AQA AS Level Physics Paper 2, June 2022: Question 6

1 mark · Medium difficulty · Multiple Choice

Estimate the stiffness of a spring used in a baby bouncer attached to a door frame.

Practise this question

Question

A multiple-choice question showing two diagrams of a baby bouncer hanging from a door frame, one empty and one with a baby sitting in it. The question asks to estimate the range of stiffness of the spring, with four options provided: A (1-10 N m^-1), B (10-100 N m^-1), C (100-1000 N m^-1), and D (1000-10 000 N m^-1).
Question text

06 A baby bouncer consists of an inextensible harness attached to a spring.

The stiffness of the spring is in the range:

[1 mark]

A 1–10 N m−1

B 10–100 N m−1

C 100–1000 N m−1

D 1000–10 000 N m−1

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer is C, corresponding to the range 100-1000 N m^-1.

06 C (AO3) 100–1000 N m−1

How to answer it

Estimating Physical Quantities: Baby Bouncer Spring

What this question tests

This question assesses your ability to apply physics knowledge to everyday estimation problems (AO3 - Application and Analysis). You must evaluate orders of magnitude for realistic physical parameters, specifically combining Hooke's Law with typical human mass and extension values.

Question 06

Spring Stiffness Estimation

✅ Correct Answer

C (100–1000 N m⁻¹)

Mark: 1 mark for selecting C

💡 Key Knowledge

  • Hooke's Law: F = kΔx , where F is force, k is stiffness, and Δx is extension.
  • Rearranging gives stiffness: k = F / Δx
  • Typical mass of an infant using a baby bouncer: roughly 10 kg .
  • Weight ( F ) = mg ≈ 10 kg × 9.81 m s⁻² ≈ 100 N .
  • Typical extension ( Δx ) under the baby's weight: roughly 0.1 m (or 10 cm).

📐 Step-by-Step Estimation

  1. Step 1: Estimate Force (Weight). An infant takes up bouncers up to about 1 year old. Average mass ≈ 10 kg . Weight F ≈ 100 N .
  2. Step 2: Estimate Extension. When the baby sits in it, the spring stretches noticeably, roughly by 0.1 m to 0.5 m . Let's test Δx = 0.2 m .
  3. Step 3: Calculate Stiffness ( k ). k = 100 N / 0.2 m = 500 N m⁻¹ .
  4. Step 4: Match Range. 500 N m⁻¹ falls comfortably inside option C (100–1000 N m⁻¹).

🧠 Exam Technique

When faced with order-of-magnitude multiple choice questions, don't panic if you don't know the exact value. Use reasonable upper and lower bounds for everyday objects. Even if your estimated numbers vary slightly, the calculated order of magnitude will point you directly to the correct bracket.

❌ Common Errors

  • Choosing extremely soft springs (like toy slinkies, A or B) which would bottom out completely under a 10 kg infant.
  • Confusing mass (kg) with weight (N) and forgetting to multiply by gravitational field strength ( g ≈ 9.81 ).

Topics

Physics · 3.1 Measurements and their errors · 3.4 Mechanics and materials

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2022. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.