Question

How do you find the Young’s modulus from a load extension graph?

Answer 1

Hint: When attempting questions based on Young’s modulus like the one given to us above, keep in mind the different factors affecting Young’s modulus and how they affect it, and what are the effects of the factors on the materials elasticity because Young’s modulus is basically a measure of elasticity of materials.

Complete step-by-step solution:
Young’s modulus is basically to tell us about the stiffness of a material, or tell us how easily it can be bent or stretched, and to what limit it can be bent till it breaks or gets permanently deformed. Higher the young’s modulus, greater will be the stiffness of the material. Formula wise Young’s modulus is equated to be the ratio of longitudinal stress and strain.
Also called as the modulus of elasticity, this term can be used as a measurement of a certain material’s elastic capabilities, on its resistance to be deformed or not. The materials express or exhibit their elastic qualities when they are put under stress , the stress is the causal factor of their deformation, although if the material is truly elastic it will jump back to its previous state as soon as the stress is removed.
Now when we talk about Young’s modulus , we also get to know more about Hooke’s law relating to Young’s modulus. Earlier times described Hooke’s law as a relation between stress and strain but now this slightly modified fundamental law gives us a direct relationship between the force applied on a particular object and consequently its induced strain.
The Young’s modulus of any material can be acquired or calculated by a stress strain graph which can be derived from load extension graphs. The slope of this graph will be the answer. The slope of this load extension graph is the key to determining Young’s modulus, the only condition is that the material has to obey Hooke's law.

 Note:
Another mechanical property of solids is one by the name of Bulk modulus. This is a term which tells us about the compression a particular material can handle under a given amount of externally applied pressure. Here the ratio of change in pressure to fractional volume compression is the key to finding the bulk modulus.