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GCSE level Physics exam revision notes on density
Density and particle theory: Part 5.1
What is density? Formula units for density? Why is density important? Exam
practice density questions with worked out answers (at the end of the
page)
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INDEX physics notes: Density,
particle models, factors affecting density
This page contains some online questions.
Jot down
your answers and check against the worked out answers at the end of
this page
5.1a
What is density? What is the formula for density?
Why is density important?
Examples of density and how to do density calculations
Density is a measure of how compact a
material is - it indicates how much space or volume a given mass occupies.
The greater the mass of material in a given
volume, the greater the density of the material.
The density of a material depends on what it
is made up of (atoms and their arrangement) and its physical state.
The more spread out the particles, the
lower the material's density - which is why gases have a very low density.
The more closely the particles are packed
together, the greater the density - which is why solids have the highest
density.
See the
particle model of the states of
matter
The density for a given material is the same
whatever its shape or size for a given physical state.
 The
scientific symbol for density is the Greek letter rho (ρ)
The formula for density is:
ρ
= m
÷ v
DENSITY (kg/m3)
= MASS (kg)
÷
VOLUME (m3)
Density units in physics are usually kg/m3.
However, in chemistry, density data is often
quoted in g/cm3 because most quantitative measurements in a
school/college chemistry laboratory are usually quoted in grams (g) and ml (cm3),
so I've sometimes quoted both sets of units,
so don't get them muddled! and note that:
g/cm3 = kg/m3
÷ 1000 (can you
work out why?)
Its advisable to be able to convert mass
and volume units e.g.
mass: 1 kilogram = 1000 grams, so:
g ÷ 1000 = kg and kg x 1000 = g
volume: ml = cm3, 1
cubic metre = 1 million cm3,
so: cm3 ÷
106 = m3 and m3
x 106 = cm3
5.1b Why is density data important? Examples of densities
Density is very important property to know about a material
e.g. if the density of an object is less
than that of water (~1000 kg/m3) it floats.
If the density of an object is more
than that of water it sinks!
In general: if the object has a
density < fluid it floats and if density of object is > fluid it sinks.
However, although shape doesn't
affect density, shape does affect flotation on non-flotation, otherwise, how can a steel ship float on
water?!
Examples of density in kg/m3
(at ~room temperature, 20oC)
The table lists the densities of many
common materials, all of them are useful materials for some application
or other.
Note that
gases are so much less dense
than liquids or solids
Refer to
Part 5.6
Density and the
particle model
of the states of matter
|
Material |
Density |
Comments |
|
hydrogen |
0.09 |
The
element H, least dense material, 'floats' in less dense air |
|
helium |
0.18 |
The
element He, next least dense material, 'floats' in less
dense air - balloons |
|
air |
1.3 |
Mainly
nitrogen N2 and oxygen O2 molecules. |
|
carbon dioxide |
1.9 |
|
|
cork |
240 |
|
|
wood |
380 - 700 |
Important construction material |
|
solid paraffin wax |
720 |
|
|
petrol |
710 - 770 |
Important fuel |
|
crude oil |
840 - 970 |
Variable composition of hydrocarbons, floats on water -
polluting oil spills |
|
ice |
920 |
Floats
on water, less dense than water. |
|
water |
1000 |
Useful
solvent, transferring thermal energy in central heating
systems |
|
seawater |
1030 |
More
dense than pure water, you float more easily! |
|
rubber |
1520 |
Useful
material for flexible joints or shock absorbers. |
|
brick |
1920 |
Important construction material |
|
concrete |
2370 |
Important construction material. |
|
glass |
2580 |
Important construction material |
|
marble rock |
2560 |
Mainly
calcium carbonate CaCO3, useful for sculptures,
kitchen work tops |
|
quartz rock |
2640 |
Mainly
silicon dioxide, silica, SiO2, useful for kitchen
worktops |
|
aluminium |
2640 |
Important metal, used for light alloys - aircraft
construction |
|
bromine |
3120 |
One of
only two liquid elements at room temperature |
|
iron |
7500 |
The
element Fe, cast iron has many uses - we experience as
'heavy' objects! |
|
steel |
7900 |
Mainly
Fe, with added elements, important construction material. |
|
copper |
8800 |
Copper
wiring and piping. |
|
lead |
11340 |
'Heavy' metallic element, used in lead roofing |
|
mercury |
13600 |
One of
only two liquid elements at room temperature |
|
gold
|
19300 |
Very
dense important metal in jewellery |
|
osmium |
2260 |
The
most dense element in the periodic table |
The
role of density and whether an object sinks or floats in a fluid is explained in the section
on
Forces section 7. 'floating
and sinking'
Density and particle theory: 5.5
Calculations involving density data, density formula - practice questions for objects of
different shapes!
