Density of materials (including RP5) — AQA GCSE Physics

SPEC 4.3.1.1 PARTICLE MODEL — DENSITY OF MATERIALS

Density & RP5

Module 3 opener. The recall equation, the three-method practical, and the unit-conversion trap that costs students marks every June.

Why This Lesson Earns Marks

Density opens the particle model. AQA tests it in three guaranteed ways: a recall of the equation, an RP5 method description, and an ESUA calculation with a unit-conversion twist.

3

RP5 Methods

RECALL

= m/V Not On Sheet

×10⁻⁶

cm³ → m³

By The End

Define density. Apply = m/V with full ESUA. Describe the three RP5 methods for regular solids, irregular solids, and liquids. Convert cm³ to m³ correctly — the single biggest source of lost marks on this topic.

What Density Is

Density compares how much mass is packed into a given volume. Two cubes the same size made of lead and aluminium feel very different in your hand — that's a density difference.

Definition [DEF]

Density is the mass per unit volume of a substance.

Mark-Scheme Phrasing

Examiners want the words "per unit volume". Writing "how heavy something is" or "mass divided by size" loses the mark. Learn this line word-for-word.

The Equation Recall List

The density equation is on the AQA recall list — the spec requires you to recall and apply it. Memorise it; don't rely on the equation sheet being there.

= m / V

SymbolQuantitySI Unit

(rho)Densitykilograms per cubic metre (kg/m³)

mMasskilograms (kg)

VVolumecubic metres (m³)

Alternative Units

Density is often quoted in g/cm³ in everyday contexts. To convert g/cm³ → kg/m³, multiply by 1000. Water is 1.0 g/cm³ = 1000 kg/m³.

Particle Model — Why Density Differs

The same material can be a solid, liquid or gas. The mass of each particle doesn't change — but the arrangement does, which changes how many particles fit into a given volume.

Mark-Scheme Chain

Solids: particles tightly packed in a regular arrangement → many particles per m³ → high density. Liquids: particles close but disordered → similar density to solids. Gases: particles spread far apart → very few particles per m³ → very low density.

Spec Link

The spec asks you to apply = m/V to changes where mass is conserved. When a substance changes state, the number of particles — and so the total mass — stays the same; only the volume changes. Same m, different V → different .

Reference Densities — Know These

Examiners use these values in calculation questions. Knowing them lets you sense-check your final answer — if you get 11 kg/m³ for lead, you've made a unit error.

MaterialDensity (kg/m³)Notes

Air~1.2About 1000× less than water

Water1000The benchmark — memorise

Aluminium~2700Light metal — aircraft frames

Iron / steel~7800Common in calculation questions

Lead~11 300Heaviest density you'll typically see

Sense Check

After every density calculation, ask: is this value sensible? A metal should be in the thousands of kg/m³, not single digits or millions. If it isn't, check your units — almost always cm/m or g/kg.

Required Practical 5

RP5 asks you to measure densities for three different sample types. Each needs a different method because volume is measured differently in each case. Mass is always on a balance.

RP5 Brief

Use appropriate apparatus to make and record the measurements needed to determine the densities of regular and irregular solid objects and liquids. Volume from dimensions for regular shapes; volume by displacement for irregular shapes.

Regular Solid

Measure dimensions, calculate V.

Irregular Solid

Use water displacement.

Liquid

Weigh empty & full cylinder.

Method 1 — Regular Solid

For a cube, cuboid, sphere or cylinder — any shape where the volume can be calculated from measured dimensions.

Steps

Zero the balance. Place object on the pan and record mass m.

Measure dimensions with the appropriate instrument: ruler for cm-scale lengths, Vernier callipers for mm-precision, micrometer for sub-mm thicknesses or small diameters. Take readings at different orientations and use the mean.

Calculate volume using the right formula: cube V = l³, cylinder V = πr²h, sphere V = (4/3)πr³.

Calculate density = m/V.

Method 2 — Irregular Solid

Use a Eureka can (overflow can) or measuring cylinder to find the volume by water displacement. The volume of water displaced equals the volume of the object.

Steps

Mass: zero balance, weigh the object to find m.

Fill Eureka can with water until it just stops dripping from the spout. Place an empty measuring cylinder under the spout.

Lower the object gently into the water using a thin string — submerge fully without splashing.

Volume of water collected in the measuring cylinder = volume of the object.

Calculate = m/V.

Alternative Method — Direct Cylinder

If no Eureka can is available, AQA also credits a simpler method: part-fill a measuring cylinder with water, note initial volume V ₁, lower the object in, note final volume V ₂. Volume of object = V₂ − V₁. Same = m/V calculation.

Use A Thin String

The string itself has volume — if it's thick, it adds to the water displaced and your V reading is too high. A thick string can also absorb water, changing the mass reading if you weigh wet. Use thin, low-absorbency string and weigh the object dry, separately before submerging.

Method 3 — Liquid

You can't put a liquid on a balance directly — it spreads. Instead, use a mass-difference method: weigh the empty cylinder, then the cylinder plus liquid, and subtract.

Steps

Zero the balance. Place an empty, dry measuring cylinder on it. Record mass m₁.

Pour a known volume of the liquid into the cylinder — read V from the bottom of the meniscus, at eye level.

Re-weigh the cylinder plus liquid. Record m₂.

Mass of liquidm = m₂ − m₁.

Calculate = m/V.

RP5 — Variables & Controls

For RP5 the "independent variable" is the object or liquid being tested — you're comparing densities across different samples. The dependent variable is the calculated density.

Independent

The object / liquid under test.

Dependent

Density, calculated from m and V.

Controls

Balance zeroed, temperature, no air bubbles.

