Understanding Torque Truss Problems: Examining Question 3.22 with Diagram

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SUMMARY

The discussion focuses on solving Torque Truss Problem 3.22, where the user analyzes forces and torques in a mechanical system. The user created a free body diagram and calculated the normal force (Fn) as 400N, with torque calculations yielding T1 as -705N and T2 as 2.02T. The user identified an error in their calculations, expecting the tension (T) to be 280N but arriving at 349N. The oversight involved neglecting the torque due to the weight of the rafters.

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Okay, I have uploaded the question to imageshack because it would be to difficult to understand the question without the diagram. Basically, I've done a lot of work on it and know I'm on the right track. If someone could point out where I have made a mechanical error it would be greatly appreciated. The question I am on is number 3.22, the one in the top right corner of the page.

http://img37.imageshack.us/img37/350/phys122yv.jpg

So first off I made a free body diagram. Two Fn's going up, two 150's going down and a 500 going down. I solved for Fn and got 400N.

Then I solved the triangle to find that the angle between the cord and the board is 54 degrees. Finally I did torque calculations as follows:

T1 = 400(Fn) * 3 * sin 36
T1 = -705N

T2 = T * 2.5 * sin 54
T2 = 2.02T

2.02T = 705
T = 349N?

The answer should be 280 Newtons. Where have I gone wrong?
 
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What about the torque due to the weight of the rafters?
 
Damnit. I knew I forgot something.

Haha thanks bud!
 

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