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

1.2 Motion – Comparing Weights and Masses Using a Balance

Learning Objective

Students should be able to explain how a balance can be used to compare the weights (and therefore the masses) of different objects.

Key Concepts

• Mass – the amount of matter in an object, measured in kilograms (kg) or grams (g).
• Weight – the force exerted on a mass by gravity, measured in newtons (N). The relationship is \$W = mg\$, where \$g\$ is the acceleration due to gravity (\$\approx 9.8\ \text{m s}^{-2}\$ on Earth).
• Balance – a device that compares the gravitational forces on two masses placed at equal distances from a fulcrum.
• Equilibrium – when the torques on either side of the balance are equal, the beam remains horizontal.

Why Use a Balance?

A balance does not measure weight directly; it compares the gravitational forces on two objects. Because the acceleration due to gravity \$g\$ is the same for both objects (assuming they are at the same location), the comparison of forces is equivalent to a comparison of masses.

Principle of Operation

1. Place the unknown object on one pan of the balance.
2. Place known standard masses on the other pan until the beam is horizontal (i.e., in equilibrium).
3. The total mass of the standard weights equals the mass of the unknown object.

Step‑by‑Step Procedure

1. Zero the balance if it has a tare function.
2. Ensure the balance is on a level surface; use the built‑in spirit level if provided.
3. Place the object whose mass is to be determined on the left pan.
4. Gradually add standard masses to the right pan until the beam is level.
5. Record the total mass of the standard weights; this is the mass of the unknown object.
6. If required, calculate the weight using \$W = mg\$.

Example

Determine the mass of a metal block using standard masses of 50 g, 20 g, and 10 g.

1. Place the metal block on the left pan.
2. Add a 50 g mass to the right pan – the beam tilts left.
3. Add a 20 g mass – the beam still tilts left.
4. Add a 10 g mass – the beam becomes horizontal.

Therefore, the mass of the metal block is \$50\ \text{g} + 20\ \text{g} + 10\ \text{g} = 80\ \text{g}\$.

The weight of the block is \$W = mg = 0.080\ \text{kg} \times 9.8\ \text{m s}^{-2} = 0.784\ \text{N}\$.

Comparison Table: Mass vs. Weight

Common Misconceptions

• Thinking a balance measures weight directly – it actually compares forces, which are proportional to mass when \$g\$ is constant.
• Assuming the balance can differentiate between objects of equal mass but different densities – it cannot; only mass matters.
• Neglecting the need for the balance to be level – an unlevel balance gives erroneous comparisons.

Suggested Diagram

Summary

A balance provides a reliable method for comparing masses (and therefore weights) because the gravitational acceleration \$g\$ is the same for both sides of the device. By achieving equilibrium, the masses on each side are equal, allowing students to determine unknown masses using known standards.

Practice Questions

1. A student places an unknown object on the left pan and balances it with a 200 g standard mass and a 50 g standard mass on the right pan. What is the mass of the unknown object? Calculate its weight on Earth.
2. Explain why a balance would give the same reading for an object on Earth and the same object on the Moon, even though the weight is different.
3. Two objects have the same mass but different shapes. Will a balance show any difference when they are compared? Justify your answer.