5.6 Calculations involving density
Q1
Irregular shaped solid object
A stone weighing 27.2 g displaced 8.5 cm3
of water (8.5 ml), calculate its density in (a) in g/cm3 and then
(b) in kg/m3.
Worked out ANSWERS of density problem calculations
Q2 A regular
solid block
A block of iron had dimensions of 3.0 cm
x 5.0 cm x 12.0 cm and weighed 1.420 kg, calculate the density of iron.
Worked out ANSWERS of density problem calculations
Q3 A
regular solid cylinder of an alloy has a diameter of 3.0 cm, a length of 12.0 cm
and a mass of 750 g.
Calculate the density in kg/m3
Tricky, involves several unit conversions
Worked out ANSWERS of density problem calculations
Q4
A cube of material
has a side length of 2.5 cm.
If the material has a density of 5000
kg/m3, what is the mass of the cube in g and kg?
Worked out ANSWERS of density problem calculations
Q5
If the density of air is 1.30 kg/m3
(a) Calculate the mass of air in a room
measuring 7 m by 6 m by 3 m.
(b) Explain what happens
to the density of air in the room if the atmospheric pressure increases.
Worked out ANSWERS of density problem calculations
Q6
Steel has been cast into long rectangular bars 25 metres long and a
cross-section of 20 cm by 30 cm.
If the density of steel is 7900 kg/m3,
what is the minimum number of bars needed to transport at least 230 tonnes
of the steel?
Worked out ANSWERS of density problem calculations
Key points Density and particle theory: What is the
density of a material and practice exam questions on calculating density
Information
sources for Doc Brown's key points: IGCSE-GCSE physics are based on
textbooks and syllabus-specifications for students taking the UK AQA, Edexcel,
OCR 21st Century Science, OCR Gateway science suite, WJEC, CCEA and CIE GCSE
physics 9-1 level science examinations
A structured set of summary revision notes on
density,
tailored to the core requirements of WJEC, CCEA, CIE, AQA,
Edexcel, and OCR GCSE/IGCSE Physics specifications.
What Is Density?
- Definition:
Density is the mass per unit volume of a substance.
- Formula:
Density = Mass / Volume, ρ = m / V
where:
- ρ = density (kg/m³)
- m = mass (kg)
- V = volume (m³)
- Units:
- SI unit:
kilograms per cubic metre (kg/m³)
- Sometimes given in g/cm³
(1 g/cm³ = 1000 kg/m³)
- Material Comparison:
- Solids
are usually more dense than liquids and gases.
- Gases
have the lowest density due to widely spaced particles.
Required Practical: Measuring Density
| Object Type |
Method |
| Regular solids |
Measure dimensions (length × width
× height) for volume; use a balance for mass. |
| Irregular solids |
Use a displacement method
with a eureka can to find volume; measure mass with a balance. |
| Liquids |
Measure volume with a measuring
cylinder; subtract container mass to find liquid mass. |
For methods and density calculations see
Parts
5.2
Measuring the density of an irregularly shaped
solid object and calculations
5.3
Measuring the density of an regular shaped
solid object and calculations
5.4
Three ways of
measuring the density of a liquid, methods and calculations
Typical Exam Board Requirements about
density and calculations
|
Key Focus Areas |
| Density formula, required
practical, particle model link. |
| Density calculations, practical
methods, unit conversions. |
| Density and particle spacing,
practical skills. |
| Density of solids/liquids,
practical techniques, unit handling. |
| Density and kinetic theory,
floating/sinking, practicals. |
| Density definition, formula,
applications, practicals. |
Common Misconceptions about density
- “Heavy objects always sink”
– Not true; density, not weight, determines floating.
- “Density changes with shape”
– Shape affects volume, but density depends on mass per volume,
not shape alone.
- “Gases have no density”
– Gases do have density, just much lower than solids and liquids.
Student Tips about density and
calculations
- Use correct units:
Convert g/cm³ to kg/m³ when needed.
- Draw diagrams:
Visualise particle spacing in different states.
- Practice calculations:
Rearranging the formula and applying it to exam-style questions.
- Revise practicals:
Know how to measure volume and mass accurately.
- Link to floating/sinking:
Use density to explain buoyancy.
Keywords, phrases and learning objectives for density
Know what
density is and appreciate its an important piece of data about a
material.
Know the formula for
density and how to calculations involving density.
WHAT NEXT?
