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Archimedes’ principle

  1. Mar 26, 2007 #1
    1. The problem statement, all variables and given/known data

    It is found that a 3.70-kg aluminum ball has an apparent mass of 2.20 kg when submerged in a particular liquid.
    Calculate the density of this liquid in kg/m3.

    2. Relevant equations

    Bouyancy force=density*volume*gravity
    Volume=mass/density

    3. The attempt at a solution

    1. Look-up density of Al: density=2.7*10^3 kg/m^3

    2. Volume of ball=(mall ball)/(density of ball)=0.00137m^3

    3. Bouyancy force on ball=2.2*9.81=21.582N=weight of fluid displaced (Archimede's principle)

    4. So the mass of 0.00137m^3 of the fluid can be solved by...
    weight of fluid=(mass of fluid)g
    mass of fluid=2.2kg

    5. density of fluid=(mass fluid)/(volume of fluid)=1606 kg/m^3...

    Did I use the apparent mass correctly in step 3?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 26, 2007 #2
    Bouyancy force on ball=(3.70-2.20)*9.81.

    Regards,

    Nacer.
     
  4. Mar 27, 2007 #3
    Can you explain why and did I do the rest of problem correctly?
     
    Last edited: Mar 27, 2007
  5. Mar 27, 2007 #4
    try a free body diagram where the ball is suspended in the fluid from a spring scale. Ordinarily the weight measured would be g*3.7, only in this case the scale measures 2.2*g kg. the difference is the upwards directed buoyancy force. (which as you have noted is density*volume*g.)

    in this case, the problem is a bit of a curve ball as normally the x being sought is the density or volume of the object and not the medium, which is what I think got you a little tangled up above. that help at all?
     
  6. Mar 27, 2007 #5
    This look correct?

    1. Look-up density of Al: density=2.7*10^3 kg/m^3

    2. Volume of ball=(mass ball)/(density of ball)=0.00137m^3

    3. Buoyancy force on ball=(3.7-2.2)g=14.715N=weight of fluid displaced (Archimedes's principle)

    4. So the mass of 0.00137m^3 of the fluid can be solved by...
    weight of fluid=(mass of fluid)g
    mass of fluid=1.5 kg

    5. density of fluid=(mass fluid)/(volume of fluid)=1095 kg/m^3
     
  7. Mar 27, 2007 #6
    i didn't run the numbers but I think you nailed it. Didn't need to multiply and then divide by g, but thats a small nitpick.
     
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