P1.4P1. Motion, Forces and Energy
Density — Combined Science 0653 - Physics Revision Notes & Topical Questions
5 min read 10 parts Lesson 5 of 15 1 quiz
Lesson summary
P1.4 Density — COMBINED SCIENCE notes: Define density, calculate it from mass and volume, measure it for solids and liquids, and predict floating and sinking.Density = the mass per unit volume of a material.ρ = m ÷ V, with ρ in kg/m³, m in kg and V in m³.What the symbols mean: ρ …
- Rearranged forms
- Unit conversions
- Property of the material
- Same volume
- Volume of regular shapes
- Resolution of instruments
Part 1 of 8Density
Density
Density the mass per unit volume of a material.
- ρ = m ÷ V, with ρ in kg/m³, m in kg and V in m³.What the symbols mean: ρ = density (kg m−3 or g cm−3) · m = mass (kg) · V = volume (m3)
- Mass and volume in g and cm³ give a density in g/cm³.
Rearranged forms
- Rearranged forms m = ρ × V and V = m ÷ ρ.
Unit conversions
- 1 g/cm³ = 1000 kg/m³, and water has a density of about 1.0 g/cm³.
Property of the material
- Property of the material a bigger sample has more mass and more volume, but the same density.
Part 2 of 8Density of solids, liquids and gases
Same volume
- Same volume a low-density material has a smaller mass than a high-density material.
Gases
- Gases they are less dense than solids and liquids of the same substance because their particles are spread over a much larger volume.
Volume of regular shapes
- Volume of regular shapes cuboid V = l × w × h, sphere V = 4/3 πr³ and cylinder V = πr²l.
Part 3 of 8Density of a regular solid
1
Place the object on a zeroed digital balance and record its mass.
2
Measure its dimensions with a ruler, Vernier callipers or a micrometer, choosing the instrument by size.
3
Repeat the measurements and take averages.
4
Calculate the volume from the average dimensions.
5
Calculate the density using ρ = m ÷ V.
- Resolution of instruments
- a ruler reads to 1 mm, Vernier callipers to 0.1 mm and a micrometer to 0.01 mm.
Part 4 of 8Density of an irregular solid
1
Record the mass of the object on a zeroed digital balance.
2
Fill a eureka can with water to just below the spout and place an empty measuring cylinder under the spout.
3
Lower the object gently into the can so that it is fully submerged.
4
Read the volume of water that collects in the measuring cylinder.
5
Repeat and take averages.
6
Calculate the density using ρ = m ÷ V.
- Alternative
- lower the object into a measuring cylinder of water and take the rise in level as the volume.
Part 5 of 8Density of a liquid
1
Place an empty measuring cylinder on a digital balance and record its mass.
2
Pour in the liquid and read the volume at the bottom of the meniscus.
3
Record the new mass of the cylinder and liquid.
4
Subtract the mass of the empty cylinder to find the mass of the liquid.
5
Calculate the density using ρ = m ÷ V.
Part 6 of 8Reducing errors and risks
Reducing errors and risks
Systematic error
- Systematic error zero the balance before every measurement of mass.
Random error
- Random error repeat the length measurements and take an average.
Splashing
- Splashing lower objects into the eureka can gently to avoid losing water.
Safety
- Safety handle glassware carefully and do not pour water onto a balance because of the electric shock risk.
Part 7 of 8Floating and sinking
Upthrust
Upthrust the upward force of a fluid on an object, opposite to its weight.
- It depends on the density of the fluid and the volume of fluid displaced.
Floating
- Floating an object floats when its upthrust equals its weight, which happens when its density is less than the fluid density.
Sinking
- Sinking an object sinks when its density is greater than the fluid density, because it cannot displace enough fluid to balance its weight.
Examples in water
- Examples in water polystyrene and wood float, and iron sinks.
Immiscible liquids
- Immiscible liquids the less dense liquid floats on top of the denser liquid.
Hollow objects
- Hollow objects a steel ship floats because its average density, including the air inside, is less than that of water.
Part 8 of 8More from the specification
More from the specification
Density
- Mass per unit volume, rho = m/V, measured in kg/m3 or g/cm3, so a denser object floats lower or sinks in a fluid.
Measuring density
- Find the mass on a balance,
- and the volume either by measuring a regular shaped object or using displacement in a measuring cylinder for an irregular one;
- reading the meniscus at eye level avoids error.
Mass and weight
- Mass is the amount of matter in kg, while weight W = mg is the gravitational force on it in newtons.
Gravitational field strength
- The force per unit mass, g, about 10 N/kg on Earth, and weight changes where g differs, but mass does not.
Flotation
- An object floats when its average density is less than the fluid, for example potassium is less dense than water.
Gravitational field
- A region in which a mass experiences a gravitational force.
Independent variable
- The variable that is changed on purpose.
Apparatus
- The equipment used to carry out an experiment.
Variable
- Anything that might change during an experiment.
Key terms
| Term | Meaning |
|---|---|
| Density | Mass per unit volume of a material, ρ = m ÷ V. |
| Upthrust | The upward force exerted by a fluid on an object in it. |
| Displacement | Finding volume from the volume of liquid pushed out of the way by a submerged object. |
| Eureka can | A can with a spout that collects displaced water. |
| Regular solid | A solid with a simple shape whose volume can be calculated from its dimensions. |
| Irregular solid | A solid whose volume must be found by displacement. |
| Immiscible | Liquids that do not mix and form separate layers. |
Avoid these mistakes
1
Mixing units — use g with cm³ or kg with m³, never g with m³.
2
Reading the volume from the top of the meniscus — read the bottom.
3
Forgetting to subtract the empty cylinder when finding the mass of a liquid.
4
Saying heavy objects always sink — it is density, not mass, that decides.
5
Not zeroing the balance — this causes a systematic error.
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