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Homework Help: Buoyancy of a piece of wood floating in water

  1. Sep 20, 2013 #1
    1. The problem statement, all variables and given/known data
    A piece of wood floats in water with 65% of its volume under water.Find the relative density of the wood.

    2. Relevant equations

    Buoyancy = (Weight of object) / (Relative density of object)

    3. The attempt at a solution

    B = W/s

    1= .65/s

    s = .65/1

    s= .65

    My book says this is the right answer but I can't understand how? I guess .65 and 1 are ratios.
    But how did they get the one?
  2. jcsd
  3. Sep 20, 2013 #2


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    Look up the density of water.
  4. Sep 20, 2013 #3
    Density of water = 1000 kg/m^3

    I'm not sure what I am suppose to do with this?
    Last edited: Sep 20, 2013
  5. Sep 20, 2013 #4
    The buoyancy is given by that formula only if the object is completely submerged.
    If not, only the "weight" of the submerged part will enter the formula.
    So you will have
    B=(0.65*W)/RD where RD is relative density.
    But the object is floating so B should balance the entire weight of the object.
    So B=W and then is follows the rest.

    The problem here is that you are applying a formula without a good understanding of the phenomena involved, I suppose. I don't think this is the best way to describe the buoyant force in introductory physics.
  6. Sep 20, 2013 #5
    Let V represent the volume of the piece of wood, and let ρw represent the density of the wood. What is the weight of the piece of wood? If 65% of the wood is under water, how much wood volume is under the water (in terms of V)? This is the volume of water displaced. If ρ is the density of water, what is the weight of the water that was displaced? From a force balance on the wood, the weight of the wood (downward force on the wood) must be equal to the weight of the water displaced (upward force on the wood). This should give you enough information to calculate the density of the wood.

  7. Sep 20, 2013 #6
    Alright thanks I understand now.
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