11th Physics Topic Hooke’s Law – Stress and Strain from Mechanical Properties of Solid

11th Physics Topic - Hooke’s Law – Stress and Strain from Mechanical Properties of Solid 

The ratio of the magnitude of the applied force to the cross-sectional area of the wire is called the stress acting on the wire, while the ratio of the change in length to the original length of the wire is called the strain of the wire. Above equation is a statement of Hooke’s law of elasticity, which says that in an elastic body the stress is directly proportional to the strain, that is,

                                                        stress ∝ strain

The stress is what is applied to the body, while the resulting effect is called the strain. To make an equality out of this proportion, we must introduce a constant of proportionality. This constant depends on the type of material used, since the molecules, and hence the molecular forces of each material, are different. This constant, called Young’s modulus of elasticity is denoted by the letter Y. thus above equation becomes

                                                       F/A = Y ∆L/LO

If we apply a force to a rubber band, we find that the rubber band stretches. Similarly, if we attach a wire to a support, as shown in figure 1, and sequentially figure 2 stretching an object. Apply forces of magnitude F, 2F, and 3F to the wire, we find that the wire stretches by an amount ∆L, 2∆L, and 3∆L, respectively. (Note that the amount of stretching is greatly exaggerated in the diagram for illustrative purposes.)

The deformation, ∆L, is directly proportional to the magnitude of the applied force F and is written mathematically as

∆L ∝ F

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