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12.1.3Particle Model

Core Practical: Determining Density — Edexcel GCSE Combined Science 1SC0 - Physics Revision Notes & Topical Questions

5 min read 9 parts Lesson 4 of 13

📚 Edexcel GCSE Combined Science 1SC0 - Physics Hub / Topical Revision
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Part 1 of 7Aim and principle

The aim is to find the density of different materials by measuring the mass and the volume of a sample and applying ρ = m ÷ V.

Aim and principle
The skill is in measuring each quantity as accurately as possible, in choosing equipment with appropriate resolution and in reducing error.
The method depends on whether the object is a regular solid, an irregular solid or a liquid.

Part 2 of 7Regular solid

Examplesa metal cuboid, cylinder or cube.

1
Measure the mass on a balance (resolution 0.1 g or 0.01 g). Zero the balance first.
2
Measure the dimensions with a ruler (cm) or, for better precision, vernier callipers or a micrometer.
  • For a cuboid measure length, width and height; for a cylinder measure diameter and height.
3
Calculate volume: cuboid V = l × w × h; cylinder V = πr2h.
4
Calculate density ρ = m ÷ V.

Take each length at several places and average, because the object might not be perfectly uniform. Measuring a small dimension with a ruler gives a large percentage uncertainty; a micrometer gives a far smaller one.

Part 3 of 7Irregular solid

Examples

  • a stone or a piece of metal with an odd shape.
  • The volume cannot be found from dimensions, so use displacement.

1
Measure the mass of the object on the balance.
2
Partly fill a measuring cylinder with water and read the initial volume at eye level, at the bottom of the meniscus.
3
Lower the object gently on a thread. Read the new volume.
4
The volume of the object is the difference of the two readings.
  • Alternatively use a displacement (eureka) can: fill it until water just stops dripping from the spout,
    • then lower the object in and collect the displaced water in a measuring cylinder.
  • The volume of the water collected equals the volume of the object.

The object must be fully submerged and must not absorb water or dissolve.

Part 4 of 7Liquid

Place an empty measuring cylinder on the balance and zero (tare) it, or record its mass.

1
Add a measured volume of liquid, for example 50 cm3, and record the new mass.
2
The mass of the liquid is the difference.
3
Density = mass of liquid ÷ volume of liquid.
4
For a more reliable result add the liquid in steps (10, 20, 30, 40, 50 cm3), measure the mass each time and plot mass against volume; the gradient of the line of best fit is the density,
  • and a line that does not pass through the origin signals a systematic error such as a mass offset.

Part 5 of 7Sources of error and improvements

Possible errors

  • reading the meniscus from above or below;
    • air bubbles clinging to the object;
    • water splashing or spilling;
    • water remaining in the eureka can spout;
    • the balance not being zeroed;
    • a ruler with a coarse scale.

Sources of error and improvements
Improvements: take readings at eye level; tap to remove bubbles; use a string of negligible volume; use a larger sample so the measurement is a larger fraction of the equipment resolution; repeat and average.
State the final answer with the appropriate number of significant figures, matching the least precise measurement.

Safety

  • take care with glassware and wipe up spills quickly;
    • wear eye protection.

Part 6 of 7Choosing methods and reporting results

When choosing a method, consider the size and shape of the object.

Choosing methods and reporting results
For a small regular solid, a micrometer for the diameter and a balance with 0.01 g resolution give the best precision; for a large irregular object that will not fit into a measuring cylinder, use a eureka can.
For a liquid, a burette or pipette gives more precise volumes than a beaker.
Calculate the percentage uncertainty: if a length of 2.00 cm is measured with an uncertainty of 0.05 cm, the percentage uncertainty is 2.5%;
  • because volume uses three lengths the uncertainty grows roughly threefold.

Report the final density with units and a sensible number of significant figures, and compare with a data-book value.

Choosing methods and reporting results
If the result differs by more than the estimated uncertainty, discuss systematic errors such as trapped bubbles or an unzeroed balance.
Repeating a measurement at least three times and calculating the mean is a standard way of improving reliability,
  • and removing an anomalous reading is acceptable if you can explain it.

Part 7 of 7Worked examples

  1. A student finds that a stone has mass 84.5 g. It is lowered into a measuring cylinder containing 40 cm3 of water and the level rises to 70 cm3. Calculate the density.

  2. The mass of an empty cylinder is 92.0 g; with 40.0 cm3 of a liquid it is 124.0 g. Find the density of the liquid.

  3. A cylinder has diameter 2.0 cm, height 8.0 cm and mass 196 g. Find its density.

Key terms

TermMeaning
Displacement methodFinding volume from the amount of water pushed aside by a submerged object.
MeniscusCurved surface of a liquid in a tube, read at the bottom.
ResolutionThe smallest change an instrument can detect.
Eureka canContainer with a spout for collecting displaced liquid.
Systematic errorError that shifts all readings in the same direction.
TareReset a balance to zero with a container on it.

Avoid these mistakes

1
Reading the measuring cylinder from above or at the top of the meniscus.
2
Using the diameter instead of the radius in V = πr2h.
3
Forgetting to subtract the mass of the container.
4
Not submerging the object completely so the displaced volume is too small.
5
Giving an answer to many more significant figures than the data justifies.

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