Hooke's law

Hooke's  law

Introduction : Robert hooke , an english physicist studied the mechanical properties of solid and studied the tension in the solid and gave some law called as hooke's law. He studied elastic limit of a material and obtained very important result which gave a momentum to the world of mechanics. Let us discuss it in detail in this topic.

Elastic limit : The value of stress , upto which the stress is directly proportional to strain is called as Elastic limit.

Hooke's Law : Within elastic limit, stress is directly proportional to strain.

Mathematically,

Stress vs Strain graph

The constant is called as modulus of elasticityy

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Modulus of elasticity : It is defines as ratio of stress to strain.

Modulus of elasticity cam be classified into three category based on the types of stress and strain.

1) Young's Modulus (Y) : Young’s modulus is the ratio of longitudinal stress to longitudinal strain.

Consider a wire of length 'L' having radius 'r' and a mass 'm' is suspended below it. Due to this mass, a small extension 'l' is obtained in the wire and and 'L+l' is the final length of the wire. Thus the young's modulus for this system is given as,

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2) Bulk Modulus (K) : Bulk modulus is the ratio of volume stress to volume strain.

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3) Bulk Modulus (η) : modulus of rigidity is the ratio of shearing stress to shearing strain.

_{│<<<Strain│   │Stress and strain curve>>>│}