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6.8 Required Practical: Density

GCSE Physics · AQA · Chapter 6: Molecules and Matter

A free GCSE Physics lesson for AQA (8463) from OBA School: measuring the density of regular solids, irregular solids and liquids: method, variables, hazards, results and evaluation. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Describe methods to measure the density of a regular solid, an irregular solid (displacement) and a liquid
  • Choose measuring instruments with a suitable resolution and read them correctly
  • Process results: calculate volumes and densities, find a mean and an uncertainty, use the gradient of a mass–volume graph
  • Identify sources of error and suggest improvements, and work safely

Key words

  • Eureka can: A can with a spout near the top. An object lowered in pushes out (displaces) its own volume of water through the spout.
  • Tare: Setting a balance to read zero with a container on it, so it then shows only the mass of what is added.
  • Resolution: The smallest change an instrument can measure, e.g. 1 cm³ on a 100 cm³ measuring cylinder.
  • Random error: Unpredictable scatter in repeat readings, e.g. from judging a meniscus. Reduced by repeating and taking a mean.
  • Systematic error: An error that shifts every reading the same way, e.g. a balance that is not zeroed. Repeating does not remove it.
  • Uncertainty: The range within which the true value probably lies. Estimate it as half the range of repeat results.

Aim and apparatus

Aim: to find the density of solids and liquids by measuring their mass and volume and using ρ = m / V.

  • electronic balance (resolution 0.1 g or 0.01 g); Used for mass of objects and liquids
  • 30 cm ruler, vernier callipers, micrometer; Used for dimensions of regular solids
  • eureka can, measuring cylinders (10, 50 and 100 cm³), thread; Used for volume of irregular solids by displacement
  • beaker or measuring cylinder, the liquid under test; Used for mass and volume of a liquid

Method 1: a regular solid

1. Check the balance reads zero, then measure the mass of the object.

2. Measure each dimension with the instrument that has a suitable range and the finest resolution (vernier callipers for a few cm; a micrometer for a few mm).

3. Measure each dimension at three different places and take the mean.

4. Calculate the volume, then the density.

Worked example: an aluminium rod

diameter = 2.00 cm, so r = 1.00 cm; height = 5.00 cm; mass = 42.4 g
V = π r² h = π × 1.00² × 5.00 = 15.7 cm³
ρ = 42.4 ÷ 15.7 = 2.70 g/cm³

Answer: 2.70 g/cm³ = 2700 kg/m³

Method 2: an irregular solid (displacement)

1. Measure the mass of the dry object on a zeroed balance.

2. Fill the eureka can above the spout and let the extra water run out. Wait until it stops dripping.

3. Put an empty measuring cylinder under the spout.

4. Tie the object to a thin thread and lower it gently until it is completely under water. Collect all the water that flows out.

5. Read the volume of water in the cylinder at eye level, at the bottom of the meniscus. This is the volume of the object.

6. Repeat steps 2–5 two more times and find the mean volume. Calculate the density.

A small object can instead be lowered straight into a part-filled measuring cylinder: its volume is the rise in the reading.

Method 3: a liquid – using a graph

1. Put an empty measuring cylinder on the balance and press tare so it reads 0.0 g.

2. Pour in 20 cm³ of the liquid. Record the volume and the mass.

3. Add the liquid in steps of 20 cm³ up to 100 cm³, recording the mass each time.

4. Plot mass (y-axis) against volume (x-axis) and draw a line of best fit. The gradient is the density.

Worked example: gradient of the graph

Use a large triangle: Δm = 71.1 − 23.7 = 47.4 g; ΔV = 90 − 30 = 60 cm³
density = 47.4 ÷ 60 = 0.79 g/cm³

Answer: 0.79 g/cm³ = 790 kg/m³ (a value close to that of ethanol)

For this graph method: independent variable = volume of liquid; dependent variable = mass of liquid; control variables = same liquid, same temperature, same balance and cylinder.

Results, errors, improvements and safety

Worked example: mean and uncertainty

Three repeat densities for a stone: 2.68, 2.74, 2.71 g/cm³
mean = (2.68 + 2.74 + 2.71) ÷ 3 = 2.71 g/cm³; range = 2.74 − 2.68 = 0.06
uncertainty = half the range = ± 0.03 g/cm³

Answer: 2.71 ± 0.03 g/cm³

  • water still dripping from the spout when the cylinder is placed; Effect volume too large, density too small; Improvement wait until the dripping stops
  • water left in the spout / splashes when the object drops in; Effect volume too small, density too large; Improvement lower gently on thin thread; tap the spout
  • air bubbles stuck to the object; Effect volume too large; Improvement shake gently to release bubbles
  • thick string under the water; Effect volume too large; Improvement use thin thread
  • measuring cylinder with a coarse scale; Effect large uncertainty in volume; Improvement use the smallest cylinder that holds the water
  • balance not zeroed; Effect systematic error in every mass; Improvement zero / tare before each reading
  • heavy metal blocks; Risk falling on feet or hands; Control keep away from bench edges; carry carefully
  • spilled water; Risk slipping; Control mop up spills at once
  • glass measuring cylinders; Risk cuts if broken; Control stand on a flat surface away from the edge

Common mistakes

  • Placing the measuring cylinder under the spout before the eureka can has stopped dripping.
  • Calculating the volume of a cylinder with the diameter instead of the radius in π r² h.
  • Using a gradient triangle that is too small, or reading points that are not on the line of best fit.
  • Calling a balance that is not zeroed a random error. It is a systematic (zero) error.

Revision questions

Try these, then check your answers below each one.

Question 1. What is the best way to measure the volume of an irregularly shaped stone? (Choose from: Lower it into water and measure the volume of water it displaces, Measure its length, width and height with a ruler, Weigh it on a balance, Measure its diameter with a micrometer.)

Answer: Lower it into water and measure the volume of water it displaces

Working: Use displacement: lower the stone into a eureka can (or part-filled measuring cylinder). The volume of water displaced equals the volume of the stone.

Question 2. A stone of mass 91.8 g displaces 34 cm³ of water from a eureka can. Calculate its density in g/cm³.

Answer: 2.7 g/cm³

Working: ρ = 91.8 ÷ 34 = 2.7 g/cm³.

Question 3. Why should you check that a balance reads zero before using it? (Choose from: To avoid a systematic (zero) error in every mass, To reduce random errors, To make the balance more sensitive, To make the object lighter.)

Answer: To avoid a systematic (zero) error in every mass

Working: A balance that does not read zero adds the same error to every reading: a systematic (zero) error. Repeating the measurement would not remove it.

Related lessons

Continue in the full course

This lesson is section 6.8 (AGCPH0608) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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