# Verifying Hooke's Law and Finding the Young's Modulus of Elasticity of a Steel Wire

## Abstract

Elasticity is the physical property of a material that returns to its original shape after the stress that made it deform is removed. The relative increase in deformation with stress applied is called the strain. Hooke's law states that, within the elastic limit, the stress applied to a material is proportional to the strain, i.e., that more stress will produce greater strain. The constant, or slope of the plot of stress and strain, is called Young's modulus. In this experiment, the Young's modulus of a steel wire was determined. Since variations of the external stress applied produce very small deformation on the wire, an optical level using laser magnification was used. A plot of the stress and strain so produced in one experimental test gave a straight line verifying Hooke's law of elasticity. However, using a second wire, the plot of stress and strain (and therefore Young's modulus) did not agree within experimental uncertainty with the published value for a standard steel wire. Possible factors contributing to the discrepancy may have been the age and wear of the steel wire, or the fuzziness of the laser beam used in the experiment.

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Verifying Hooke's Law and Finding the Young's Modulus of Elasticity of a Steel Wire

Elasticity is the physical property of a material that returns to its original shape after the stress that made it deform is removed. The relative increase in deformation with stress applied is called the strain. Hooke's law states that, within the elastic limit, the stress applied to a material is proportional to the strain, i.e., that more stress will produce greater strain. The constant, or slope of the plot of stress and strain, is called Young's modulus. In this experiment, the Young's modulus of a steel wire was determined. Since variations of the external stress applied produce very small deformation on the wire, an optical level using laser magnification was used. A plot of the stress and strain so produced in one experimental test gave a straight line verifying Hooke's law of elasticity. However, using a second wire, the plot of stress and strain (and therefore Young's modulus) did not agree within experimental uncertainty with the published value for a standard steel wire. Possible factors contributing to the discrepancy may have been the age and wear of the steel wire, or the fuzziness of the laser beam used in the experiment.