IGCSE Physics 0625 · Chapter 2 notes · ~7 min read
Mass, weight & density
The most mixed-up pair in physics — mass and weight — plus density, floating and the experiments you must be able to describe.
Mass vs weightGravitational field strengthDensityMeasuring densityFloating & sinking
RSby Riyaz Sir
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No tag = Core (everyone)EXTENDED Extended onlyhighlight = comes up again and againTest yourself at the end
In 30 seconds
- Mass (kg) = how much matter. It never changes. Weight (N) = the pull of gravity on that mass. It changes with g.
- W = m × g, with g = 9.8 N/kg on Earth and 1.6 N/kg on the Moon.
- Density = mass ÷ volume — how tightly the matter is packed. Water = 1.0 g/cm³.
- An object floats if its density is less than the density of the liquid.
By the end you can
- State the difference between mass and weight and calculate each.
- Use ρ = m ÷ V, converting between g/cm³ and kg/m³.
- Describe how to find the density of a liquid, a regular solid and an irregular solid.
- Predict whether something floats or sinks from density data.
1Mass and weight
Mass is not weight
| Mass | Weight | |
|---|---|---|
| What it is | amount of matter in an object | gravitational force on the object |
| Unit | kilogram (kg) | newton (N) |
| Changes between places? | No | Yes (depends on g) |
| Measured with | balance | newton-meter (spring balance) |
| Type | scalar | vector (points down) |
W = m g
weight (N) = mass (kg) × gravitational field strength (N/kg)Gravitational field strength (g) — the weight of each kilogram: g = Wm. On Earth g = 9.8 N/kg, which is also the free-fall acceleration in m/s².
Picture itg tells you how many newtons each kilogram weighs. On Earth every kilogram is pulled with 9.8 N; on the Moon only 1.6 N, so you could jump much higher there.
Worked example
An astronaut has mass 80 kg. Find the weight on Earth (g = 9.8 N/kg) and on the Moon (g = 1.6 N/kg).
- Earth: W = mg = 80 × 9.8 = 784 N
- Moon: W = 80 × 1.6 = 128 N
- The mass is still 80 kg on both
Exam tipMany questions say "take g = 10 N/kg". Use whichever value the question gives you.
Common mistake"My weight is 60 kg." kg is the unit of mass. Weight is in newtons.
- A balance compares masses, so it gives the same reading on the Moon. A spring balance measures weight, so its reading would change.
- EXT Weight is the effect of a gravitational field on a mass.
2Density
Density
Density — the mass of each unit volume of a material. Dense materials pack lots of matter into a small space.
ρ = mV
ρ (rho) in kg/m³ or g/cm³ · m in kg or g · V in m³ or cm³- Rearranged: m = ρV and V = m ÷ ρ. Use a triangle with m on top and ρ, V underneath.
- Keep units matching: g with cm³ gives g/cm³; kg with m³ gives kg/m³. 1 g/cm³ = 1000 kg/m³.
| Material | Density (g/cm³) |
|---|---|
| air | 0.0012 |
| oil | about 0.8 |
| ice | 0.92 |
| water | 1.0 |
| aluminium | 2.7 |
| iron / steel | 7.9 |
| copper | 8.9 |
| lead | 11.3 |
Worked example
A metal block measures 4.0 cm × 3.0 cm × 2.5 cm and has a mass of 237 g. Find its density. What metal could it be?
- Volume = 4.0 × 3.0 × 2.5 = 30 cm³
- ρ = m ÷ V = 237 ÷ 30
- = 7.9 g/cm³ — iron or steel
Measuring density
- Regular solid: measure length, width, height with a ruler → V = l × w × h. Find the mass on a balance. Then ρ = m ÷ V.
- Irregular solid that sinks: use displacement. The rise in water level equals the volume of the object.
- Liquid: mass of the cylinder + liquid, minus the mass of the empty cylinder, gives the mass of the liquid. Read its volume on the scale.
Worked example
A stone has mass 60 g. It raises the water level from 40 cm³ to 64 cm³. Find the density.
- Volume of stone = 64 − 40 = 24 cm³
- ρ = 60 ÷ 24
- = 2.5 g/cm³
Common mistakeForgetting to subtract the mass of the empty container when finding the mass of a liquid.
3Floating and sinking
Floating and sinking
- Floats if ρ object < ρ liquid. Sinks if ρ object > ρ liquid. Equal densities: hangs in the liquid.
- A steel ship floats because it is mostly air inside — its average density is less than water.
- EXT Immiscible liquids (liquids that do not mix) layer by density: oil (0.8 g/cm³) floats on water (1.0 g/cm³); mercury (13.6 g/cm³) sinks below water.
Picture itThink of a crowd: dense materials are like people squeezed close together — they push down through lighter, more open material and sink beneath it.
4Test yourself
Test yourself — cover the answers first
Quick check
- What is the weight of a 5.0 kg object on Earth (g = 9.8 N/kg)?
- Find the density of 12 g of a material with volume 3.0 cm³.
- Convert 2.7 g/cm³ to kg/m³.
- Will an object of density 0.80 g/cm³ float in water?
- Which measuring instrument gives a different reading on the Moon: a balance or a spring balance?
Exam-style
- An empty measuring cylinder has mass 62.0 g. With 40.0 cm³ of a liquid it has mass 94.0 g. Calculate the density of the liquid and say whether it floats on water.
- Describe how to find the density of a small irregular stone. [4]
- The Moon has g = 1.6 N/kg. A bag of sugar has mass 2.5 kg on Earth. Find its mass and weight on the Moon.
Show answers
- 5.0 × 9.8 = 49 N
- 12 ÷ 3.0 = 4.0 g/cm³
- 2.7 × 1000 = 2700 kg/m³
- Yes — its density is less than water (1.0 g/cm³).
- The spring balance (it measures weight).
- mass of liquid = 94.0 − 62.0 = 32.0 g
ρ = 32.0 ÷ 40.0 = 0.80 g/cm³
it is less than 1.0 g/cm³, so it floats on water - Find its mass on a balance
Half-fill a measuring cylinder with water and record the volume
Lower the stone in on a thread and record the new volume
volume of stone = new reading − old reading, then ρ = m ÷ V - mass = 2.5 kg (it does not change)
weight = mg = 2.5 × 1.6 = 4.0 N
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