How to find the angle of a pinned rod at a certain depth

AI Thread Summary
To determine the inclination angle θ of a pinned rod submerged in water, one must analyze the forces acting on the rod, including gravitational and buoyant forces. The gravitational force on the rod is calculated using its volume and density, while the buoyant force depends on the volume of water displaced. As the water level increases, the volume of the rod submerged changes, affecting the forces in play. A free body diagram can help visualize the force balance, particularly when the water level is at different depths, such as 3.5 m and 7 m. Understanding how the portion of the rod above water relates to the angle θ is crucial for solving the problem effectively.
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Homework Statement



The uniform 5 m-long round wooden rod (ρ = 800 kg/m3 ) is tied to the bottom by a string with length 1 m. Determine the inclination angle θ if the water level is 3.5 m. What if the water level is 7m?

Homework Equations



Fb = ρgV

The Attempt at a Solution



So I'm really struggling with the conceptualization of this one.
I know that
Fg on rod = ρrod⋅Vrod⋅g
FB = ρwater⋅Vdisplaced⋅g

if the depth of the water is 1 m, then there is no y-force on the string. This means that at a water depth of 1 m, the gravitational force is equal to the buoyancy force.
This means that the volume of water displaced is...
( I calculated it out )... 0.02011 m3

What, however, must I do when I begin to increase the water level?
 

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Nice exercise ! You know how much of the stick is above water as a function of ##\theta##, right ? The make a free body diagram (a force balance).
 
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