Finding the tension of a support cable to balance the beam

AI Thread Summary
To find the tension in the support cable balancing the beam, the correct approach involves calculating the torques around the fulcrum. The downward gravitational force on the beam and the upward force from the cable must be balanced. The center of mass (COM) of the system is crucial, calculated as 1.28 m based on the masses and their distances from the fulcrum. The equation for torques must account for the weights and their respective distances from the fulcrum to solve for the tension. Ultimately, the tension in the cable is determined to be 170 N.
JohnTheGreat101
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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
 

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