Question

Does diameter affect spring constant

Answer 1

Explanation

1. We know that, Spring constant is a constant or term that is often used in Hooke’s law, which states that a particular force $\mathrm{F}$ is needed to extend or compress a spring by some specified distance $\mathrm{x}$ which when scaled linearly with respect to that distance comes out to be ${\mathrm{F}}_{\mathrm{s}}=\mathrm{kx}$ , where $\mathrm{k}$ is the constant factor and is known as the spring factor $\mathrm{k}=\frac{{\mathrm{F}}_{\mathrm{s}}}{\mathrm{x}}$.
2. Since the spring constant is a measure of the stiffness of the spring.
3. If the spring constant of a coil is to be calculated which is made of a wire of diameter $d$ then relation between spring constant $\mathrm{k}$ and Diameter of coil $D$ is given by, $\mathrm{k}=\frac{{\mathrm{Gd}}^4}{8{\mathrm{D}}^3\mathrm{n}}$ (where, $G$ is modulus of rigidity, $d$ is diameter of wire, $D$ is diameter of coil, and $n$is number of active coil).
4. Therefore if the diameter of coil $D$ is large the spring will be stiffer because the spring constant is inversely proportional to the diameter of the coil $D$. With an increase in the diameter of the coil $D$, the spring constant will decrease.

Hence, the diameter affects the spring's constant