Why is a catenary not a parabola

Can a catenary be a parabola? Ask Question. Asked 7 months ago. Active 7 months ago. Viewed 88 times. No Name No Name 3 3 silver badges 11 11 bronze badges.

For example a suspension bridge has this property. Add a comment. Active Oldest Votes. Your answer accurately responds to the question as explicitly phrased, but it seems clear that Thomas was intending a situation which is perfectly possible.

The companion sheet [pdf] could do with some improvements, but at least it looks at the catenary question. A catenary is the shape a rope adopts under its own weight, which is proportional to arc length. If the load is proportional to horizontal length, the shape is a parabola. And the big load on the above bridge is the horizontal road, so the parabola shaped arc holding it up will be axially loaded only, without bending.

Man, do I have to do everything around here? Catenary Parabola. Catenaries are defined not by quadratics nor other polynomials , but by hyperbolic trig functions. Specifically, hyperbolic cosine. And these functions have interesting calculus properties rather than interesting algebraic ones. Hyperbolic trig functions including catenaries are the first interesting solutions to that baby.

Christopher , there is a difference. Did Singapore inform any of your thoughts about these issues? It bothers me that some students are already—I saw this teaching college calculus walking away with the idea that any curve with constant concavity is a parabola.

That conversation would have been utterly on point during the creation of that poster. Just as those are designed to make it impossible not to ask and then answer questions, I think this image makes it impossible for your audience not to ask too. And yeah, it does seem to be a parabola, or at least better approximated by one than by a catenary.

A parabola would be the right shape if the load is all on the road and the arch has negligible weight. A catenary would be the right shape if the load were all in the arch and none on the road. I suspect that the arch shape in question is neither, but an appropriate intermediate shape given the load on it. Does anyone commenting on this actually design bridges?

Or at least have taken a class on designing bridges? Following the link one finds a companion sheet to the poster which actually gives a short discussion of the parabola v catenary. The companions sheet could do with some improvements, but at least it looks at the catenary question.

I thought a catenary was the shape adopted by a wire hanging from its endpoints, but I find it hard to believe a wire would ever take on the shape shown in that graph, unless the middle part were lying on the ground. Am I making an easy-to-explain error? The vertical scale in the middle graph represents 3 orders of magnitude more distance than the vertical scale in the other graphs. Of course! Thanks very much, I should have seen that.

If we take the units as metres, the wire is hanging from 7km up, and is hanging so close to vertical nobody can tell the difference except right near the bottom. Nice post, as usual. How do you know if a parabola is maximum or minimum? How do you tell if a parabola will open up or down?

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