What is the shape of an elastic band when suspended with a weight in the middle?

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Discussion Overview

The discussion centers on the shape of an elastic band when it is suspended from two points with a weight placed in the middle. Participants explore the theoretical implications of this setup, including the effects of the band’s own weight and the application of principles from mechanics.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about the specific shape the elastic band takes when a weight W is suspended from it, suggesting a comparison to the droop without the weight.
  • Another participant questions whether the weight of the elastic band itself is significant in determining its shape.
  • A participant confirms the significance of the elastic band’s weight.
  • There is a suggestion to use the action principle to derive a second-order equation related to the problem, with a note that there may not be a standard name for this equation.
  • One participant agrees with the previous points and likens the situation to that of a catenary.

Areas of Agreement / Disagreement

Participants express differing views on the significance of the elastic band's weight and the appropriate mathematical framework to describe the shape, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

The discussion does not clarify the assumptions regarding the elastic properties of the band or the specific conditions under which the weight is applied, leaving these aspects open to interpretation.

Loren Booda
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What shape does an elastic band describe when hanging from two opposite points and suspending midway a weight W (causing deformation comparable to the droop without W)?
 
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Are we basically saying that the weight of the elastic band is significant?
 
Yes.
 
Use the action principle to derive the necessary 2nd order equation? I don't think there's a standard name for it.
 
Sounds right, as for a caternary.
 

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