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Fluids - A lost shipping container is found resting on the ocean floor

  1. Dec 7, 2009 #1
    1. The problem statement, all variables and given/known data

    A lost shipping container is found resting on the ocean floor and completely submerged. The container is 6.3 m long, 2.1 m wide, and 2.6 m high. Salvage experts attach a spherical balloon to the top of the container and inflate it with air pumped down from the surface. When the balloon's radius is 1.8 m, the shipping container just begins to rise towards the surface. What is the mass of the container? Ignore the mass of the balloon and the air within it. Do not neglect the buoyant force exerted on the shipping container by the water. The density of seawater is 1025 kg/m3.

    Container

    L = 6.3 m
    w = 2.1 m
    h = 2.6 m
    V = ?

    Balloon / Air

    r = 1.8 m
    p = 1.29 kg / m3
    V =
    FB =

    Water

    p = 1025 kg / m3
    FB =

    2. Relevant equations

    Archimedes' Principle

    FB = Wfluid

    Vcontainer = L * w * h

    Vballoon = 4/3 [tex]\pi[/tex]r3

    p = m / v

    F = ma

    3. The attempt at a solution

    First I found the volumes for the container and the balloon.

    Vcontainer = L * w * h

    Vcontainer = 6.3 * 2.1 * 2.6

    Vcontainer = 34.398 m3


    Vballoon = 4/3 [tex]\pi[/tex]r3

    Vballoon = 4/3 [tex]\pi[/tex]1.83

    Vballoon = 24.429

    I then tried to find the buoyant force of the air.

    FB = Wair

    FB = mg

    FB = pVg

    FB = 1.29 * 24.429 * 9.8

    FB = 308.83 N

    And then for the sea water.

    FB = Wwater

    FB = mg

    FB = pVg

    FB = 1025 * 34.398 * 9.8

    FB = 345527.91 N

    After this, I used newton's 2nd law...

    F = ma

    m = F / a

    m = FBair + FBwater / g

    m = 308.83 N + 345527.91 N / 9.80 m/s2

    m = 35289 kg ----> 3.5 * 104 kg

    But.......this appears to be wrong...Um...thoughts?

    Thanks!
     
    Last edited: Dec 8, 2009
  2. jcsd
  3. Dec 7, 2009 #2

    mgb_phys

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    Homework Helper

    Check the bouyancy of the balloon

    You can ignore the mass of the air - otherwise it's the same calcuation as the container
     
  4. Dec 8, 2009 #3
    Hmmm....

    The buoyant force equals the weight of the displaced fluid which is the sea water, not the air. So the equation should have been:

    FB = Wwater

    = mg

    = pVballoong

    = 1025 * 24.429 * 9.8

    = 245389 N

    So, using that....

    F = mg

    m = F / g

    m = 245389.30 N + 345527.91 N / 9.80 m/s2

    m = 60297.67 kg ----> 6.0 * 104 kg

    How is that?
     
  5. Dec 8, 2009 #4

    mgb_phys

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    Assuming you pressed the right buttons - yes.
    You can simplify it a little by ignoring 'g' - since you cancel it out.
    You just want the mass of seawater contained in the volume of shipping container and volume of balloon.
     
  6. Dec 8, 2009 #5
    Didn't know what you meant by the g's cancelling, but I went back a few steps and tried this...Please excuse pi appearing as an exponent, I have no idea why that happens.

    p(4/3 [tex]\pi[/tex]r3)[STRIKE]g[/STRIKE] + p(L*w*h)[STRIKE]g[/STRIKE] = m[STRIKE]g[/STRIKE]

    p(4/3 [tex]\pi[/tex]r3) + p(L*w*h) = m

    1025 kg/[STRIKE]m3[/STRIKE] (24.429 [STRIKE]m3[/STRIKE]) + 1025 kg/[STRIKE]m3[/STRIKE] (34.398 [STRIKE]m3[/STRIKE])

    1025 kg (24.429) + 1025 kg (34.398)

    25039.725 kg + 35257.95 kg

    = 60297.675 kg ---> 6.0 * 104 kg

    Do I pass?
     
  7. Dec 8, 2009 #6

    mgb_phys

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    Homework Helper

    Thats exactly it, since you are asked for the mass it doesn't really make sense to multiply the masses of seawater by g to calculate upward force then divide the weight by g to get mass
    So you should get the same answer!
     
  8. Dec 8, 2009 #7
    Great! Thanks a bunch for your help! :)
     
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