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

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SUMMARY

The discussion focuses on calculating the inclination angle θ of a 5 m-long round wooden rod submerged in water at varying depths. The rod has a density of 800 kg/m³ and is secured by a 1 m string. Key equations used include the gravitational force on the rod (Fg = ρrod⋅Vrod⋅g) and the buoyant force (Fb = ρwater⋅Vdisplaced⋅g). The analysis reveals that at a water depth of 1 m, the gravitational force equals the buoyant force, leading to a displaced volume of 0.02011 m³, and emphasizes the importance of creating a free body diagram for further calculations as water depth increases.

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  • Study the effects of varying water levels on buoyancy and stability
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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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