# Mass, Weight and Density

> Physics · CIE IGCSE 0625
> Source: https://www.owlsprep.com/study/cie-0625-u1-mass-weight-and-density/

This guide covers core definitions of mass, weight and density, key linking formulas, and tiered practice for CIE IGCSE Physics 0625 Core and Extended exams, including experimental density techniques (Core) and predicting floating from density data (Extended).

**Prerequisites:** [Basic SI units for CIE IGCSE Physics](https://www.owlsprep.com/study/cie-0625-u1-si-units/)

## Learning objectives

- Define mass and weight, and distinguish between the two quantities
- Recall and use the relationship W = mg to calculate weight
- Define density, recall and use ρ = m/V to solve Core calculation problems
- Describe experimental methods to determine the density of regular/irregular solids and liquids (Core), and use density data to predict floating and sinking (Extended)

## Mass vs Weight (Core)

Mass is a measure of the amount of matter in an object, measured in kilograms (kg). It is a scalar quantity (magnitude only) and does not change with location. Weight is the force of gravity acting on an object, measured in newtons (N). It is a vector quantity (has magnitude and direction) and changes depending on local gravitational field strength.

**Weight** — The gravitational force acting on an object, equal to the product of its mass and local gravitational field strength.

*Notation:* W = m \times g

*Example:* A 5kg mass on Earth (g=9.8N/kg) has a weight of 49N.

**Worked example:** Calculate the weight of a 2.5kg bag of flour on Earth, where g = 9.8 N/kg. State the unit of your answer.

1. Step 1: Recall the weight formula

   $$W = m \times g$$
2. Step 2: Substitute given values: m = 2.5 kg, g = 9.8 N/kg

   $$W = 2.5 \times 9.8$$
3. Step 3: Calculate result and add correct units

   $$W = 24.5 \text{ N}$$

> **Exam tip:** Always use the value of g provided in the question; if no value is given, use g = 9.8 N/kg (the value printed on the exam paper's front cover).

## Density Core Concepts (Core)

Density describes how much mass is contained in a given volume of a substance. It is an intensive property, meaning it does not depend on the size of the sample of the substance. The SI unit of density is kilograms per cubic metre (kg/m³), but grams per cubic centimetre (g/cm³) is also commonly used in IGCSE problems.

**Density** — Mass per unit volume of a substance.

*Notation:* \rho = \frac{m}{V}

*Example:* A 10cm³ block of aluminium with mass 27g has a density of 2.7 g/cm³.

**Worked example:** A block of iron has a mass of 1580 kg and a volume of 0.2 m³. Calculate the density of iron.

1. Step 1: Recall the density formula

   $$\rho = \frac{m}{V}$$
2. Step 2: Substitute m = 1580 kg, V = 0.2 m³

   $$\rho = \frac{1580}{0.2}$$
3. Step 3: Compute result and add correct units

   $$\rho = 7900 \text{ kg/m}^3$$

> **Exam tip:** Use the conversion factor 1 g/cm³ = 1000 kg/m³ to switch between common density units quickly.

## Rearranging Core Formulas (Core)

You will often be asked to rearrange the weight and density formulas to find unknown mass or volume from given values. The formula triangle method is a quick, error-free way to rearrange these equations for any unknown quantity.

> **mnemonic**
>
> For density: Cover the quantity you want to find. Cover ρ = m/V → m = ρ×V, cover V = m/ρ. For weight: Cover W = m×g → m = W/g, cover g = W/m.

**Worked example:** A liquid has a density of 0.8 g/cm³. What volume of this liquid has a mass of 120 g?

1. Step 1: Rearrange density formula to solve for volume

   $$V = \frac{m}{\rho}$$
2. Step 2: Substitute m = 120 g, ρ = 0.8 g/cm³

   $$V = \frac{120}{0.8}$$
3. Step 3: Calculate result with correct units

   $$V = 150 \text{ cm}^3$$

## Experimental Determination of Density (Core)

All candidates should be able to describe and carry out experiments to measure the density of regular solids, irregular solids that sink, and liquids. All methods use the density formula, with different techniques to measure mass and volume accurately.

- **Regular solids**: Measure mass with a digital balance, measure dimensions with a ruler, calculate volume using geometric formula, compute density.
- **Irregular solids**: Measure mass with a digital balance, find volume via water displacement: record initial water volume in a measuring cylinder, submerge the solid, record final volume, the difference is the solid's volume.
- **Liquids**: Measure mass of empty beaker, add liquid and measure total mass, subtract empty beaker mass to get liquid mass, measure liquid volume with a measuring cylinder, compute density.

