# Mass and weight

> Physics · CIE A-Level
> Source: https://www.owlsprep.com/study/cie-9702-u3-mass-and-weight/

This sub-topic clarifies the key difference between mass and weight, two frequently confused concepts in CIE A-Level Physics. You will learn to calculate weight and distinguish between inertial and gravitational mass.

**Prerequisites:** [Physical quantities and SI units](https://www.owlsprep.com/study/cie-9702-u2-physical-quantities/); [Forces as vectors](https://www.owlsprep.com/study/cie-9702-u3-forces-as-vectors/)

## Learning objectives

- Distinguish between mass and weight correctly for exam questions
- Calculate weight using the relationship $W=mg$
- Explain the difference between inertial and gravitational mass
- Avoid common unit and conceptual mistakes

## Definitions and Core Differences

**Mass** — An intrinsic property of an object that measures the amount of matter it contains. It is a scalar quantity and constant regardless of location.

*Notation:* $m$

*Example:* A 3 kg bowling ball has the same mass on Earth and the Moon.

**Weight** — The gravitational force acting on an object's mass. It is a vector quantity that points towards the centre of the local gravitational field.

*Notation:* $W$

*Example:* A 3 kg ball weighs ~29.4 N on Earth but only ~4.8 N on the Moon.

The most common mistake in CIE exams is treating these two quantities as interchangeable. Mass is a property of the object, weight is a force that depends on the local gravity.

**Worked example:** A student measures a stone's mass as 4.5 kg on Earth. What are the mass and weight of the stone on the Moon, where $g = 1.6 \text{ N kg}^{-1}$?

1. Mass is intrinsic, so it does not change with location:
2. $$\text{Mass} = 4.5 \text{ kg}$$
3. Weight is calculated using the formula $W = m g$:
4. $$W = (4.5 \text{ kg})(1.6 \text{ N kg}^{-1}) = 7.2 \text{ N}$$
5. Final answer: mass = 4.5 kg, weight = 7.2 N towards the Moon's centre.

> **Exam tip:** Always check units: mass is in kilograms (kg), weight is in newtons (N), marks are often awarded for correct units.

## Gravitational Field Strength and Weight Calculations

**Gravitational Field Strength** — The gravitational force per unit mass acting on any object placed at a point in a gravitational field. Its unit is $\text{N kg}^{-1}$, equivalent to $\text{m s}^{-2}$.

*Notation:* $g$

*Example:* On Earth's surface, $g \approx 9.8 \text{ N kg}^{-1}$ for CIE calculations.

Rearranging the definition $g = \frac{W}{m}$ gives the standard formula for weight: $W = m g$. This formula is used in almost all dynamics problems, from projectile motion to equilibrium.

**Worked example:** A hiker has a weight of 735 N on Earth, where $g = 9.8 \text{ N kg}^{-1}$. What is their weight on Venus, where $g = 8.9 \text{ N kg}^{-1}$?

1. First calculate the hiker's constant mass from Earth weight:
2. $$m = \frac{W_{\text{Earth}}}{g_{\text{Earth}}} = \frac{735}{9.8} = 75 \text{ kg}$$
3. Use the constant mass to calculate weight on Venus:
4. $$W_{\text{Venus}} = m g_{\text{Venus}} = 75 \times 8.9 = 667.5 \text{ N} \approx 670 \text{ N (2 s.f.)}$$

**Check your understanding**

Check your understanding:

1. What is the correct unit for weight in CIE A-Level Physics?

   - kg
   - N
   - N kg⁻¹
   - m s⁻²

   *Answer:* N

   *Why:* Correct! Weight is a force, so its unit is the newton (N).

## Inertial vs Gravitational Mass

Mass can be classified by the property it measures. For CIE A-Level, you only need to know the basic distinction between the two types, which are experimentally shown to be equivalent.

**Inertial Mass** — A measure of an object's resistance to acceleration when an external force is applied. It is defined from Newton's Second Law as $m_i = \frac{F}{a}$.

**Gravitational Mass** — A measure of how much gravitational force an object experiences in a given gravitational field. It determines weight via $W = m_g g$.

**Worked example:** A 12 N force accelerates an object at $3.0 \text{ m s}^{-2}$. What is the object's inertial mass, and what is its weight on Earth ($g = 9.8 \text{ N kg}^{-1}$)?

1. Calculate inertial mass from Newton's Second Law $F = m a$:
2. $$m_i = \frac{F}{a} = \frac{12}{3.0} = 4.0 \text{ kg}$$
3. Since inertial mass = gravitational mass for all objects, calculate weight:
4. $$W = m g = 4.0 \times 9.8 = 39.2 \text{ N}$$

> **Exam tip:** If asked to distinguish the two, remember: inertial mass resists acceleration, gravitational mass interacts with gravity.

## Common pitfalls

- **Wrong:** Claiming weight is a scalar quantity like mass
  - Why it fails: Weight is a force, which always has direction (towards the centre of mass of the gravitational source), so it is a vector
  - Correct: Always state that mass is scalar and weight is a vector force when asked to compare them
- **Wrong:** Changing mass when calculating weight on another planet
  - Why it fails: Mass is an intrinsic property of the object that does not depend on location
  - Correct: Keep mass constant, only recalculate weight using the new local value of $g$
- **Wrong:** Writing the unit of mass as N or weight as kg
  - Why it fails: CIE examiners consistently award and deduct marks for correct units, this is an easy mistake to avoid
  - Correct: Memorise: mass = kilogram (kg), weight = newton (N)
- **Wrong:** Mixing up inertial and gravitational mass definitions in exams
  - Why it fails: Students often confuse which type of mass relates to acceleration vs gravity
  - Correct: Remember: INertial = INertia (resistance to acceleration), G Ravitational = G Ravity

## Cheatsheet

| Quantity | Symbol | Type | Unit | Key Property |
| --- | --- | --- | --- | --- |
| Mass | $m$ | Scalar | kg | Constant, intrinsic property |
| Weight | $W$ | Vector | N | Depends on local $g$ |
| Gravitational field strength | $g$ | Scalar | N kg⁻¹ | Force per unit mass |
| Inertial mass | $m_i$ | Scalar | kg | Measures resistance to acceleration |
| Gravitational mass | $m_g$ | Scalar | kg | Measures gravitational interaction |
| Weight formula |  |  | $W = mg$ |  |

## What's next

Now that you understand the core difference between mass and weight, you are ready to build on this foundation for more advanced dynamics concepts. All of Newton's laws of motion rely on the correct distinction between mass (an intrinsic property) and weight (a gravitational force), and you will use the formula $W = mg$ in almost every subsequent topic, from projectile motion and equilibrium to circular motion and gravitation. Getting this concept right early helps you avoid losing easy marks in both multiple choice and written paper questions, where this distinction is frequently tested.

- [Forces, density and pressure](https://www.owlsprep.com/study/cie-9702-u4-overview/)
- [Common force types](https://www.owlsprep.com/study/cie-9702-u4-common-force-types/)
- [Force equilibrium](https://www.owlsprep.com/study/cie-9702-u4-force-equilibrium/)

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