Question

Does cutting a spring change the spring constant?

Answer 1

Explanation:

Formula used:
The applied force, $F=kx$
$x$ is the increase in length of the spring due to the applied force.
$k$ is the spring constant.

Complete step-by-step solution:

1. When a mass is attached to a spring that is connected to a rigid rod, and then a force is applied to this spring, the spring is increased by some length.
2. The applied force $F\propto x$ . Where $x$ is the increase in length of the spring due to the applied force.
3. The spring constant is the force that is required to increase the unit length of a spring.

Let the spring be cut into three equal pieces. Hence, due to the equal force applied to these parts, each part is increased by the same length $\frac{x}{3}$ .

Therefore, the spring constant for each part, $k^{\prime }={\displaystyle \frac{F}{{\displaystyle \frac{x}{3}}}}={\displaystyle \frac{3F}{x}}=3k$

Hence, the spring constant for each part of the spring will be three times the spring constant of the whole spring.

So, it is concluded that the spring-constant changes after cutting the spring.