How to setup linear force equations

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To set up the linear force equations for the planter and rod system, begin by identifying the forces acting along both the vertical and horizontal axes, including gravitational forces and tension. Choose the hinge point as the pivot for torque calculations, ensuring to account for the angle of the rod with the wall. The torque balance equation can be established using the formula 0 = T[Lcos(θ)] - Mg[(3/4)Lsin(θ)] - mg[(L/2)sin(θ)], where T is the tension in the wire. The discussion emphasizes the importance of visualizing the system with sketches to clarify the forces involved. Understanding the relationship between the forces and torques is crucial for solving for the tension and hinge forces accurately.
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A planter of mass M=3kg is hung from a rod of mass m=1kg (3/4) of the way to the end. There is a horizontal wire attached to end of the rod pulling on it with tension Ft. The botom of the rod is hinged to the wall making an angle of 60 degrees with the wall. The assembly is to remain at rest.

  1. Setup the linear force balance equations, one along each axis you choose.
  2. Choose a pivot point and setup the torque balance about that point.
  3. Solve for the tension in the wire and the two force components at the hinge.
I know I am just blatantly asking a question but this is the final question on my homework and I do not have a single clue how to do it. If you could explain all the steps involved please.

for the first one I tried think of it like, going down but I don't know how to get that into equations

I really need some help on this
 
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Have you tried making a sketch of the planter, the rod, and the wire?
 
SteamKing said:
Have you tried making a sketch of the planter, the rod, and the wire?
Yes I made the sketch and I believe I have solved number 2

0=T[Lcos(theta)]-Mg[(3/4L)sin(theta)]-mg[(L/2)sin(theta)]

I still don't get number 1, do you know how to start number 1 once you have the sketch?
 
Did you show the forces acting on the rod on your drawing? You are given the mass of the rod and the planter, and the tension force in the wire is to be called Ft.

I don't understand how you could solve 2) without doing anything about 1).
 

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