Calculating parabola of drooping chain

  • Context: Undergrad 
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    Chain Parabola
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Discussion Overview

The discussion revolves around the mathematical modeling of a chain suspended between two posts that droops in the middle, forming a curve. Participants explore the variables involved in determining the shape of the curve, which some identify as a catenary rather than a parabola. The conversation includes both theoretical considerations and practical problem-solving approaches.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant suggests that the relationship determining the curve involves chain tension, weight, and angle, and seeks additional variables.
  • Another participant corrects the initial assumption that the shape is a parabola, stating it is actually a catenary.
  • Several participants discuss a specific problem involving two posts and a chain, with one participant noting it can be solved without knowledge of the catenary.
  • Hints are provided about visualizing the problem, including drawing to scale and approximating the chain's path with a triangle.
  • Some participants express frustration over the problem's difficulty, while others find humor in the challenge.
  • There are mentions of integrating the length of the chain into smaller segments to analyze the curve, but no consensus on the best approach is reached.
  • One participant reflects on how those less familiar with mathematical concepts might solve the problem more easily than those who are knowledgeable.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method to solve the problem or the nature of the curve, with multiple competing views and approaches remaining throughout the discussion.

Contextual Notes

The discussion includes various assumptions about the problem's parameters and the mathematical relationships involved, but these assumptions are not universally agreed upon. The complexity of the problem and the differing levels of mathematical understanding among participants contribute to the ongoing debate.

  • #31
NateTG said:
Consider approximating the chain's path with a triangle.

Correct!
-Mike
 
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  • #32
This thread gave me a good laugh at the expense of ShawnD. I'm sorry Shawn, but, whenever you do get the answer, you'll have to admit that this was pretty funny. What amused me the most, though, was:
I've asked a 3rd year chem honors student as well as a 2nd year mechanical engineer and neither of them can figure it out.
I think this would only work on the educated people. Uneducated people would naturally start out with an oversimplified model and get the answer so easily. It's those of us that know it should be a catenary, for instance, that have a beet red face when they get to the answer. If it makes you feel any better, I would have gone down the same path as you if Chi Meson would not have said it's a brain teaser.
 
  • #33
In a lot of cases, there is no substitute for a pencil and a piece of paper.
 
  • #34
Michael D. Sewell said:
In a lot of cases, there is no substitute for a pencil and a piece of paper.
Very true. But, if you're already thinking about catenaries, then you would probably stare at your scribbled napkin for an embarrasingly long time in the pub.
 
  • #35
turin said:
If it makes you feel any better, I would have gone down the same path as you if Chi Meson would not have said it's a brain teaser.

To think I nearly gave it away at the start. I actually had to edit out the answer before I posted. What a "benny" I would have been.
 
  • #36
Chi Meson said:
To think I nearly gave it away at the start. I actually had to edit out the answer before I posted. What a "benny" I would have been.
That sure would have been a shame. I would have missed out on the good chuckle. I don't feel bad about it either. I can't imagine how many times I've been the one to provide the chuckle.
 
  • #37
Hahaha, this is a good one. I actually started doing it when I just thought about it for a second.
I think I'll try it on people.
 
  • #38
What... we're not people?
 
  • #39
I mean OTHER people. sheesh.
[Warning: Paranoid thought ahead!] How am I to know you're not all crazy chat bots? hmmmm?
 
  • #40
I think the LESS one knows about math and physics the MORE likely they are to come up with the solution quickly. If you crack a nut with a 5lb sledge hammer you don't get the meat.
 
  • #41
Integral said:
I think the LESS one knows about math and physics the MORE likely they are to come up with the solution quickly. If you crack a nut with a 5lb sledge hammer you don't get the meat.

My girlfriend took about ten minutes with a ruler and caculator to see if her new bread tin had the same volume as her old one even though the shape was different. When I filled one with water, and then dumped it into the other she was not amused. That was one of the most stupid things I have ever done. -Mike
 
  • #42
Time to find a new girlfriend! :wink:

- Warren
 
  • #43
The only thing worse then losing an argument to a woman.. Is winning one.
 
  • #44
Integral said:
The only thing worse then losing an argument to a woman.. Is winning one.

Integral,
This is obvious proof that you are not 17 years old.


chroot,
The girlfriend's ok, I'm the idiot.

Shawn,
Did you draw that triangle yet?
Mike
 

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