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Object Weight given only difference in weights in and out of water

  1. Jul 27, 2009 #1
    1. The problem statement, all variables and given/known data


    A chunk of carbon steel with density, ρ = 7.84 g/cm3 , is completely submerged in fresh water. The chuck of steel weighs 39 N more in air than in water. Please answer the following:
    (a) Find the buoyant force acting on the chuck of steel.
    N
    (b) Find the the volume of the chuck of steel.
    m3
    (c) What is the mass of the chuck of steel?

    2. Relevant equations


    Fw(air)=Fw(water) + 39 N

    d=m/v

    Fb=gp(f)V

    BUT I dont know how to find the volume.

    density of air is 1.16 kg/m3
    density of water is 1.0x10^3


    3. The attempt at a solution

    once I get the VOLUME I can find the relative weights by using rho*g*v
    and Fw(water)+ 39N = Fw(air)
     
  2. jcsd
  3. Jul 27, 2009 #2
    The buoyant force (upward direction) in the air is less than in the water, therefore
    Fw(air)=Fw(water) -39 N
    And you know that (mg-Fw(air))/g = m
     
  4. Jul 27, 2009 #3

    rl.bhat

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    Weight of the displaced water = 39 N = m*g = density of water*volume*g.
     
  5. Jul 27, 2009 #4
    ok, a little hazy. Fw(water) is 39N=dens water*v*g? than V = .00398

    if so, Fw(water)-39N=Fw (air) than Fw(air) is /38.96??
     
  6. Jul 27, 2009 #5
    -38.96 (which cant be right) *rather than /38.96
     
  7. Jul 27, 2009 #6

    rl.bhat

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    Fw(in air ) = density of steel*volume*g.
     
  8. Jul 27, 2009 #7
    OHH,...

    so what you are saying is that I use previously acquired volume of .00398 in this eq.

    I am sorry if I am frustrating. I mean well!

    OH no... do I convert 7.84 g/cm^3 to kg/m^3 ??

    if so 7.84 g/cm^3 (100cm*100cm*100cm) * 1kg = 7840 kg/m^3
    (1m^3) 1000 G


    Fw(air) = 7.84 g/cm3

    OR

    Fw (air) = 7840 kg/m^3 * .00398 m^3 * 9.81 m/s

    is that right?

    then to get weight in water I subgract (39N/9.81) ?
     
  9. Jul 27, 2009 #8

    rl.bhat

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    then to get weight in water I subgract (39N/9.81) ?
    No.
    The weight in water = F(air) - 39 N.
     
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