Key Learning Objectives
- Calculate spring extension: Extension = Stretched Length − Original Length.
- Apply Hooke's Law: Force (N) = Spring Constant (N/m) × Extension (m) [F = k × e].
- Identify the limit of proportionality on a force-extension graph.
Topic Summary & Core Notes
Investigate how springs stretch under load. Learn Hooke's Law (F = k × e), extension graphs, spring constant (k), and elastic limit vs plastic deformation.
Key Rules, Formulas & Definitions
Extension Equation
Extension (e) = New Length − Original Unstretched Length
Hooke's Law Equation
Force (N) = Spring Constant (k in N/m) × Extension (e in m) [F = k × e]
Spring Constant Formula
k = Force ÷ Extension (Gradient of linear force-extension graph)
2 Step-by-Step Worked Examples
Worked Example 1
Worked Example 1: Calculating Spring Constant
Question: A spring has an original length of 10 cm. When a 4 N weight is hung from it, its length increases to 18 cm. Calculate the spring constant in N/m.
Step-by-Step Solution:
- Step 1: Calculate extension in cm: Extension = 18 cm − 10 cm = 8 cm.
- Step 2: Convert extension to metres: 8 cm ÷ 100 = 0.08 m.
- Step 3: Apply Hooke's Law: k = F ÷ e = 4 N ÷ 0.08 m = 50 N/m.
Final Answer: 50 N/m
Senior Examiner Insight: Always convert extension from centimetres to metres before calculating spring constant.
Worked Example 2
Worked Example 2: Elastic vs Inelastic Deformation
Question: Explain what happens when a spring is stretched beyond its 'limit of proportionality'.
Step-by-Step Solution:
- Step 1: Linear relationship breaks: Force and extension are no longer directly proportional (the graph curves).
- Step 2: Inelastic deformation: When the load is removed, the spring will not return to its original length, remaining permanently deformed.
Final Answer: The spring exceeds its elastic limit, resulting in permanent (inelastic) deformation.
Senior Examiner Insight: Use the technical term 'inelastic/plastic deformation' rather than saying 'it gets ruined'.
Common Pitfalls & Examiner Warnings
Common Mistake: Using total stretched length instead of extension
Extension is Stretched Length MINUS Original Length; using total length yields incorrect results.
Common Mistake: Forgetting to convert cm to metres
Spring constant units are N/m, requiring extension in metres (cm ÷ 100).
Common Mistake: Assuming Hooke's Law holds forever
Hooke's Law only applies up to the limit of proportionality.
Interactive Self-Check Quiz (3 Questions)
Question 1 of 3
A spring with spring constant k = 200 N/m extends by 0.05 m. What force was applied?
Click to Reveal Answer & Mark Scheme
Correct Answer: A) 10 N
Detailed Explanation: F = k × e = 200 N/m × 0.05 m = 10 Newtons.
Mark Scheme & Scoring Points: 1 mark for 10 N.
Question 2 of 3
What is the physical meaning of the gradient on a linear Force (y-axis) vs Extension (x-axis) graph?
Click to Reveal Answer & Mark Scheme
Correct Answer: B) Spring constant (k)
Detailed Explanation: Gradient = Change in Force ÷ Change in Extension = F / e = k (Spring Constant).
Mark Scheme & Scoring Points: 1 mark for Spring constant (k).
Question 3 of 3
What term describes a material that returns to its original shape once the stretching force is removed?
Click to Reveal Answer & Mark Scheme
Correct Answer: B) Elastic deformation
Detailed Explanation: Elastic deformation is fully reversible once applied forces are removed.
Mark Scheme & Scoring Points: 1 mark for Elastic deformation.
Created by Fiaraz Iqbal
Former Headteacher & Senior Science / Maths Examiner
Fiaraz produces structured video walkthroughs, Tier 3 literacy packs, and exam mark scheme breakdowns to help secondary students achieve top grades.
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