When a force is applied to a spring (or elastic material), it STRETCHES or COMPRESSES.
HOOKE'S LAW:
Within the ELASTIC LIMIT, extension is DIRECTLY PROPORTIONAL to the applied force.
EQUATION:
F = k × e
F = force applied (newtons, N)
k = spring constant (N/m) — stiffness of the spring
e = extension (metres, m) — increase in length from natural length
A STIFFER spring has a LARGER k value — more force needed per metre of extension.
EXAMPLE:
A spring with k = 50 N/m is stretched by 0.2 m:
F = 50 × 0.2 = 10 N
Rearranging:
e = F ÷ k
k = F ÷ e
Force–Extension Graphs
FORCE-EXTENSION GRAPH for a spring:
X-axis: extension (m). Y-axis: force (N).
LINEAR (STRAIGHT) SECTION:
Obeys Hooke's Law — force proportional to extension.
Gradient = spring constant k = F ÷ e.
BEYOND THE ELASTIC LIMIT:
Graph curves — no longer proportional.
Larger extension per unit force.
RETURN BEHAVIOUR:
ELASTIC deformation: spring returns to original length when force removed.
INELASTIC deformation: spring does NOT return to original length — permanently stretched.
The elastic limit is the point beyond which deformation becomes inelastic.
REQUIRED PRACTICAL (RP18):
Add masses to a spring. Measure extension at each mass.
Plot force vs extension. Find spring constant from gradient.
Identify where Hooke's Law is obeyed and where it breaks down.
More Than One Force Needed
To change the SHAPE of an object, MORE THAN ONE FORCE must be applied.
Reason: if only one force is applied, the object would accelerate in that direction instead of deforming.
Two equal and opposite forces are needed to stretch, compress or bend an object.
EXAMPLE:
Stretching a rubber band: you pull both ends — two forces in opposite directions.
Compressing a spring: push both ends together — two forces towards each other.
STORAGE OF ELASTIC PE:
A stretched spring stores elastic potential energy:
Ee = ½ × k × e²
All the work done stretching the spring (within elastic limit) is stored as Ee.
When released, this converts to kinetic energy.
APPLICATIONS:
Springs in mattresses, car suspensions, watches, catapults, archery bows.
Elastic bands, bungee cords, rubber in tyres.
⚠️ Common Mistake
Extension (e) is NOT the total length of the spring — it is the INCREASE in length from the natural (unstretched) length. If a 10 cm spring stretches to 14 cm, e = 4 cm = 0.04 m.
📐 Variables
FForce (F) is measured in newtons (N)
kSpring constant (k) is measured in N/m (N/m)
eExtension (e) is measured in metres (m)
📐 Key Equations
F = k × e
📌 Key Note
Hooke's Law: F = ke. k = spring constant (N/m), stiffness. Extension = increase in length (not total length). Elastic limit: beyond this, Hooke's Law breaks down — graph curves. Elastic deformation: returns to shape. Inelastic: permanent. RP18: force–extension graph, gradient = k.
🎯 Matching Activity — Hooke's Law
Match each scenario to the correct force or extension. — drag the symbols on the right to match the component names on the left.
F = 10 N
Drop here
e = 0.05 m
Drop here
Elastic limit exceeded
Drop here
Inelastic deformation
Drop here
Spring stretched beyond elastic limit — does not return to original length
Spring k = 50 N/m, extension = 0.2 m — F = ke = 50 × 0.2
Spring k = 200 N/m, force = 10 N — e = F/k = 10/200
Graph of F vs e curves away from straight line — Hooke's Law no longer obeyed
⚽ FIFA Worked Examples
Hooke's Law
A spring with k = 80 N/m is stretched by 0.15 m. Calculate the force applied.
F
F = k × e
I
k = 80 N/m, e = 0.15 m
F
F = 80 × 0.15
A
F = 12 N
🧪 Required Practical
🔬 RP18 (Physics) — Investigate force–extension relationship for a spring. Add masses, measure extension. Plot F vs e graph. Find k from gradient. Identify elastic limit.
Know the method, variables, equipment and how to analyse results.
🎯 Test Yourself
Question 1 of 2
1. A spring of natural length 10 cm is stretched to 16 cm by a 3 N force. What is the spring constant?
2. Why do you need to pull both ends of a rubber band to stretch it?
⭐ How Well Do You Understand This Topic?
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🤖 Ask Mr Badmus AI
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