Question

Does the length of the spring affect the spring constant?

Answer 1

Explanation:

We know that,

1. $\mathrm{Spring}\mathrm{Force}=-(\mathrm{Spring}\mathrm{Constant})\times \left(\mathrm{Displacement}\right)$
2. $\mathrm{F}=-\mathrm{kx}$
3. The negative sign indicates that the reaction force is pointing in the opposite direction.
4. Where, $\mathrm{F}$ is the restoring force of the spring, directed towards equilibrium. $\mathrm{k}$ is the spring constant. $\mathrm{x}$ is the spring’s displacement from its equilibrium position.
5. $\because \mathrm{k}=\frac{-\mathrm{F}}{\mathrm{x}}$
6. As from the spring constant equation, the spring constant and length are inversely proportional.
7. Therefore if the length of the spring is increased spring constant decreases and If the spring is cut to half of its original length then the spring constant increases to twice that of the original value.

Hence, we conclude that the length of the spring affects the spring constant.