**Worked example:** A student measures the density of an irregular stone. They record the mass of the stone as 180 g. The initial volume of water in a measuring cylinder is 40 cm³, and after adding the stone, the volume rises to 100 cm³. Calculate the density of the stone in g/cm³.

1. Step 1: Calculate volume of the stone via displacement

   $$V = 100 - 40 = 60 \text{ cm}^3$$
2. Step 2: Substitute values into density formula

   $$\rho = \frac{m}{V} = \frac{180}{60}$$
3. Step 3: Calculate result with units

   $$\rho = 3 \text{ g/cm}^3$$

> **Exam tip:** Always mention reading the measuring cylinder at eye level to the meniscus to avoid parallax error when describing density experiments for marks.

## Predicting Floating and Sinking from Density (Extended only)

Extended candidates use density data to predict whether an object floats or sinks in a liquid, and whether one liquid floats on top of another. An object floats in a liquid if its density is less than the density of the liquid, and sinks if its density is greater than the density of the liquid.

- **Object in a liquid**: Compare the density of the object with the density of the liquid. Less dense than the liquid = floats; more dense = sinks.
- **Two liquids that do not mix (immiscible)**: The less dense liquid floats on top of the denser liquid, forming separate layers with the densest liquid at the bottom.

**Worked example:** Oil has a density of 0.92 g/cm³, water has a density of 1.0 g/cm³, and a plastic bead has a density of 0.95 g/cm³. The oil and water do not mix. Describe what happens when the oil, water and bead are placed together in a beaker.

1. Step 1: Compare the two liquids. Oil (0.92 g/cm³) is less dense than water (1.0 g/cm³), so the oil floats and forms a layer on top of the water.
2. Step 2: Compare the bead with each liquid. The bead (0.95 g/cm³) is more dense than the oil (0.92 g/cm³) but less dense than the water (1.0 g/cm³).
3. Step 3: Conclude the bead sinks through the oil layer but floats on the water, resting at the boundary between the oil and water layers.

> **Exam tip:** For floating questions, always compare density values directly: less dense floats, more dense sinks. State the comparison explicitly to earn the mark.

## Common pitfalls

- **Wrong:** Claiming mass changes when an object is taken to the moon
  - Why it fails: Mass is a measure of matter, which is constant for an object regardless of location; only weight changes with gravitational field strength.
  - Correct: State mass is constant, while weight on the moon is 1/6 of its value on Earth.
- **Wrong:** Using mismatched units in density calculations, e.g. mass in grams and volume in m³
  - Why it fails: Unit mismatch gives an incorrect density value by a factor of 1,000 or more.
  - Correct: Use consistent units: kg and m³ for kg/m³, g and cm³ for g/cm³, convert units before calculating if needed.
- **Wrong:** Forgetting to subtract the mass of the empty beaker when measuring liquid mass (Extended)
  - Why it fails: This overestimates the mass of the liquid, leading to an incorrectly high calculated density.
  - Correct: Measure the mass of the empty beaker first, subtract this from the total mass of beaker + liquid to get the true liquid mass.
- **Wrong:** Stating density in g/cm³ when the question asks for SI units
  - Why it fails: The SI unit of density is kg/m³, g/cm³ is a non-SI common unit.
  - Correct: Convert g/cm³ to kg/m³ by multiplying by 1000 when SI units are requested.

## Cheatsheet

| Quantity | Symbol | SI Unit | Formula/Method | Tier |
| --- | --- | --- | --- | --- |
| Mass | m | Kilogram (kg) | - | Both |
| Weight | W | Newton (N) | W = m × g | Both |
| Density | ρ | kg/m³ | ρ = m / V | Both |
| Regular solid density | - | kg/m³ | Calculate volume via dimensions | Core |
| Irregular solid density | - | kg/m³ | Measure volume via displacement | Core |
| Liquid density | - | kg/m³ | Subtract empty beaker mass for liquid mass | Core |
| Floating / immiscible liquids | - | - | Compare densities: less dense floats, more dense sinks | Extended |

## What's next

Now that you have mastered mass, weight and density for CIE IGCSE Physics 0625, you can move on to related topics in the Motion, Forces and Energy unit. Next, you will learn about effects of forces including Hooke’s Law for springs, which builds on your understanding of forces measured in newtons. Practise describing density experiments carefully, as density determination is commonly assessed in the practical papers (Paper 5 or Paper 6). Make sure you memorize the core formulas for weight and density, as they appear regularly across all papers in both calculation and definition questions. Practice rearranging these formulas for different unknown quantities to build speed for your exam.

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