Equilibrium, Torque and Tension

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1. The problem statement, all variables and given/known data

A truss is made by hinging two uniform, 150-N rafters as depicted in the diagram below. They rest on an essentially frictionless floor and are held together by a horizontal tie rope. A 500-N load is held at their apex. Find the tension in the rope.



2. Relevant equations

τ=lα; Sum (torque CW) + Sum (torque CCW) = 0; Fx+Fy+Fz=0

3. The attempt at a solution

I think I am most confused at how to include the unknown tension force Ft into building the equilibrium equation. I assume the rope exert a tension force on the left rafter (Ft1) and another one at the right rafter (Ft2, equal magnitude as Ft1 but dir reversed). After I include Ft1 and Ft2 into the torque equation (I took the left rafter contact point with the ground as the axis of rotation), almost all the terms canceled out and it left me with something like Ft * something = 0, which, in turn, suggesting my result will be 0, which, is not correct, obviously.

Can someone explains to me what did I do wrong? And, how to solve this problem correctly? Thank you.

Attached Thumbnails

 

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Write out the equilibrium quations separately to both rafters, including the force from the hinge at the upper end.

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