Know that weights (and masses) may be compared using a balance

1.2 Motion – Comparing Weights with a Balance ⚖️

1.2.1 Mass vs Weight

Mass is the amount of matter in an object and is measured in kilograms (kg). It is the same everywhere in the universe. Weight is the force of gravity on that mass and is measured in newtons (N). It changes with the strength of gravity.

The relationship is given by the simple equation:
$W = m \, g$ where $m$ is mass and $g$ is the acceleration due to gravity (≈9.8 m s^-2 on Earth).

1.2.2 Analogy: Apples on a Scale 🍎

Imagine you have two apples. One apple is heavier than the other. If you put them on a balance scale, the side with the heavier apple will tip down. The scale is measuring the weight of each apple. Even if the apples are in space (no gravity), their mass remains the same, but the scale would show zero weight because $g = 0$.

1.2.3 Using a Balance to Compare Weights

1. Place the unknown object on one side of the balance.
2. On the other side, add known masses (e.g., 1 kg, 2 kg, 5 kg) until the balance is level.
3. The total mass on the known side equals the mass of the unknown object.
4. Multiply that mass by $g$ to find the weight if required.

1.2.4 Example Problem

A 3 kg block is placed on a balance. Which combination of standard masses will balance it?
Answer: 2 kg + 1 kg = 3 kg. The weight of the block is $W = 3\,\text{kg} \times 9.8\,\text{m\,s}^{-2} = 29.4\,\text{N}$.

1.2.5 Quick Reference Table