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Origin: sally.csie.ntu.edu.tw

※ 引述《threedices (三顆骰子)》之銘言：
: [領域]                             靜力學
: [來源]                             習題
: [題目]
: A chain of mass M hangs between two walls, with its ends at the same height.
: The chain makes an angle of θ with each wall.
: Find the tension in the chain at the lowest point, using the fact that the
: height of a hanging chain is given by y(x)=(1/a)cosh(ax).
:   ||                 ||
:   ||\               /||
:   || \             / ||
:   ||θ\           /θ||
:   ||   \_________/   ||
: [瓶頸]   看了好久不懂怎麼把cosh跟θ和tension連貫起來..能不能指點一下  <(_ _)>

沒給繩長嗎?

我的想法是這樣
把繩從中間切一半 看右半邊繩
則三力使繩子達平衡:

左端的水平張力T1 繩子所受重力Mg/2 右端牆給的拉力F
畫出力圖可知T1= (Mg/2)tanθ
而又 y'=sinh(ax)
帶入最右端x值(未知?)假定為L
可得 y'=sinh(aL)=1/tanθ

=>T1 = Mg/2sinh(aL)

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