Elasticity
4.0 Hooke’s Law and Modulus of Elasticity
4.0 Hooke’s Law and Modulus of Elasticity
Hooke’s law states that, within the proportional limit the stress developed is directly proportional to the strain produced in a body.
$$\begin{equation} \begin{aligned} Stress \propto Strain \\ Stress = E \times Strain \\ E = \frac{{Stress}}{{Strain}} = Constant \\\end{aligned} \end{equation} $$
The $E$ is a constant and is known as modulus of elasticity.
Modulus of elasticity depends on the nature of the material of the body and is independent of its dimension (i.e. length, volume etc). The SI unit of modulus of elasticity is $N{m^{ - 2}}$ or Pascal.
Note:
- For producing same strain in two different materials, more force will be needed for material having greater modulus of elasticity ($E$) and vice versa. As, $$E \propto Stress$$
- For producing same stress in two different materials, the material which is expanded or compressed easily or in other words the material which shows greater strain has less modulus of elasticity ($E$) and vice versa. As, $$E \propto \frac{1}{{Strain}}$$
Example: As rubber can be expanded and compressed easily as compared to the steel, thus we say that the modulus of elasticity ($E$) of rubber is less than that of steel.
So, $${E_{Steel}} > {E_{Rubber}}$$
