Calculating parabola of drooping chain

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    Chain Parabola
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SUMMARY

The discussion centers on the mathematical analysis of a chain hanging between two posts, forming a catenary rather than a parabola. Key variables include chain tension, weight, and angle. Participants explore the relationship between these variables and the geometry of the problem, ultimately revealing that the solution can be approached without complex formulas by approximating the chain's path as a triangle. The conversation emphasizes the importance of visualizing the problem to arrive at a solution.

PREREQUISITES
  • Understanding of catenary curves and their properties
  • Basic knowledge of calculus for analyzing curves
  • Familiarity with geometry, particularly triangles
  • Concept of tension and weight in physical systems
NEXT STEPS
  • Research the mathematical properties of catenary curves
  • Study calculus applications in physics, particularly in mechanics
  • Explore geometric approximations in problem-solving
  • Learn about tension and weight distribution in chains and cables
USEFUL FOR

Mathematicians, physics students, engineers, and anyone interested in solving geometric problems related to tension and curves.

  • #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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