Is there an easy way to calculate tension and torque in a hanging rope?

[fiziksfun]

1. 'A rope of negligible mass is stretched horizontally between two supports that are 3.44 meters apart. When an object of weight 3160 N is hung at the center of the rope, the is observed to sag by 35.0 cm. What is the tension in the rope?'



2. Does this have anything to do with torque??



3. ATTEMPTS:

I divided 3.44 by 2 (1.72) to find the horizontal length from one support to the object. From that I found that the length of the rope from the object to one of the supports is 1.72^2 + .35^2 = X^2 (it's a triangle), x=1.75

I can assume because the object is in the center of the rope that the tension on both sides of the rope is equal. Can I also assume the forces sum to 0 because its stagnant? BAH I'm so confused, I don't know what to do!
The correct answer is 7920. Help!

 

[fliinghier]

it's not torque. draw a free-body diagram of the rope and label all the forces.

 

[fiziksfun]

I drew a free-body diagram and I'm still confused. I really have no idea how to do this. How can I solve for tension!? I don't know the tension along the x-axis or the y-axis ? I know the angle - 11.5 degrees.

 

[fliinghier]

you DO know the downward force on the rope. you also know that the forces at either side should do what? is the rope moving? you have an angle and a side, you can get the other side, provided you draw a right triangle with the vectors.

 

[fiziksfun]

ahhh i see, the rope is not moving so forces in the x and y direction are balanced.. i think i understand. so EFy = (<-- supposed to be sigma) = 0 = -W + 2Frope,y .. so Frope,y = 1580 on each side and the angle is 11 degrees .. so 1580*sin11=7925 .. about the right answer .. but that is the tension in the rope for only one side ? Oh dear, well thank you anyway !

 

[fliinghier]

remember that sin = opposite/hypotenuse

 

[moncheri]

i think that sin = opposite / hypotenuse .. o/a = tan

 

[fliinghier]

oops, I'm tired :(

besides the original poster still used the sin funtion to calculate the hypotenuse by multiplying by the opposite if i follow correctly.