I and Tim float a long string of closely spaced helium-filled

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Discussion Overview

The discussion revolves around the shape formed by a string of closely spaced helium-filled balloons, specifically questioning why this shape resembles a catenary. The scope includes theoretical considerations of potential energy and the forces acting on the string.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant suggests that the shape of the string minimizes potential energy.
  • Another participant explains that a catenary is formed under the influence of weight and tension, noting that the weight is effectively negative due to the buoyancy of the helium balloons.
  • A further explanation is provided regarding the differential equations governing the catenary shape, indicating that the same principles apply to the balloons, albeit in an inverted manner.
  • One participant expresses confusion regarding the explanation provided about the catenary and its relationship to the balloons.

Areas of Agreement / Disagreement

Participants present differing levels of understanding regarding the explanation of the catenary shape, with some agreeing on the principles involved while others express confusion. The discussion remains unresolved in terms of clarity and comprehension of the concepts.

Contextual Notes

There are limitations in the explanations provided, particularly regarding the mathematical derivation of the catenary and the assumptions made about the forces acting on the string. The discussion does not fully resolve these aspects.

Pranav Jha
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I and Tim float a long string of closely spaced helium-filled balloons over his used-car lot. We
secure both ends of the string to the ground several meters apart so that the balloons float over the lot in forming the shape of a catenary. Why that shape?
 
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My claim is that the shape of the string is such that the potential energy of the sting is minimized.
 


Feldoh said:
My claim is that the shape of the string is such that the potential energy of the sting is minimized.

Please explain that statement
 


Catenary is formed under two forces - weight and tension. Here, you made the weight negative, by attaching balloons.

Now, if you want to know why catenary is the curve made by free-hanging rope, you need to look at the differential equations for it. But it should be clear why balloons force the same shape, only upside down.
 


K^2 said:
Catenary is formed under two forces - weight and tension. Here, you made the weight negative, by attaching balloons.

Now, if you want to know why catenary is the curve made by free-hanging rope, you need to look at the differential equations for it. But it should be clear why balloons force the same shape, only upside down.

sorry but i am still clueless about how to understand your explanation
 

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