Question

In Hooke's law, the constant of proportionality signifies?

Answer 1

Hooke's law

1. Hooke's law states that stress is always proportional to strain and the ratio of stress and strain is constant, i.e$\frac{\mathrm{stress}}{\mathrm{strain}}=\mathrm{constant}$,
2. From this law, we know that applied stress is proportional to strain, i.e, $F\propto x$

Proportionality constant

1. Thus, the applied stress, $F=-kx$ $\Rightarrow k=-\frac{F}{x}$, where k is the constant of proportionality.
2. The negative sign indicates here that the direction of the applied force is opposite to the restoring force of the spring.
3. The constant K is the modulus of elasticity or spring constant. The unit of spring constant or modulus of elasticity is N/m.
4. The dimension of spring$\left[K\right]=-\frac{ML{T}^{-1}}{L}=M{T}^{-1}$ the spring constant is.