How High Should the Cable Be Anchored for Equilibrium?

[jtulibarri]

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?

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

 

[learningphysics]

(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?

 

[ogb p]

, but I do know that in order to find the minimum height h, we need to consider the forces acting on the rod and sign system. We have the weight of the sign (m*g), the weight of the rod (m*g), and the tension force from the cable. The rod is in equilibrium, meaning that the net force acting on it is equal to zero. This means that the sum of all the forces must be equal to zero.

To start, we can consider the forces acting on the rod. We have the weight of the rod acting downwards, and the tension force from the cable acting upwards. Since the rod is not moving, the net force in the vertical direction must be zero. This means that the tension force must be equal to the weight of the rod.

Next, we can consider the forces acting on the sign. We have the weight of the sign acting downwards, and the force from the rod acting upwards. Again, since the sign is not moving, the net force in the vertical direction must be zero. This means that the force from the rod must be equal to the weight of the sign.

Now, we can use these relationships to set up an equation to solve for the minimum height h. We know that the tension force must be equal to the weight of the rod, which is equal to the weight of the sign. So we can set up the equation:

Tension force = weight of the rod = weight of the sign
760N = (9.8kg)(9.8m/s^2) = (65kg)(9.8m/s^2)

Solving for the minimum height h, we get:

h = (760N)/(65kg)(9.8m/s^2) = 1.15m

So the minimum height above the pivot for anchoring the cable to the wall is 1.15m. This means that the cable should be anchored at a height of 1.15m above the pivot point in order to keep the rod and sign system in equilibrium. I hope this helps! Remember, when solving problems like this, it's important to consider all the forces acting on the system and use the principles of equilibrium to set up and solve equations. Good luck!