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Buyoant force problem

  1. Apr 12, 2013 #1
    1. The problem statement, all variables and given/known data

    What is the buoyant force on 0.760 kg of ice held completely submerged underwater.

    2. Relevant equations



    3. The attempt at a solution

    My book gives
    Fb = (m_w) x (g) = (density of water / density of ice)x ( mass of ice) x (g)
    g is gravity m_w is mass of water.
    I really don't understand this. What is really confusing me is is the density of water / density of ice
    I don't get it.
    Thanks
     
  2. jcsd
  3. Apr 12, 2013 #2
    As I understand,
    buyont force=mass of the water removed by ice * g
    now mass of water removed by the ice= volume of the water*density of the water
    since, volume of the water removed by the ice will be equal to the volume of ice itself.
    so mass of the water=volume of ice* density of water
    so,
    Fb= volume of ice* density of water*g
    Fb= (mass of ice/density of ice)*density of water*g
    or Fb=(density of water / density of ice)x ( mass of ice) x (g)
    I hope it may help.
     
  4. Apr 12, 2013 #3
    Think about the concept of Archimedes's principal. Forget the formula. The buoyancy force is equal to the weight of the water displaced.
     
  5. Apr 12, 2013 #4
    ohk...remove the removed by displaced...:)
     
  6. Apr 12, 2013 #5

    haruspex

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    What physical quantity would (mass of ice) /(density of ice) represent?
    What would multiplying that by (density of water) give you?
     
  7. Apr 12, 2013 #6
    What physical quantity would (mass of ice) /(density of ice) represent?
    This would be the volume or the ice?

    What would multiplying that by (density of water) give you?
    Then it would give you the total density of the mass and the ice?

    But my solution did the density of water/ density of ice
    multiplied by the mass of the ice.
    I'm sorry I'm having a hard time putting this together.
     
  8. Apr 12, 2013 #7

    haruspex

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    Yes.
    No, you're multiplying a volume by a density, so it should give you a mass - but the mass of what?
    Remember, the volume of the ice is equal to the volume of water it displaces.
     
  9. Apr 12, 2013 #8
    The mass of water?
    I just got really confused because of how it was written and I need to understand the principle that the volume of an object submerged (or partially) is equal to the volume of the water that is displaced. ( Whatever it is in)

    I did this

    M_i / Di = Vi
    Vi x D_w = M_w
    Because Vi= V_w

    So then we has mass of water so mass of water times gravity is the good old
    F = ma
    Right or not correct my thinking.
    Thanks to the help
     
  10. Apr 12, 2013 #9
    Think about the problem this way.

    You are given the mass of the ice. Look up the density of ice and find the volume.
    This is the volume of water displaced.
    Look up the density of water, and knowing the volume of water displaced, find the mass of the water displaced.
    Multiply the mass of water displaced by g to get the weight.
    That is all there is to it.
     
  11. Apr 12, 2013 #10

    haruspex

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    The mass of water displaced, yes.
    Yes. So do you now see how the formula in the book works?
     
  12. Apr 13, 2013 #11
    As to formulas, you need force = mass X g and density = mass/volume
    (volume of ice) = (mass of ice)/(density of ice)
    (volume of water ) = (volume of ice)
    (mass of water) = (volume of water)(density of water)
    (force) = (mass of water)g

    Put it all together and you get the formula
     
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