Solve Mechanics Question: Hanging Thread, Gravity, Angle @

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mechanics question..please help!

Homework Statement


a thread hangs between 2 hinges A and B. gravity is acting. The angle(acute) made by tangent to rope at point A and the line AB is @. find the tension at the lower most point..i.e the mid point of the rope?


Homework Equations



don know!

The Attempt at a Solution

 

Discussion

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ok ...i take the tension to be t1 at point A...and t2 at bottom most point then
t1sin@=mg...then how to proceed??
 


EDIT: [strike]Yes, that's OK. [/strike]Sorry, I was half asleep this morning, that is not OK. The weight of the rope is divided equally amongst points A and B. Sorry about that . Now the direction of the tension t2 at the bottom most point is in the horizontal direction, right? So try taking a free body diagram of the left half of the rope and then what does Newton 1 tell you when looking in the x direction at point A?
 
Last edited:


oh ...okkkk...so i do this
for left half of the rope ...
in x direction ...
its ... t1cos@=t2..(1
then t1sin@=mg/2...(2

so i divide 1/2 and
cot@=2*t2/mg..
so t2=(mg cot@)/2...!
right??!
 


oh ..thank you!...this is an awesome site for doubt clarification!