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Pressure and buoyancy

  1. Mar 30, 2008 #1
    1. The problem statement, all variables and given/known data
    An iron anchor of density 7870 kg/m3 appears 290 N lighter in water than in air.
    What is the volume of the anchor?



    2. Relevant equations
    Fnet = 0 (we are doing static fluids) = forces up - forces down

    Fbuoyant = density of liquid*g*volume of object

    density = mass/ volume, so mass = density*volume

    Weight in the air = mg, so weight in the water = (mg - 290N)

    density of water = 1000 kg/m^3

    3. The attempt at a solution

    Fnet = Fbuoyant - (mg - 290N)
    0 = 1000 * g * volume - (7870* 9.8*volume - 290N)
    -290N = 9800 * volume - 77126 * volume
    factor out volume, and

    -290/ -67326 = volume = .00431 m^3

    (the units work out right, I just left them out here to try to make things clearer)
    unfortunately this answer is wrong....
    any help would be great!
    thanks
     
  2. jcsd
  3. Mar 30, 2008 #2
    It's simpler than it looks.

    All you need is the Fbouyant equation, with 290 N on the left hand side and the values for g and the density of water on the right. Then solve for V. (This assumes that you can neglect the density of air (=1.29 kg/m**3) in comparison to the density of water, and, since the bouyant force is only given to 3 figures, this seems to be the case.)
     
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