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

__Compressive and Tensile Forces__

__Compressive and Tensile Forces__

- Deformation is caused by a force

__Hooke’s Law__

__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__

__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, Strain, and Young’s Modulus__

- Stress is the force applied per unit cross-sectional area.
- σ =
^{F}/_{A}in Nm^{-2}or Pascal

- σ =
- Strain is the fractional increase in the original length of the wire:
- ε =
^{e}/_{l}(it has no unit)

- ε =
- Young’s Modulus is the ratio of stress to strain
- E =
^{σ}/_{ε}in Nm^{-2}or Pascal

- E =
- 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}kΔL^{2}

- W =