- #1
Joe8
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Homework Statement
Chain of mass M hangs between 2 walls with its ends at the same height. The chain makes an angle θ with each wall. Find the tension at the lowest point of the chain.
a) By considering the forces on half of the chain.
b) By using the fact that the height of the chain is given by y(x) = (1/α) cosh(αx), and considering the vertical forces on an infinitesimal piece at the bottom. This will give the tension in terms of α. Then find α in terms of the given angle θ.
Attempt:
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Homework Equations
The Attempt at a Solution
a) I called the tension force at the end of the chain attached to the wall T1 and the tension at the bottom To. Assuming that To is horizontal with no vertical component ( I am not sure that this is a fair assumption):
T1 Sinθ = To (ΣFx=0)
T1 Cosθ= Mg/2 (since we are working on half the chain and ΣFy=0)
Therefore To=Mg(tanθ)/2
b) Now here I have no idea. If I use the same assumption that allowed me to solve a (that the forces at the bottom segment of the chain are horizontal) then there is only the weight (dm * g) in the vertical direction...[/B]