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

  1. Feb 17, 2017 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant equations

    Fb = ρgV

    3. 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?
     

    Attached Files:

  2. jcsd
  3. Feb 17, 2017 #2

    BvU

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    Gold Member

    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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