Matter, density, and materials

A solid sample has mass 240 g and volume 300 cm³. Which statement is correct?

1. A

   Its density is 0.80 g cm⁻³.

2. B

   Its density is 1.25 g cm⁻³.

3. C

   Its density is 60 g cm⁻³.

4. D

   Density cannot be found without knowing its shape.

1. a

   Select and show Select the correct statement and show the calculation with units.

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   Correct choiceA

   1. 1

      Selects option A: the sample density is 0.80 g cm⁻³.

   2. 2

      Uses density = mass ÷ volume = 240 ÷ 300.

   3. 3

      Obtains 0.80 g cm⁻³ with the correct unit.

A student adds loads to a spring and measures extension from its unloaded length.

1. a

   Describe Describe the pattern from 0 N to 4 N and support it with evidence.

   2
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   1. 1

      States that extension is directly proportional to force over 0–4 N.

   2. 2

      Supports this by noting each 1 N adds 1.5 cm, or that force ÷ extension is constant.

2. b

   Calculate Calculate the spring constant in N m⁻¹ within the proportional region.

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   1. 1

      Converts an extension correctly, for example 6.0 cm = 0.060 m.

   2. 2

      Uses k = F ÷ x.

   3. 3

      Obtains k = 4.0 ÷ 0.060 = 66.7 N m⁻¹, or about 67 N m⁻¹.

3. c

   Evaluate Use the evidence to identify where the simple Hooke's-law model becomes unreliable.

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   1. 1

      Identifies that departure begins above 4 N, with the 5 N reading no longer following the earlier ratio.

   2. 2

      Predicts 7.5 cm at 5 N from the proportional pattern but observes 8.5 cm.

   3. 3

      Concludes that calculations using the constant 67 N m⁻¹ should be restricted to the proportional region.

A designer is choosing a material for a bicycle luggage rack. The rack must be light, safely support repeated loads, resist outdoor use, and be affordable.

1. a

   Compare Calculate yield strength divided by density for each material and use it as one measure of strength for mass.

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   1. 1

      Calculates aluminium alloy: 240 ÷ 2.7 ≈ 89 in consistent comparative units.

   2. 2

      Calculates mild steel: 260 ÷ 7.8 ≈ 33 and magnesium alloy: 190 ÷ 1.8 ≈ 106.

   3. 3

      Identifies magnesium alloy as having the greatest value by this single measure.

2. b

   Recommend Recommend a material using at least three pieces of evidence and a clear priority.

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   1. 1

      Makes a defensible recommendation consistent with a stated design priority.

   2. 2

      Uses at least three accurate comparisons from density, strength, recycled content, and cost.

   3. 3

      Recognises a trade-off rather than claiming that one row is universally best.

3. c

   Evaluate Identify one important limitation of this table and state what should be tested next.

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   1. 1

      Identifies missing evidence relevant to repeated outdoor use, such as fatigue life, corrosion resistance, joint strength, or coating requirements.

   2. 2

      Proposes a corresponding controlled durability, corrosion, or loaded-cycle test.