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Homework Help: A SHM problem of floating

  1. Feb 15, 2007 #1
    1. The problem statement, all variables and given/known data
    There is a ship of mass M floating on a river. The upper portion of the ship has a uniform cross-sectional area A and the density of water is d. Now the ship is displaced a further depth y into the water and released.
    What is the resultant force acting on the ship when it is displaced a further depth y into the water?

    3. The attempt at a solution
    d = m / v where m is the mass of water and v is volume of water being pushed by ship
    m = d (A*y)
    net F= Mg - mg
    net F= g [ M - d (A*y) ]

    The correct answer is F= - dgAy. Why isn't the weight of the ship taken into account?
    Thank you so much!
  2. jcsd
  3. Feb 15, 2007 #2


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    The ship is floating on the river. So the buoyancy force for the part of the ship that was below the waterline when y = 0 equals its weight Mg.
  4. Feb 15, 2007 #3
    Initially, [tex]F_b=dAy_o[/tex] where [tex]y_o[/tex] is the intial depth of the ship. The depth of the ship when its pushed down by a length dy (or y) is [tex]y_o+dy (or y_o+y)[/tex]
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