1.3.3Motion, Forces and Energy
Measuring Density — Cambridge IGCSE Physics 0625 Revision Notes & Topical Questions
5 min read 9 parts Lesson 23 of 91 1 quiz
Lesson summary
1.3.3 Measuring Density — IGCSE PHYSICS notes: Describe how to measure the density of regular solids, irregular solids and liquids using suitable instruments.Density = mass ÷ volume, so two measurements are needed — the mass m and the volume V of the sample.The method used to fin…
- Alternative
- Systematic error
- Random error
- Electrical safety
- Displacement method
- Eureka can
Part 1 of 7Principle and apparatus
Density
Density mass ÷ volume, so two measurements are needed — the mass m and the volume V of the sample.
The method used to find the volume depends on whether the sample is a regular solid, an irregular solid or a liquid.
Apparatus and resolution:
- 30 cm ruler — measures lengths up to 30 cm with a resolution of 1 mm.
- Vernier callipers — measure lengths up to about 15 cm with a resolution of 0.1 mm.
- Micrometer — measures lengths up to about 3 cm with a resolution of 0.01 mm.
- Digital balance — measures mass with a resolution of 0.01 g.
- Eureka (displacement) can and measuring cylinders — measure volumes of irregular solids and liquids.
Part 2 of 7Regular solid
1
Place the object on a digital balance and record its mass.
2
Measure its dimensions (length, width, height or radius) with a ruler, Vernier callipers or a micrometer, chosen to suit its size.
3
Repeat the measurements at several places and take an average.
4
Calculate the volume from the dimensions: cuboid V = length × width × height, cylinder V = πr2h (r is half the diameter), sphere V = 4/3 πr3.
5
Calculate the density using ρ = m/V.
Part 3 of 7Irregular solid by displacement
1
Find the mass of the object on a balance.
2
Fill a eureka can with water until it is just below the spout and place an empty measuring cylinder under the spout.
3
Lower the object carefully into the can so that it is fully submerged and no water splashes.
4
Measure the volume of displaced water in the measuring cylinder; this equals the volume of the object.
5
Repeat, average, then calculate ρ = m/V.
Alternative
- Alternative place the object in a measuring cylinder containing a known volume of water and measure the rise in level.
- Volume of the object = final reading − initial reading.
A floating object must be pushed under with a thin rod, or a heavier object attached, so that it is fully submerged.
Part 4 of 7Liquid
1
Place an empty measuring cylinder on a digital balance and record its mass (or press tare to zero it).
2
Pour in the liquid and read its volume at the bottom of the meniscus with the eye level with the liquid.
3
Record the new mass of the cylinder with the liquid.
4
Mass of liquid = mass of cylinder with liquid − mass of empty cylinder.
5
Repeat, average, then calculate ρ = m/V.
- A graph of mass against volume for different volumes is a straight line through the origin and its gradient is the density.
Part 5 of 7Sources of error and improvements
Sources of error and improvements
Systematic error
- Systematic error a balance with a zero error gives all masses too high or too low.
- Zero the balance before every measurement, including after removing the cylinder when measuring a liquid.
Random error
- Random error the main cause is the measurement of length.
- Take repeat readings and calculate an average.
Air bubbles on a solid in water make the measured volume too large.
A meniscus read with the eye above or below the level gives a parallax error.
Wet surfaces add to the measured mass.
Dropping the object into the can causes splashing and an incorrect volume.
A larger sample, a narrower measuring cylinder and a more sensitive balance improve reliability.
Part 6 of 7Safety
Glassware
- Glassware handle measuring cylinders and cans carefully to avoid breakage.
Electrical safety
- Electrical safety do not pour water into a measuring cylinder while it is on the digital balance, because of the risk of electric shock.
Spills
- Spills stand during the experiment so you can react quickly to spills.
Part 7 of 7More from the specification
1Gravimetric density measurement on Earth
- Gravimetric density measurement on Earth weighing displacement volumes under local gravitational acceleration on Earth establishes accurate material densities.
2Density Formula and Units
- Density ρ is defined as mass per unit volume of a material (ρ = m / V), typically measured in kilograms per cubic metre (kg m⁻³) or grams per cubic centimetre (g cm⁻³).
3Measuring Density of Regular and Irregular Solids
- Regular solid volumes are determined by geometric measurement,
- whereas irregularly shaped objects are submerged in a displacement can to determine displaced fluid volume.
4Mass vs Weight and Gravitational Field Strength
- Mass is the amount of matter in an object (kg),
- whereas weight is the downward gravitational force acting on it,
- (W = mg in newtons)
- where g is gravitational field strength.
5Upthrust and Archimedes' Principle
- Archimedes' principle states that an object submerged in a fluid experiences an upward buoyant force (upthrust) equal to the weight of fluid displaced by the object.
6Weight
- Gravitational force on a mass.
7Upthrust
- Upward force exerted by a fluid.
8Variable
- A factor that can change in an investigation.
9Gravitational field
- Region where mass experiences gravitational force.
10Field strength
- G = Fg/m.
11Independent variable
- The variable deliberately changed, here time
12Dependent variable
- The variable measured, here temperature
Key terms
| Term | Meaning |
|---|---|
| Displacement method | Finding a volume from the rise in liquid level when an object is submerged. |
| Eureka can | Overflow vessel used to collect displaced liquid. |
| Meniscus | Curved liquid surface; read at its lowest point. |
| Tare | Resetting a balance to zero with a container on it. |
| Zero error | A reading shown when the true value is zero. |
| Resolution | Smallest change an instrument can detect. |
Avoid these mistakes
1
Forgetting to subtract the mass of the container — the mass of the liquid is the difference between the two readings.
2
Using the final water volume as the volume of the object — the volume is the difference between final and initial readings.
3
Reading the meniscus from the top or at an angle — read the bottom of the curve at eye level.
4
Not fully submerging the solid or ignoring air bubbles — both give a wrong volume.
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