Tension at midpoint of thread hanging between two hinges

[twinklealices]

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

 

[PhanthomJay]

You need to know the mass of the rope in order to calculate the tension. Assume the mass is M. Then you must realize that the vertical force and tension at A are related by basic trig. You must show some attempt at a solution for further assistance.

 

[twinklealices]

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

 

[PhanthomJay]

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?

 

[twinklealices]

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??!

 

[PhanthomJay]

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 yes, right you are!
And welcome to PF!

 

[twinklealices]

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