📖 In-Depth Theory
Hooke's Law
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.