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Calculating upthrust on a solid object

  1. Oct 15, 2009 #1
    Calculating upthrust on an object

    1. The problem statement, all variables and given/known data

    An object made entirely of one material has a volume of 30m3. It floats in a liquid of density 30 g/cm3 with only half it's mass below the liquids surface. The object is then placed in a liquid of the same volume but with a density of 1 g/cm3. If the final upthrust that will act on the object is expressed in the form a*10bN give the values of a and b. Assume g to be 10 ms2

    2. Relevant equations

    d=m/v

    3. The attempt at a solution

    1st liquid

    3000=m/30
    =90000
    90000/2 = 45000 Kg displaced

    45000 * 10 = 450000 N upthrust (archimedes)
    45000/3 = 15000 N upthrust in 2nd liquid

    a=1.5, b=4

    I honestly have no idea really.
     
    Last edited: Oct 15, 2009
  2. jcsd
  3. Oct 15, 2009 #2

    rl.bhat

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    Hi azsx11, welcome to pF.
    How did you get
    3000 = m/30?
     
  4. Oct 16, 2009 #3
    Sorry, I got my order wrong.

    d = 30 g/cm3 = 30000 Kg/m3

    30000 = m/30

    m= 900000 Kg

    etc...

    Is this the right way to approach the question?
     
  5. Oct 16, 2009 #4

    rl.bhat

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    When the body is floating, weight of the body is equal to the weight of the displaced liquid.
    So what is the weight of the object?
    In the second liquid whether the object sinks or floats?
    If it sinks, what is the weight of the displaced liquid?
     
  6. Oct 16, 2009 #5
    This is what i've tried to do.

    900000/2 - half of the object is submerged.

    = 450000 Kg displaced

    450000*10 = 4500000 N upthrust.

    (I'm not sure if that's correct)

    If it sinks the weight of the displaced liquid is equal to the objects weight.

    = 900000 Kg

    900000*10 = 9000000 N

    Am I on the right track?
     
  7. Oct 16, 2009 #6

    rl.bhat

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    If it sinks the weight of the displaced liquid is equal to the objects weight.
    It is no true.

    If it sinks the weight of the displaced liquid is equal to the loss of objects weight.
     
  8. Oct 17, 2009 #7
    Sorry, i'm none the wiser.

    Was my calculation up to that point correct?
     
  9. Oct 19, 2009 #8

    rl.bhat

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    In the second case, volume of the displaced liquid is..........?
    What is the density of the water?
    What is the mass of the water and its weight?
    Hence what is the upthrust?
     
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