Deformation of Solids - Hooke's Law and Young's Modulus
Compressive and Tensile Forces
- Deformation is caused by a force
- 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