AQA GCSE Combined Science: Trilogy Physics Paper 2 (Higher), 2019: Question 5

✅ Correct answer

Force ∝ extension

💡 Key knowledge

• For a spring obeying Hooke’s law: F = kx
• This means force is directly proportional to extension.
• As the force increases, the spring stretches more.

🧠 Exam technique

• Read the wording carefully: the question asks for a proportionality.
• Choose the option that matches the law, not a general idea.

❌ Common errors

• Choosing force ∝ energy stored — this is not the GCSE relationship here.
• Choosing force ∝ length — it is extension that matters, not total length.
• Choosing force ∝ spring constant — the spring constant is a property of the spring, not something force is proportional to in this question.

📐 Calculation: step by step

1. Total force from all springs = 0.49 × 1200
2. F = 588 N
3. Use F = mg
4. 588 = m × 9.8
5. m = 588 ÷ 9.8
6. m = 60 kg

✅ Full-mark answer

Mass = 60 kg

A completely correct final answer scores all 4 marks.

💡 Key knowledge

• Weight is a force: W = mg
• Here the force on one spring is given, and there are 1200 identical springs.
• So first find the total force supported by all springs.

🧠 Exam technique

• Show the equation before rearranging.
• Include units at each stage: N for force, kg for mass.
• Use the given value of g = 9.8 N/kg .
• Marks were awarded for method, not just the final answer.

❌ Common errors

• Using only 0.49 N instead of multiplying by 1200 .
• Forgetting that the force on the whole mattress is the sum of the forces on all springs.
• Writing m = 588 × 9.8 instead of dividing.
• Leaving the answer in newtons instead of kilograms.

📐 Calculation: step by step

1. Use Hooke’s law: F = kx
2. Substitute values: 0.49 = k × 3.5 × 10⁻³
3. Rearrange: k = 0.49 ÷ (3.5 × 10⁻³)
4. Calculate: k = 140
5. Write the unit: N/m

✅ Full-mark answer

Spring constant = 140 N/m

The mark scheme accepts the correct answer of 140 with the unit N/m.

💡 Key knowledge

• Hooke’s law: F = kx
• k = spring constant
• x = extension or compression in metres
• The force and compression must be in the correct units before calculating.

🧠 Exam technique

• Always rearrange the equation clearly.
• Give the unit for the spring constant: N/m .
• Notice the compression is given in standard form: 3.5 × 10⁻³ m .

❌ Common errors

• Using the whole mattress force instead of the force on one spring.
• Forgetting to divide by the compression.
• Writing the unit as N instead of N/m .
• Missing the unit mark even if the number is correct.

✅ Correct answer

The springs should have a low spring constant, so they compress by a larger amount for the same force.

💡 Key knowledge

• A soft mattress gives more under your weight.
• That means the springs are easier to compress.
• Lower stiffness = larger compression for the same force.

🧠 Exam technique

• For 2 marks, give both the property and the reason.
• A good answer links the spring constant to how much the spring compresses.

❌ Common errors

• Saying “strong springs” or “stiff springs” would make it soft — this is the opposite of the correct idea.
• Just saying “it compresses a lot” without mentioning a low spring constant.
• Confusing “soft” with “long” or “large”.

Key equations

• F = mg
• F = kx

Remember

• Force in newtons (N)
• Mass in kilograms (kg)
• Extension/compression in metres (m)
• Spring constant in N/m

Final exam tip

• Show the full working for calculations.
• Check whether a force is for one spring or all springs.
• Use the correct units to secure the final mark.