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Bar in static equilibrium + hydrostatics

  1. Jan 27, 2007 #1
    1. The problem statement, all variables and given/known data

    A thin metal bar of length L is attached to a pivot point (point A in diagram). The bar is partially submerged in water and it can move freely around an axis that forms a 90 degree angle with the plane of the diagram. The density of the bar is 0.4 g cm^(-3). What percentage of the bar is submerged when it is in static equilibrium?

    [​IMG]

    2. Relevant equations

    Vectors are in bold.

    F = ma

    M = r x F

    3. The attempt at a solution

    Since the bar is in static equilibrium, both the net force and the net moment (torque) on the bar is 0.

    [​IMG]

    Force N is the normal force that the wall exerts on the bar, R is the reaction of the pivot, W is the weight of the bar and A is due to Archimedes's principle (a body immersed in a fluid experiences a buoyant force equal to the weight of the displaced fluid.)

    N = 0
    R + A - W = 0

    (Point A is used as the torque's point of origin)

    [​IMG]

    And this is where I get stuck. :confused:
    Any help would be appreciated, thanks. :)
     
  2. jcsd
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