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Buoyancy and ships/boats

  1. Feb 14, 2009 #1
    1. The problem statement, all variables and given/known data
    A boat with a density of 0.75 g/cc is floating in water. What percentage of the boat is floating above the surface of the water?


    2. Relevant equations
    I don't know any general formulas for buoyancy. I was hoping someone here could provide one.


    3. The attempt at a solution
    I understand that the density of water is 1 g/cc, so is it really as easy as understanding 1-0.75, or is that simply a coincidence. I know the answer is 25% and expected a rather low number due to the rather low density, but what is the exact procedure for solving this problem?
     
  2. jcsd
  3. Feb 14, 2009 #2

    mgb_phys

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    Every cc of boat in the water receives 1cc weight of water worth of pushing up.
    So 1g/cc of flotation, if the boat weights 0.75g/cc then you get 0.25g/cc of overall flotation.
     
  4. Feb 14, 2009 #3

    Delphi51

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    That pretty much does it.
    It would be clearer if you started with Fg = Fb
    where the buoyancy force Fb = (mass of water displaced)*g.
    The mass displaced is the density of water times the volume of water displaced.
     
  5. Feb 14, 2009 #4
    Draw a block partly submerged in the water, and use that at as a Free Body Diagram. Put the forces on it, a bouyant force and a weight force, and then set up the statics problem. Then work it out as Delphi51 says.
     
  6. Feb 15, 2009 #5
    Thanks everybody. That was my line of thinking, but I wanted to be sure I wasn't mistaken.
     
  7. Feb 15, 2009 #6
    As Archimedes is supposed to have said in his bath:
    "Eureka"
     
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