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Deformation of Solids - Hooke's Law and Young's Modulus

Compressive and Tensile Forces
  • Deformation is caused by a force

Hooke’s Law
  • A spring produces an extension when a load is attached to it.
  • According to Hooke’s law, the extension produced is proportional to the applied force (due to the load) as long as the elastic limit is not exceeded.
  • F = ke; where k is the spring constant (force per unit extension)
  • Calculating effective spring constants:
Determining Young’s Modulus
  • Measure the diameter of the wire using a micrometer screw gauge
  • Set up the arrangement as is below:
  • Attach weights to the end of the wire and measure the extension
  • Calculate Young’s modulus using the formula
Stress, Strain, and Young’s Modulus
  • Stress is the force applied per unit cross-sectional area.
    • σ = F/A in Nm-2 or Pascal
  • Strain is the fractional increase in the original length of the wire:
    • ε = e/l (it has no unit)
  • Young’s Modulus is the ratio of stress to strain
    • E = σ/ε in Nm-2 or Pascal
  • Stress-Strain Graph:

    • Gradient = Young’s modulus
  • Elastic deformation is when the deforming forces are removed, the spring returns to its original length.
  • Plastic deformation is when the deforming forces are removed, the spring does not return to its original length.
  • Strain energy is the potential energy stored in or the work done by an object when it is deformed elastically.
  • Strain energy = Area under the force-extension graph
    • W = 1/2 kΔL2