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Question

Does cutting a spring change the spring constant?


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Solution

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 Fx . 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 x3 .

Therefore, the spring constant for each part, k=Fx3=3Fx=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.


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