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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: