation gives an answer in N⋅m, you can write it as J instead — they're the same thing.

For calculation questions, always show the formula first, then substitute values with units, then calculate. This method-mark approach can earn you marks even if your final answer is wrong due to a simple arithmetic error.

Watch out for questions involving friction or air resistance. When these forces oppose motion, they do negative work, removing energy from the moving object. The work done against friction equals the thermal energy produced.