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A-LEVEL 9702 · AS · TOPIC 6
Deformation of solids
The chain of the topic: a stretching force gives Hooke's law and a spring constant, dividing by area and length turns that into stress, strain and the Young modulus, and the work done in stretching is stored as elastic potential energy. Around the hexagon are the core ideas; above is what it builds on, below is where it leads.
TOPIC 6: DEFORMATION OF SOLIDS
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
TheLucidSTEM · thelucidstem.com
BUILDS ON
T4 Forces T3 Newton's laws of force T5 Work, energy, W = Fx 6.1
6.1
6.2
6.2
TOPIC 6
DEFORMING
SOLIDS
1 · HOOKE'S LAW & SPRING CONSTANT
A force stretches a solid in proportion.
Tensile force pulls and extends; compressive force
pushes and shortens.
Extension x is proportional to load F up to the
limit of proportionality.
F = k x
k is the spring constant (N m−¹)
F
x
load gives extension x
2 · STRESS, STRAIN & YOUNG MODULUS
Scale out the size to measure the material.
Stress σ = F / A: force per unit cross-section (Pa).
Strain ε = x / L: extension per unit length, no unit.
Young modulus E is the stiffness of the material,
the gradient of stress against strain.
E = σ / ε = F L / (A x)
σ
ε
limit of proportionality
gradient = E
3 · ELASTIC & PLASTIC BEHAVIOUR
Does it spring back, or stay deformed?
Elastic: returns to its original length when the
load is removed.
Plastic: stays permanently stretched beyond the
elastic limit.
The force-extension line is straight while Hooke's
law holds, then curves over.
F
x
elastic limit
straight: elastic
4 · ELASTIC POTENTIAL ENERGY
Work done stretching is stored energy.
The area under a force-extension graph is the
work done on the solid.
While Hooke's law holds the graph is a triangle.
An elastic solid gives this energy back on release.
Eₐ = ½ F x = ½ k x²
F
x
area = Eₐ
LEADS TO
T17 Oscillations: mass on a spring, F = −k x drives SHM T5 Energy: stored elastic PE in the energy budget T7 Waves: stiffness sets the speed in a medium One restoring force F = −k x links a stretched spring to simple harmonic motion, while the stored energy ½ k x² feeds straight into energy conservation.
← Builds on IGCSE: Forces & elasticity