Variable / SourceError TypeWhy It Matters / Mark-Scheme Phrasing

Balance zeroedSystematicUn-zeroed balance shifts every reading by the same amount — calibrate before use.

Temperature constant (liquids)SystematicLiquid volume changes with temperature, so density does too.

No air bubbles on submerged objectRandomBubbles cling unpredictably → measured V is greater than true V → calculated density less than the true value .

Read meniscus at eye levelRandomIf eye is not in line, the misread varies between readings — gives a random error in V (Jun 2024 examiner report).

Reliability — Repeats, Means & Uncertainty

One measurement is never enough. Examiners regularly ask why repeats improve accuracy — and how to express the uncertainty in a final density value.

Why Repeat Measurements?

Reduces the effect of random error on the final value.

Lets you identify anomalies (readings far from the others) and discard them before averaging.

Calculate the mean of the remaining repeats — this is closer to the true value than any single reading.

Uncertainty — Max & Min

When a density is quoted with an uncertainty (e.g. 2.55 ± 0.10 g/cm³), the maximum and minimum values are simply:

max = 2.55 + 0.10 = 2.65 g/cm³ min = 2.55 − 0.10 = 2.45 g/cm³

Examiner Phrasing

"Repeats improve accuracy" alone is insufficient — you must say how. Mark schemes credit chains like "repeats allow a mean to be calculated, which reduces the effect of random error" or "anomalies can be identified and excluded before averaging".

ESUA — Worked Example

A lead cube has a mass of 89 g and a side length of 2.0 cm. Calculate its density in kg/m³. 4 marks

E

Equation: = m / V, with V = l³ for a cube. (M1)

S

Substitute (convert first):

m = 89 g = 89 / 1000 = 0.089 kg

l = 2.0 cm = 2.0 / 100 = 0.020 m

V = (0.020)³ = 8.0 × 10⁻⁶ m³

= 0.089 / (8.0 × 10⁻⁶) (M1)

U

Unit: kg/m³

A

Answer: = 11 125 ≈ 1.1 × 10⁴ kg/m³ (2 sig fig) (A1)

Sense check: published density of lead is ~11 300 kg/m³. ✔

The cm³ → m³ Trap

This is where most density marks are lost. Students convert at the end instead of the start, or they divide by 100 when they should divide by 1 000 000.

ConversionFactor

cm → m (length)÷ 100

cm² → m² (area)÷ 10 000 (10⁴)

cm³ → m³ (volume)÷ 1 000 000 (10⁶)

g → kg (mass)÷ 1000

The Safe Method

Convert each measurement to SI units first, then calculate volume by cubing or multiplying. Convert cm to m at the start (÷100), then cube. Never cube the cm value and try to convert at the end — the factor is 10⁶, easy to forget or get wrong.

Examiner Alert

Jun 2024 Q7 (Paper 1) — RP5

The examiner's report noted that students who had completed the practical themselves scored highly on this question, while those who had only read about it lost marks on the method description — especially on naming the apparatus and explaining the displacement step.

Unit Conversion (Recurring Across Series)

Calculation marks on density questions are consistently lost to unit conversion errors. The most common mistake: converting cm³ to m³ by dividing by 100 (factor for length) instead of by 1 000 000 (factor for volume). Convert before cubing — not after.

What This Means For You

Two simple habits earn you the marks: (1) for RP5 method questions, describe what you actually did in the lab using named apparatus; (2) for density calculations, convert units at the start of the substitute step, never at the end.

How Examiners Mark "Explain Density Differences"

A common 3-mark explain question: "Explain why the density of a gas is much lower than the density of a solid."

Weak — 1/3

"Gases are lighter than solids because their particles are spread out more, so they weigh less."

Why it loses: Particles don't "weigh less" — same atoms have the same mass. No PEE structure. No mention of volume.

Strong — 3/3

P: Gas density is much lower than solid density. E: In a gas, particles are spread far apart, while in a solid they are tightly packed in a regular arrangement. E: Because the same mass of substance occupies a much larger volume as a gas, = m/V gives a much lower value.

Practice Question

An aluminium block has a mass of 540 g and a volume of 200 cm³. Calculate its density in kg/m³ and state whether the block could be made of pure aluminium (density ~2700 kg/m³). 4 marks

E

Equation: = m / V

S

m = 540 g = 0.540 kg

V = 200 cm³ = 200 ÷ 10⁶ = 2.00 × 10⁻⁴ m³

= 0.540 / (2.00 × 10⁻⁴)

U

Unit: kg/m³

A

Answer: = 2700 kg/m³ (3 sig fig)

Conclusion: Yes — matches the published density of aluminium, so the block could be pure aluminium.

Practice — PEE Answer

A student measures the density of an irregular pebble by water displacement, but small air bubbles cling to the surface of the pebble when it's lowered into the water. Explain how this affects the measured density. 3 marks

P

Point: The measured density of the pebble will be lower than the true value.

E

Evidence: The bubbles increase the apparent volume of the pebble, so the water displaced is greater than the pebble's actual volume. The measured mass is unchanged.

E

Explain: Because = m/V, increasing V while keeping m the same makes the calculated smaller. The fix: gently tap or rotate the pebble underwater to release the bubbles before reading the displaced volume.

Checkpoint — You Can Now

Knowledge

Define density as mass per unit volume.

Recall = m/V with SI units kg/m³, kg, m³.

Explain density differences between solids, liquids, and gases using the particle model .

Know reference densities: water 1000, aluminium 2700, iron 7800, lead 11 300 kg/m³.

Skills

Describe the three RP5 methods : regular solid, irregular solid (displacement), liquid (mass difference).

Apply ESUA to density calculations with full unit conversion.

Convert cm³ → m³ correctly (divide by 10⁶).

Write a PEE answer for density-difference and method-error questions.