Deformation of solids · revision map · A-Level 9702, Topic 6

TOPIC 6 · DEFORMATION OF SOLIDS
CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 · ONE-PAGE REVISION MAP
thelucidstem.com
DEFORMING
SOLIDS6
Hooke's Law & Spring Constant

A force stretches a solid in proportion to the load.

F = k x
k = spring constant (N m−¹)
x = extension (m)
  • A tensile force extends; a compressive force shortens.
  • Extension x is proportional to load F up to the limit of proportionality.
  • k is the gradient of a force-extension graph (stiffer = larger k).
F x gradient = k x F
Stress, Strain & Young Modulus

Scale out the size to measure the material itself.

σ = F / A ε = x / L
stress σ in Pa (force per unit cross-section) · strain ε has no unit
E = σ / ε = F L / (A x)
  • Young modulus E is the stiffness of the material.
  • It is the gradient of the straight part of a stress-strain graph.
σ ε limit of proportionality gradient = E
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 line is straight while Hooke's law holds, then curves over.
  • Past the elastic limit, unloading leaves a permanent extension.
F x elastic limit
Elastic Potential Energy

Work done stretching is stored as energy.

Eelastic = ½ F x = ½ k x²
  • 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.
F x area = E
BUILDS ON · Forces · Energy · IGCSE Forces → DEFORMATION → LEADS TO · Oscillations · Waves
thelucidstem.com · Cambridge AS & A Level Physics 9702 · TheLucidSTEM revision map