Finding Spring Constants After Cutting a Spring

AI Thread Summary
When a spring with a constant of 8 N m-1 is cut into two equal parts, each part has a spring constant of 16 N m-1 due to the inverse relationship between length and spring constant. The discussion highlights that cutting a spring reduces its length, which increases its spring constant. It also compares the spring system to capacitors, explaining that the equivalent spring constant for two springs in series is derived from their individual constants. Additionally, a question is posed about finding the spring constants for parts cut in a 1:2:3 ratio, indicating a need for further calculation. The relationship between length reduction and increased spring constant is emphasized throughout the discussion.
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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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