Finding Spring Constants After Cutting a Spring

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Homework Help Overview

The problem involves a spring with a known spring constant that is cut into two equal parts, prompting a question about the resulting spring constants of the individual sections. The discussion explores the relationship between spring length and spring constant.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the reasoning behind the calculation of the new spring constant after cutting the spring and question the multiplication factor used. There is also a query about the spring constants when the spring is cut in a different ratio.

Discussion Status

The discussion is ongoing, with participants offering different perspectives on the relationship between spring length and spring constant. Some guidance has been provided regarding the mathematical relationships involved, but no consensus has been reached.

Contextual Notes

Participants are considering different cutting ratios and their implications on the spring constants, indicating a need for clarity on the underlying principles governing spring mechanics.

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Homework Statement



A spring with spring constant 8 N m-1 is cut into 2 equal parts. Find the spring constant of each part?

Homework Equations





The Attempt at a Solution



Spring constant of each part = 16 N m-1
Above is the answer given.
1. Why should we times 2?
2. If the spring is cut into a ratio of 1:2:3, then what should be the spring constant of each parts?
 
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Force constant is force required to produce unit extension.
In the spring for a given load, extension is proportional to the length of the spring. So when the length reduces, extension reduces and k increases.
 
Hello. Consider the spring to be like two capacitors. 1/keq = 1/k + 1/k'. So in this case we consider the entire spring with keq to be the sum of two individual spring halves that have some other spring constant k where k = k' for this problem. Doing a bit of algebra shows that k = 2*keq.[
 
Thanks a lot.
 

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