If you were to hold a string at both ends what shape would the string take(in earth's gravity). Obviously this depends on the length of string and the distance you hold the 2 ends apart so let's say that you can only change the distance of the ends from one another on a straight line parallel to the ground. What equation could you use to predict the shape of the string at any given length(of the string) and distance(of the ends)?
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4Assuming just gravity (no blowing on the thread :-) ), the first approximation would be a catenary. – NickD Nov 23 '20 at 18:38
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@NickD thank you, I tried searching it up before but I just didn't have the words to articulate what I was looking for to google. I figured this was already a well known thing. – Will Nov 23 '20 at 18:50
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I posted my answer thinking you wanted the physical equation to model the string, haha didn’t know you just wanted the mathematical description of it – yellowgrass Nov 23 '20 at 18:58
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1Does this answer your question? What is the equation for a string fixed at both ends without simplifying assumptions? – Sandejo Nov 23 '20 at 19:03
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1Not really what you asked but pretty cool https://www.myphysicslab.com/engine2D/chain-en.html – Linkin Nov 23 '20 at 19:19
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Possible duplicate: https://physics.stackexchange.com/a/279247/268448 – JAlex Nov 23 '20 at 20:10
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1@JustJohan thank you I enjoyed playing around with it. – Will Nov 24 '20 at 05:40
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@JAlex thank you, I looked around a bit to see if I could find a similar question but I didn't see that one otherwise I wouldn't have posted. – Will Nov 24 '20 at 05:41
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Are you talking about the Catenary shape?
The general equation is
$$ y(x) = a \left( \cosh \left( \tfrac{x}{a} \right) -1 \right) $$
where $y(0)=0$ is the lowest point on the curve, and the parameter $a$ defines how much it bends.
What remains constant along the curve is the horizontal component of tension $H$, which can be used to find $a$
$$ a = \frac{H}{w} $$
where $w$ is the weight per unit length.
JAlex
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