MYP Physics · topic MYP-06.02
Density as a material property
Connect the ideas, make your working visible, and test the result. Use the hints when you need a starting point; open the full solution after your attempt.
Extra challenging questions
Work through the linked stages and explain what each result means.
Is a hollow object made from the claimed metal?
Optional enrichment: this challenge may extend beyond the usual syllabus depth and assumes confidence with algebra and graph interpretation. A sealed metal object has mass 156 g. It raises a measuring-cylinder reading from 40 to 100 cm³. Each reading has uncertainty ±1 cm³, and the mass has uncertainty ±1 g. Solid samples of the claimed alloy give the mass–volume data below. Ignore the mass of air in the hollow object. Supplied data (Volume / cm³; Mass / g): (10, 78), (20, 156), (30, 234). (a) Use the reference data to find the alloy density and calculate the sealed object's cavity volume. [3 marks] (b) Estimate a conservative uncertainty in the external volume and in the average density; suggest a method improvement. [3 marks]
Solid alloy samples
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Mass / g
Horizontal axis (x): Volume / cm³
Read the exact data as a table
| Volume / cm³ | Mass / g |
|---|---|
| 10 | 78 |
| 20 | 156 |
| 30 | 234 |
These are the supplied values, not a worked answer. No fitted trend is drawn.
Show a hint
Begin with part (a): Use the reference data to find the alloy density and calculate the sealed object's cavity volume.
Reveal the worked solution
- The mass–volume gradient is 78/10 = 7.8 g cm⁻³, equivalent to 7800 kg m⁻³.
- Metal volume = mass/density = 156/7.8 = 20 cm³. The external volume is 100−40 = 60 cm³.
- Cavity volume = external volume − metal volume = 40 cm³. An average density of 2.6 g cm⁻³ does not by itself disprove the alloy claim.
- For a conservative bound, add the two reading uncertainties: ΔV = 1+1 = 2 cm³.
- The approximate fractional density uncertainty is 1/156 + 2/60 = 0.0397; absolute uncertainty is about 0.10 g cm⁻³.
- Use a narrower calibrated cylinder and read the meniscus at eye level. Ensure complete submersion without trapped external bubbles; repeated readings do not correct a trapped bubble.
Answer (a) Alloy density = 7.8 g cm⁻³; cavity volume = 40 cm³. (b) External volume = 60 ±2 cm³; average density ≈2.6 ±0.10 g cm⁻³.
Compare the assumptions, method and units with your attempt. Explain any correction before trying another question.