TOP of page
INDEX of physics notes on density and
particle models
Revision notes on exam practise
calculations using defined density formula units & calculations based on the syllabus-specifications
for students taking IGCSE/GCSE level physics examinations, summary
revision notes and key points on exam practise calculations using
defined density formula units & calculations for students taking the AQA
igcse/gcse physics notes on exam practise calculations using defined density
formula units & calculations, Edexcel gcse
physics notes on exam practise calculations using defined density
formula units & calculations, OCR 21st century GCSE
physics notes on exam practise calculations using defined density
formula units & calculations, OCR gateway
GCSE physics notes on exam practise calculations using defined
density formula units & calculations, WJEC gcse physics notes on
exam practise calculations using defined density formula units &
calculations, CCEA
gcse physics notes on exam practise calculations using defined density
formula units & calculations for students taking CIE Cambridge igcse
physics, exam revision notes on
exam practise calculations using defined density formula units &
calculations, useful for US grade 9-10 physics courses,
importance of the importance of
material density data for substances
in GCSE level physics, What you need to know about the importance of
material density data for substances for
GCSE level
physics,
Explaining the use of the importance of material density data for
substances knowledge in GCSE level physics, Examples of
the importance of material density data for substances explained
when studying GCSE level physics, What is
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Worked out
ANSWERS
to the density questions
Q1
Irregular shaped solid object
A stone weighing 27.2 g displaced 8.5 cm3
of water (8.5 ml), calculate its density.
(a) density of solid
ρ
= m ÷ v, ρ = 27.2 ÷ 8.5 =
3.2 g/cm3
(b) However, you may have to calculate the
density in kg/m3 and this is arithmetically a bit more awkward!
27.2 g = 27.2/1000 = 0.0272 kg
and 8.5 cm3 = 8.5 / 106 = 8.5 x 10-6
m3 (1 m3 = 106 cm3)
ρ
= m ÷ v, ρ = 0.0272
÷
(8.5 x 10-6) = 0.0272 ÷ 0.0000085 =
3200 kg/m3
It might be handy to know that kg/m3
is 1000 x g/cm3 !!! 3.2 x 1000 = 3200 !!!
Q2 A regular
solid block
A block of iron had dimensions of 3.0 cm
x 5.0 cm x 12.0 cm and weighed 1.420 kg, calculate the density of iron.
Volume of block = 3 x 5 x 12 = 180 cm3,
volume = 180/106 = 1.8 x 10-4 m3
(0.00018)
density of solid
ρ
= m ÷ v, ρ = 1.42
÷
0.00018 = 7889
kg/m3
Q3 A
regular solid cylinder of an alloy has a diameter of 3.0 cm, a length of 12.0 cm
and a mass of 750 g.
Calculate the density in kg/m3
radius of cylinder = diameter/2 = 3.0/2 = 1.5 cm,
cross-section area = πr2 =
3.142 x 1.52 = 7.070 cm2
volume of cylinder = 7.070 x 12.0 = 84.83
cm3, 84.83/106 = 8.483 x 10-5 m3
(remember 1 m3 = 106 cm3)
mass of cylinder = 750/1000 = 0.750 kg
(1 kg = 1000 g)
density of solid
ρ
= m ÷ v, ρ = 0.750
÷
8.483 x 10-5 = 8841 =
8840 kg/m3 (3 sf)
Q4
A cube of material
has a side length of 2.5 cm.
If the material has a density of 5000
kg/m3, what is the mass of the cube in g and kg?
l = 2.5/100 = 0.025 m, therefore volume =
l3 = 0.0253 = 1.5625 x 10-5 m3
ρ
= m ÷ v, m = ρ x v = 5000 x
1.5625 x 10-5
= 0.078 kg (x 1000 =
78 g)
Q5
If the density of air is 1.30 kg/m3
(a) Calculate the mass of air in a room
measuring 7 m by 6 m by 3 m.
Volume of room = l x b x h = 7 x 6 x
3 = 126 m3
ρ
= m ÷ v, m =
ρ x v = 1.3 x
126 = 164 kg
(3 sf)
(b) Explain what happens
to the density of air in the room if the atmospheric pressure increases.
If the pressure
increases, on average, the particles are squashed closer together.
Therefore, there is
more mass in the same volume, so the density increases.
Note: (i) The mass
of air in the room will also increase.
(ii) In any
situation where a gas is compressed, the density of the gas is
increased.
Q6
Steel has been cast into long rectangular bars 25 metres long and a
cross-section of 20 cm by 30 cm.
If the density of steel is 7900 kg/m3,
what is the minimum number of bars needed to transport at least 230 tonnes
of the steel?
V = l x b x h, l = 25 m, b = 20/100 = 0.2
m, h = 30/100 = 0.3 m
V of 1 rod = 1.5 m3
ρ
= m ÷ v, m =
ρ x v
mass of 1 bar = 7900 x
1.5 = 11850 kg.
230 tonnes
≡
230 000 kg (1 metric tonne = 1000 kg)
bars needed = 230000/11850 = 19.4 bars.
So you would need
20 bars to transport a minimum of 230 tonnes of steel.
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INDEX of physics notes on density and
particle models
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