# Difference between the meanings of the equations Stress=Young's modulus x Strain and F=-kx

According to Hooke's law: $$F=-kx .$$

Is this equation the same as the equation: $$\textrm{stress}~= ~\textrm{young's modulus}~\times~\textrm{strain}$$ (i.e. are the two equations different forms of Hooke's law) or are they different?

• Do you understand the difference between stress and force? And between displacement and strain? – lemon Sep 26 '16 at 16:40
• I do. What i was asking is that whether the second equation is a more enhanced version of the first. – MrAP Sep 26 '16 at 16:41
• Yup, it's the same idea, $F = -kx$ is just a very special case. – knzhou Sep 26 '16 at 16:47

1. $F=-kx$ for a spring (i.e., an idealized, perfectly elastic lumped component)
2. $\sigma=E\epsilon$ for elastic (i.e., small) axial deformation of a elongated rod
3. $\epsilon_{ij}=\frac{1+\nu}{E}\sigma_{ij}-\frac{\nu}{E}\sigma_{kk}\delta_{ij}$, generalized Hooke's Law, for elastic deformation of any isotropic material
4. $\sigma=C\epsilon$, where $\sigma$ and $\epsilon$ are vectors and $C$ is the stiffness tensor, for elastic deformation of any material