Question

How do you calculate elasticity from the Young Modulus?

Answer 1

Explanation:

Calculate the elasticity from Youngs Modulus

1. Young's modulus is a numerical constant that describes the elastic properties of a solid undergoing tension or compression in only one direction, as in the case of a metal rod that, after being stretched or compressed lengthwise, returns to its original length.
2. It was named after the $18th-century$ English physician and physicist Thomas Young. Young's modulus is a measurement of a material's capacity to endure changes in length when subjected to compression or tension along its length.
3. Young's modulus, also known as the modulus of elasticity, is determined by dividing the longitudinal stress by the strain. For a metal bar under tension, stress and strain can be explained as follows.

Formula for stress and strain

When a force$F$ is applied to both ends of a metal bar with a cross-sectional area of $A$, the bar stretches from its initial length $L_0$ to a new length $L_n$. (At the same time, the cross-section shrinks.)

$$\begin{gathered} \Rightarrow Stress=Thetensileforcedividedbycross-sectionalarea \\ \Rightarrow Stress=\frac{F}{A}.........\left(equation1\right) \end{gathered}$$

The length change, $L_n-L_0$divided by the initial length. (Strain has no dimensions)

$$\begin{gathered} \Rightarrow Strain=\frac{Changeinlength}{Originallength} \\ \Rightarrow Strain=\frac{L_n-L_0}{L_0}......\left(equation2\right) \end{gathered}$$

Elasticity from young modulus

Young's modulus can be expressed numerically as,

$$\begin{gathered} \Rightarrow Young’smodulus=\frac{stress}{strain} \\ \Rightarrow Young’smodulus=\frac{F{L}_0}{A\left(L_n-L_0\right)} \end{gathered}$$

This is a specific form of Hooke's law of Elasticity.