How High Should the Cable Be Anchored for Equilibrium?

AI Thread Summary
The discussion focuses on determining the minimum height for anchoring a cable to ensure equilibrium for a sign and rod system. The forces involved include the weight of the sign and the rod, with the tension in the cable needing to be factored into the torque equation. Participants emphasize the importance of calculating the torque about the pivot point, ensuring that the sum of torques equals zero. There is a need to express the vertical component of tension and the corresponding distance in the torque equation. The conversation highlights the complexities of setting up the equations correctly to solve for the height above the pivot.
jtulibarri
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a 65 kg sign hung centered from a uniform rod of mass 9.8 kg and length 2.3 m. At one end(left) the rod is attached to the wall by a pivot; at the other end(right) it's supported by a cable that can withstand a maximum tension of 760 N. What is the minimum height h above the pivot for anchoring the cable to the wall?

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i need help on setting up an equation to solve...
what i have so far i don't know how wrong or right it is.


(Force of sign)(Radius of sign)+(Force of rod)(Radius of rod)-(Tension)=0
(637N)(1.15m)+(96.04N)(1.15m)-m*g*sin(angle away from wall)=0

? i don't really know exactly where I am going with this
 
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jtulibarri said:
(Force of sign)(Radius of sign)+(Force of rod)(Radius of rod)-(Tension)=0
(637N)(1.15m)+(96.04N)(1.15m)-m*g*sin(angle away from wall)=0

? i don't really know exactly where I am going with this

you need the torque about that point to be zero... so you need:

(Force of sign)(Radius of sign)+(Force of rod)(Radius of rod)-(vertical component of Tension)*distance=0

(since horizontal component of tension exerts 0 torque about the pivot)

what is the vertical component of Tension in terms of the total tension T... what is the distance here?
 

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