Finding the tension of a support cable to balance the beam

[JohnTheGreat101]

Homework Statement

Find the tension in the support cable needed to balance the beam

Relevant Equations

0=tc + tbl - tbr - tcyl

I know the answer is 170 but I am not sure how to get there. I tried doing things backwards
g=9.8
t = fr = mgr
0= 170 + tbl - tbr - 5x9.8x1.5
0= 170 + tbl - tbr - 73.5
-96.5 = tbl - tbr
-96.5 = 18*9.8 * 0.2 - 18*9.8*1.4
-96.5 does not equal -211.68

 

[Doc Al]

Hint: Where's the center of mass of the beam?

 

[JohnTheGreat101]

Ok so I found the mass of the cable. mgr/gr = m
170/9.8x1.2 = 14.46 kg.
COM = 5 kg x 1.5m + 14.46 kg x 1.2 / 14.46 + 5 = 1.28 m

 

[Doc Al]

There are three forces acting on the beam that create torques about the fulcrum:

• The downward force of gravity on the beam. (Where does it act?)
• The upward force of the cable. (Which is what you are trying to find.)
• The downward force of the cylinder's weight on the beam.

Add up the torques due to these forces.