Evaluate density methods and systematic errors
Track how a mistaken mass or volume changes the inferred ratio and improve the relevant measurement.
Section 1.4 · Density
Core and Extended; Physics 0625, 2026–2028, section 1.4. Density is mass per unit volume. Match the units before calculating. The syllabus includes measuring liquid, regular-solid and sinking irregular-solid densities, then using density data to predict floating. Paper exercises support practical reasoning but do not demonstrate supervised practical competence. Written practice is self-checked
Before you begin
- Use density as a ratio.
- Recognise separate mass and volume measurements.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
With unchanged mass, what happens to m/V if the volume denominator is too large?
What you will learn
- Predict density overestimates and underestimates from method errors.
- Distinguish repeatability from a corrected systematic method.
Track the numerator and denominator
If an irregular solid's true mass is 48 g and volume 16 cm³, its density is 3.0 g/cm³. Trapped air increasing measured displacement to 20 cm³ gives 2.4 g/cm³, an underestimate. Losing liquid so that the recorded rise is only 14 cm³ instead gives about 3.43 g/cm³, an overestimate.
For liquid density, forgetting to subtract an empty container adds unwanted mass to the numerator and makes density too high. A regular-solid dimension error can make calculated volume too high or low. State which measured quantity is affected, then explain the ratio change; saying only that the experiment is inaccurate does not identify the mechanism.
Choose an improvement that addresses the cause
Remove attached bubbles before displacement, lower a solid without splashing, read the meniscus at eye level and use a zeroed balance. Each action addresses a particular source of error. Repeating and averaging careful trials can reduce the influence of random scatter, but repeating the same container-mass omission or unit error cannot remove that bias.
Illustrative repeated liquid-density results 0.79,0.81,0.80 g/cm³ have mean 0.80 g/cm³. Their closeness supports repeatability, not proof of accuracy or completion of a practical assessment. Compare methods under matched material and temperature conditions, retain sensible precision, and seek supervised practical experience and teacher feedback for the real laboratory skills.
Pause and explain
A liquid calculation repeatedly includes the empty container's mass. Does averaging ten such trials fix it?
Worked example
A 48 g solid truly occupies 16 cm³ but a lost-liquid error gives a measured displacement of 14 cm³. Find the inferred density and error direction.
Show the worked solution
- True density = 48/16 = 3.0 g/cm³.
- Inferred density = 48/14 ≈ 3.43 g/cm³.
- The underestimated volume causes density to be overestimated.
Answer Approximately 3.43 g/cm³, an overestimate.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A 48 g sample gives a mistaken 14 cm³ displacement rather than its true 16 cm³. Compare densities.
Give me a hint
Calculate both ratios with the same mass.
Compare my reasoning
- True density is 3.0 g/cm³.
- Mistaken density is 48/14 ≈ 3.43 g/cm³.
- A too-small measured volume produces a too-large density.
3.0 versus approximately 3.43 g/cm³; an overestimate.
Look for these in your work
- Calculate both values.
- Explain the denominator effect.
Repeated results are 0.79,0.81,0.80 g/cm³. Find their mean and say whether agreement proves accuracy.
Give me a hint
Average the values, then distinguish scatter from bias.
Compare my reasoning
- Sum = 2.40 g/cm³.
- Mean = 2.40/3 = 0.80 g/cm³.
- Agreement supports repeatability but does not exclude a shared systematic error.
0.80 g/cm³; agreement does not prove accuracy.
Look for these in your work
- Compute the mean.
- State the evidence limit.
An irregular solid's density is too low because bubbles cling to it, while a liquid's density is too high because its container mass was included. Suggest a separate correction for each.
Give me a hint
Identify the wrong denominator in one method and numerator in the other.
Compare my reasoning
- Remove trapped air and remeasure displacement for the solid.
- Subtract or tare the empty container for the liquid.
- Repeat the corrected methods, pairing each sample's mass and volume.
Remove bubbles; subtract or tare the container; repeat the corrected measurements.
Look for these in your work
- Match each correction to its cause.
- Avoid claiming repetition alone fixes bias.
Common mistakes
- Explain which part of m/V changed.
- Repeatability does not establish accuracy.
- Averaging does not correct a persistent systematic omission.
What can you explain now?
What is the mean of 0.79,0.81,0.80 g/cm³?
Compare with the explanation
0.80 g/cm³.
Sum the three results and divide by three, retaining the density unit.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Explain one high-density and one low-density method error using the numerator and denominator.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.