Density
Year 8 🚀 Forces & Motion Calculate density using ρ = m/V; explain floating and sinking.
⚖️ What is Density?
Density is how much mass is packed into a given volume. Dense objects have a lot of mass in a small space.
⚖️ Density Formula
$$\rho = \frac{m}{V}$$
$\rho$ = density (kg/m³ or g/cm³) · $m$ = mass (kg or g) · $V$ = volume (m³ or cm³)
| 🧪 Material | 📊 Density (g/cm³) |
|---|---|
| Gold | 19.3 |
| Iron/Steel | 7.8 |
| Aluminium | 2.7 |
| Water | 1.0 |
| Ice | 0.92 |
| Wood (pine) | 0.5 |
| Air | 0.0013 |
🚢 Floating and Sinking
An object floats if its average density is less than the fluid it is in. It sinks if its density is greater.
🚢 Steel ship: Steel is denser than water, but a ship has a hollow hull filled with air — the average density of the whole ship (steel + air) is less than water. It floats!
🧊 Ice: Ice (0.92 g/cm³) is less dense than water (1.0 g/cm³) → ice floats! About 92% is submerged, 8% sticks above — that's how icebergs work!
Submarines control their depth by pumping water in or out of ballast tanks, changing their average density!
🧪 Measuring Density
To find the density of an object, you need to measure its mass and its volume.
| 🔬 Object type | 📏 How to find volume |
|---|---|
| Regular solid (cuboid) | V = length × width × height |
| Regular solid (cylinder) | V = π × r² × h |
| Irregular solid | Displacement: immerse in water, measure rise in volume |
| Liquid | Pour into measuring cylinder |
Archimedes discovered water displacement while getting into his bath — he ran through the streets shouting "Eureka!" (I found it!)
Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
⚖️ Density Calculator (ρ = m/V)
Reference: Water = 1000 kg/m³ | Iron = 7874 kg/m³ | Air = 1.2 kg/m³