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