Calculating Weight Using W = mg Revision Notes | GCSE AQA Higher Physics

1. Mass vs Weight - The Confusion Ends Here

Here's something that trips up almost every GCSE student: mass and weight are NOT the same thing. You might weigh yourself on bathroom scales and say "I weigh 60 kg" - but scientifically, that's wrong.

Mass is how much stuff you're made of - the actual amount of matter in your body. This never changes whether you're on Earth, the Moon, or floating in space. Weight, however, is the pull of gravity on that mass.

Think of it this way: if you travelled to the Moon, you'd have exactly the same mass (same amount of matter), but you'd weigh much less because the Moon's gravity is weaker. Your bathroom scales would show a smaller reading, but you haven't lost any actual substance.

2. The Weight Equation - Your New Best Friend

Now we can calculate weight precisely using one of the most important equations in GCSE Physics. The weight equation connects three key quantities: weight, mass, and gravitational field strength.

Notice the units carefully. Weight is measured in newtons (N) - the same unit as any force. Mass uses kilograms (kg), and gravitational field strength has the unusual unit of N/kg (newtons per kilogram).

On Earth's surface, gravitational field strength is approximately 9.8 N/kg. This means every kilogram of mass experiences a gravitational force of 9.8 newtons. In exam questions, the value of g will always be given - it might be 9.8 N/kg, 10 N/kg for easier calculations, or a different value for other planets.

The beauty of this equation is its simplicity - multiply mass by gravitational field strength. However, many students may confuse the units or omit them, so always include units in your final answer.

3. Worked Examples - Mastering the Method

Let's work through some typical exam-style calculations. The key is to follow a systematic method: write the equation, substitute the values with units, calculate, and state the final answer with correct units.

Worked example: Basic Weight Calculation

Calculate the weight of a 75 kg person on Earth. (g = 9.8 N/kg) [3 marks]

1. $W = mg$ — [M1] Correct equation selected
2. $W = 75 \text{ kg} \times 9.8 \text{ N/kg}$ — [M1] Correct substitution with units
3. $W = 735 \text{ N}$ — [A1] Correct answer with units

Answer: 735 N

Notice how we kept the units throughout the calculation. The kg cancels with the kg in the denominator of N/kg, leaving just N for the final answer. This unit checking is crucial for avoiding mistakes.

Worked example: Rearranging for Mass

An object has a weight of 120 N on a planet where g = 4.0 N/kg. Calculate its mass. [3 marks]

1. $W = mg$, so $m = \frac{W}{g}$ — [M1] Correct rearrangement
2. $m = \frac{120 \text{ N}}{4.0 \text{ N/kg}}$ — [M1] Correct substitution
3. $m = 30 \text{ kg}$ — [A1] Units cancel correctly: N ÷ (N/kg) = kg

Answer: 30 kg

When rearranging equations, always check your units make sense. Here, we divided newtons by (newtons per kilogram), which gives us kilograms - exactly what we expect for mass.

4. Different Planets, Different Weights

One of the most fascinating applications of the weight equation is comparing how much you'd weigh on different planets. Each planet has its own gravitational field strength, which dramatically affects weight calculations.

The Moon has a gravitational field strength of about 1.6 N/kg - roughly one-sixth of Earth's value. This is why astronauts could bounce around so easily during the Moon landings. Jupiter, being much more massive, has g ≈ 25 N/kg, meaning you'd weigh over twice as much there.

Worked example: Comparing Weights on Different Worlds

A 60 kg astronaut travels from Earth (g = 9.8 N/kg) to the Moon (g = 1.6 N/kg). Calculate their weight in both locations. [4 marks]

1. $W_{Earth} = 60 \text{ kg} \times 9.8 \text{ N/kg} = 588 \text{ N}$ — [M1] Correct method and calculation for Earth
2. $W_{Moon} = 60 \text{ kg} \times 1.6 \text{ N/kg} = 96 \text{ N}$ — [M1] Correct method and calculation for Moon
3. $\frac{W_{Earth}}{W_{Moon}} = \frac{588}{96} = 6.1$ — [A1] The astronaut weighs about 6 times more on Earth
4. Weight on Earth: 588 N Weight on Moon: 96 N — [A1] Both answers with correct units

Answer: Earth: 588 N, Moon: 96 N (astronaut weighs 6 times less on Moon)

This calculation shows why the Moon landings looked so bouncy. The astronauts weighed six times less than on Earth, making it much easier to jump and move around in their heavy spacesuits.

5. Exam Technique and Common Pitfalls

Weight calculations appear frequently in GCSE Physics exams, often worth 3-4 marks. The marking scheme rewards clear method, correct substitution, and proper units. Here's how to maximise your marks every time.

The most common mistake is confusing mass and weight in the question. Read carefully - if they give you a value in kg, that's mass. If they give you a value in N, that's weight. Another frequent error is forgetting units in the final answer, which costs you the final accuracy mark.

When rearranging the equation, many students panic and make algebraic errors. Remember: if you want mass, divide weight by g. If you want gravitational field strength, divide weight by mass. Practice these rearrangements until they become automatic.

For comparison questions involving different planets, always calculate each weight separately first, then compare. Don't try to take shortcuts - the method marks are awarded for showing each step clearly.