Need some help with forces on a dangling prism Internal Assessment

AI Thread Summary
The discussion centers on analyzing the forces acting on a rectangular prism suspended by a vertical string while one side rests on the ground. The user seeks to establish the relationship between the angle of the prism and the normal force exerted upwards. They correctly identify that the sum of the tension and normal force equals the gravitational force, indicating a static equilibrium. However, confusion arises regarding how to apply torque and the differing roles of normal and tension forces in this setup compared to a ladder against a wall. The conversation emphasizes the importance of considering lever arms and the geometry of the system to derive the relationship between the angle and the normal force effectively.
yanshu liang
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Homework Statement


I made an apparatus of a rectangular prism dangling from a vertical string from one side while the other is touching the ground. The relationship I'am trying to find is between the angle of the prism relative to the ground and the normal force exerted up wards. I am stuck on how I should find the relationship between the normal force and the angle of the object relative to the ground, What I have found out so far is that Ft + Fn = Fg because the object is not moving and string is vertical so net force is zero. I think it's similar to a static ladder against the wall problem but I don't know if the horizontal normal force of a ladder touching the side of a wall functions the same as the object hanging from a string while still touching the ground. I just need some input on how Ft and Fn differ when on side is hanged from a vertical string vs when one side is leaning against the wall.
Thanks!

Homework Equations

The Attempt at a Solution


I attempted to use torque by stating net torque was zero but have no idea to proceed when there is normal force on one side and tension force on another.
http://imgur.com/a/FEiDi
upload_2017-3-12_16-30-38.png
 
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Welcome to PF!
yanshu liang said:
What I have found out so far is that Ft + Fn = Fg
Yes, good.

I attempted to use torque by stating net torque was zero but have no idea to proceed when there is normal force on one side and tension force on another.
What if you pick the origin for calculating torques at the midpoint of the edge that's in contact with the ground? Think about the lengths of the lever arms for the three forces with this choice of origin.
 
yanshu liang said:
I attempted to use torque by stating net torque was zero but have no idea to proceed when there is normal force on one side and tension force on another.
I do not understand why that should create any difficulty. Please post your attempt and say why you are stuck.
 
http://imgur.com/a/6cArN
Cos theta cancels out, the relationship I am trying to find is how does the change in theta affect the normal force of the object but since theta cancels I am not sure how to continue with this problem.
 
The horizontal distance from point where the rope is attached, to the center of mass is not equal to the horizontal distance from the center of mass to the point where the prism (isn't this a block?) touches the floor. The tickness is important. If you used a flat plate your computation would be correct. Fn would be Fg/2 and would not depend on phi,
 
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