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

In summary, the problem involves a 5 m-long round wooden rod with a density of 800 kg/m3 and a string attached to the bottom. The objective is to determine the inclination angle θ when the water level is at 3.5 m and 7 m. The relevant equations are Fb = ρgV and Fg = ρrod⋅Vrod⋅g, with the volume of water displaced being 0.02011 m3 at a water depth of 1 m. To solve the problem, a free body diagram and force balance must be made using the known information.
  • #1
hdp12
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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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  • #2
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).
 

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

1. How do I find the angle of a pinned rod at a certain depth?

To find the angle of a pinned rod at a certain depth, you will need to use the principles of trigonometry. First, draw a diagram of the pinned rod with the depth marked. Then, use the tangent function to calculate the angle. The tangent of the angle is equal to the opposite side (depth) divided by the adjacent side (length of the rod).

2. What is the importance of finding the angle of a pinned rod at a certain depth?

Finding the angle of a pinned rod at a certain depth is important in various fields such as engineering, construction, and geology. It allows us to accurately measure and understand the stability and structural integrity of objects such as bridges, buildings, and geological formations.

3. Can I use a protractor to find the angle of a pinned rod at a certain depth?

No, a protractor is not an accurate tool for measuring the angle of a pinned rod at a certain depth. It is best to use a calculator or a scientific calculator to accurately calculate the angle using trigonometric functions.

4. How does the depth affect the angle of a pinned rod?

The depth has a direct effect on the angle of a pinned rod. As the depth increases, the angle of the rod will also increase. This is because the tangent function is proportional to the depth, meaning that a greater depth will result in a larger angle.

5. Are there any limitations to finding the angle of a pinned rod at a certain depth?

Yes, there are limitations to finding the angle of a pinned rod at a certain depth. This method assumes that the rod is perfectly straight and that there are no other external forces acting on it. In real-life situations, there may be other factors that can affect the angle of the rod, such as wind or uneven ground.

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