DENSITY is a measure of how much mass is packed into a given volume — how 'compact' a material is.
EQUATION:
ρ = m ÷ V
ρ = density (kg/m³)
m = mass (kg)
V = volume (m³)
Rearranging:
m = ρ × V
V = m ÷ ρ
Common density values:
Water: 1000 kg/m³
Aluminium: 2700 kg/m³
Iron/steel: 7800 kg/m³
Air: ~1.2 kg/m³
Gold: 19,300 kg/m³
Ice: 917 kg/m³ (less dense than liquid water — why ice floats)
DENSITY AND FLOATING:
Objects FLOAT in a fluid if their density is LESS than the fluid.
Objects SINK if their density is GREATER than the fluid.
Particle Model Explanation of Density
The particle model explains density differences between states and materials:
SOLIDS:
Particles tightly packed in a regular lattice.
High density — many particles in a small volume.
LIQUIDS:
Particles close together but able to flow.
Slightly lower density than solids (usually) — particles slightly further apart.
Exceptions: water is denser than ice (ice has a more open lattice structure).
GASES:
Particles far apart — mostly empty space.
Very low density — much lower than solids or liquids.
Example: air is ~800× less dense than water.
DIFFERENT MATERIALS:
Denser materials have either heavier atoms (higher atomic mass) or more tightly packed atomic structures.
Gold (dense): heavy atoms + tightly packed.
Aluminium (less dense): lighter atoms.
Polystyrene (very low density): mostly air — open foam structure.
Measuring Density — Required Practical
REQUIRED PRACTICAL (RP17) — Determine densities of regular and irregular solids and liquids.
REGULAR SOLID (e.g. a cuboid or cylinder):
Measure dimensions with a RULER, MICROMETER or VERNIER CALLIPERS.
Calculate volume: V = l × w × h (cuboid) or V = πr²h (cylinder).
Measure mass with a BALANCE.
Calculate: ρ = m ÷ V
IRREGULAR SOLID (e.g. a stone):
Measure mass with a BALANCE.
Fill a measuring cylinder with water, note initial volume.
LOWER the solid into the water using a thread.
Note the new volume — the rise = volume of the solid (DISPLACEMENT METHOD).
Calculate: ρ = m ÷ ΔV
LIQUID:
Place an empty measuring cylinder on a balance and zero it (tare).
Pour a known volume of liquid in.
Read the mass.
Calculate: ρ = m ÷ V
SOURCES OF ERROR:
Air bubbles trapped under the object in displacement.
Parallax error reading the meniscus in a measuring cylinder.
Not drying the solid before measuring mass after displacement.
⚠️ Common Mistake
Units for density are kg/m³ (SI) or g/cm³ (also common). Do NOT mix — if mass is in grams and volume in cm³, density comes out in g/cm³. Convert to kg/m³ by multiplying by 1000. Also: 1 cm³ = 1 × 10⁻⁶ m³.
📐 Variables
ρDensity (ρ) is measured in kg/m³ (kg/m³)
mMass (m) is measured in kilograms (kg)
VVolume (V) is measured in m³ (m³)
📐 Key Equations
ρ = m ÷ V
📌 Key Note
ρ = m/V. Units: kg/m³. Denser = more mass per volume. Solids > liquids > gases (usually). Ice less dense than water (exception). Float if ρ_object < ρ_fluid. RP17: regular solids — measure dimensions; irregular solids — displacement method.
🎯 Matching Activity — Density Calculations
Match each scenario to the correct density or mass value. — drag the symbols on the right to match the component names on the left.
2700 kg/m³
Drop here
Floats
Drop here
Sinks
Drop here
Displacement method
Drop here
Aluminium block: mass = 270 g, volume = 100 cm³ (in consistent units: 0.27 kg ÷ 1×10⁻⁴ m³)
Object with density 8000 kg/m³ placed in water (density 1000 kg/m³)
Object with density 800 kg/m³ placed in water (density 1000 kg/m³)
Used to find the volume of an irregularly shaped solid
⚽ FIFA Worked Examples
Density Calculation
A block has mass 540 g and volume 200 cm³. Calculate its density in g/cm³.
F
ρ = m ÷ V
I
m = 540 g, V = 200 cm³
F
ρ = 540 ÷ 200
A
ρ = 2.7 g/cm³ (aluminium)
🧪 Required Practical
🔬 RP17 (Physics) — Determine densities of regular solids (measure dimensions), irregular solids (displacement), and liquids (measure cylinder with balance). ρ = m/V.
Know the method, variables, equipment and how to analyse results.
🎯 Test Yourself
Question 1 of 2
1. A liquid has mass 800 g and volume 1000 cm³. What is its density in g/cm³?
2. Why does ice float on water?
⭐ How Well Do You Understand This Topic?
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