Parabola problem - some data given.

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Discussion Overview

The discussion revolves around a homework problem involving the shape of a wire strung between two mountains, specifically focusing on whether the wire's profile can be accurately modeled as a parabola despite the physical reality suggesting it would be a catenary. The scope includes mathematical reasoning and conceptual clarification regarding the nature of curves in physics and mathematics.

Discussion Character

  • Homework-related
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant outlines the problem, noting the distance between the mountains and the sag of the wire, and attempts to derive a parabolic equation based on given points.
  • Another participant asserts that the arc of the wire will not be a parabola but a catenary, challenging the appropriateness of using a parabolic model.
  • Some participants acknowledge the requirement to provide a parabolic equation despite the physical model being a catenary, questioning the purpose of such an exercise.
  • There is a suggestion that the task may involve fitting a parabola to approximate the catenary, raising concerns about the practicality of this approach.
  • One participant notes that there are enough points provided to fit a parabola, indicating a potential path forward in the problem-solving process.

Areas of Agreement / Disagreement

Participants express disagreement regarding the appropriateness of modeling the wire's shape as a parabola versus a catenary. While some acknowledge the requirement to find a parabolic equation, others question the validity and purpose of this approach given the physical context.

Contextual Notes

There are unresolved questions about the limitations of using a parabolic model to describe a catenary curve, and the discussion reflects varying interpretations of the problem's requirements and the mathematical implications of curve fitting.

yoghu
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Homework Statement



Essentially there is a power line which must be strung between posts on two mountains which are 1669.602m apart.

The first mountain is 5m higher than the second.

To overcome tension the wire is strung with a sag, 1m of sag for every 75m, or part thereof. This sag is relative to the lower pylon.

Determine an equation for the profile of the wire between the two mountains, if the arc is to be in a PARABOLIC shape.

Homework Equations



I've worked out that 1669.602/75 = (22. something) which means there must be 23m of sag, as it states part thereof. Relative to the lower pylon, I understand this to mean the turning point will be 23m below the smaller mountain.

Due to the difference in heights, this is obviously not a symmetrical parabola.

The Attempt at a Solution


I've tried letting the turning point be the origin, and having 3 points
(X2 - 1669.602 , 28)
(1669.602-X1, 23)
(0,0)
where x2 is the distance from the turning point to the second mountain, and X1 is the distance between the first mountain to the turning point.

I've also tried letting the first mountain be the origin, with 3 points
(0,0)
(?,-28) - minimum point
(1669.602,-5)

But I'm very stuck on what to do with these possible points. Please help.
 
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but the arc will NOT be a parabola ! It will be a catenary.
 
phinds said:
but the arc will NOT be a parabola ! It will be a catenary.

I know, but the question specifically asks for a parabolic equation.

It also asks to discuss limitations of this shape, so that's where I'd bring in your point.
 
yoghu said:
I know, but the question specifically asks for a parabolic equation.

It also asks to discuss limitations of this shape, so that's where I'd bring in your point.

But how can you produce an equation for a parabola to describe a curve that isn't a parabola? What would be the POINT of such an exercise?
 
phinds said:
But how can you produce an equation for a parabola to describe a curve that isn't a parabola? What would be the POINT of such an exercise?


I have no idea, and I don't know why.

Do you have any idea on how to do it??
 
phinds said:
But how can you produce an equation for a parabola to describe a curve that isn't a parabola? What would be the POINT of such an exercise?

It's a mathematical exercise in curve fitting. The mountain/powerline theme is just window dressing that provides a minds-eye picture of the setup.
 
gneill said:
It's a mathematical exercise in curve fitting. The mountain/powerline theme is just window dressing that provides a minds-eye picture of the setup.

So is one then supposed to first find the correct curve (the catenary) and then use that do find the closest possible parabola curve? Seems like an amazing waste of time. What am I missing?
 
phinds said:
So is one then supposed to first find the correct curve (the catenary) and then use that do find the closest possible parabola curve? Seems like an amazing waste of time. What am I missing?

There is enough information to fit a parabola; consider that you effectively have three given points through which the curve passes.
 
gneill said:
There is enough information to fit a parabola; consider that you effectively have three given points through which the curve passes.

DOH ! NOW I see what you meant in post #6. I'm just overcomplicating things. Thanks for the clarification.
 

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