Is a spring longer hanging or flat on a table?

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Homework Help Overview

The discussion revolves around the comparison of a spring's length when it is hanging versus when it is laid flat on a table. The subject area involves concepts of mechanics and material properties of springs.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the idea that the spring may stretch more when hanging due to the weight of the spring itself. There are attempts to relate this to mathematical expressions and free body diagrams, with questions about how to incorporate the mass and tension of the spring into a mathematical framework.

Discussion Status

Some participants express agreement with the initial thought that the hanging spring is longer. Others are questioning how to mathematically represent the situation, indicating a productive exploration of the problem without reaching a consensus.

Contextual Notes

There is a mention of the complexity introduced by the spring's mass and varying tension along its length, which may affect the analysis. Assumptions about the spring's behavior under tension are also being discussed.

dav1d
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Homework Statement



Is a spring longer hanging or flat on a table?

Homework Equations


logic.


The Attempt at a Solution



I think the answer would be hanging because then the mass of the spring pulls it down a bit, thus stretching it more than when it is flat.
 
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I would agree.
A good example of the type of spring we are talking about is a slinky toy.
 


But how do I write it using math/formulas.
 


It would be difficult to do that, because the spring must be considered massive, and hence will have different tensions at different points.

But I guess you can prove it if you make an assumption that if any point in the spring has tension, then it is possible only if it is elongated.

Now just divide the spring into two parts, and draw the free body diagram of the bottom part. Now prove that a certain tension must exist at the join point, to keep the bottom part of the spring in equilibrium.
 

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