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Absolute pressure, buoyant force, tension problem

  1. Apr 25, 2015 #1
    1. The problem statement, all variables and given/known data
    A diving sphere has a mass of 150,000.0kg and an external diameter of 7.000 meters. The sphere is anchored with a cable on the bottom of an ocean, at a depth of .8000 km. The density of sea water is 1025.0kg/m3.
    A) What is the absolute pressure at that depth in pascals?
    B) What is the buoyant force felt by the sphere when it is completely submerged?
    C) Calculate the tension of the cable.
    2. Relevant equations
    A) P = Ps+DgH
    P=?
    Ps=1.01E+5Pa
    D=1.025E+3kg/m3
    G=9.81m/s2
    H=.8000km

    B) P=F/A, A=pi R2
    P=(from above)
    BF=?
    R=3.5m

    C) WF=m*g
    TF+WF=BF
    m=150,000kg
    g=9.81m/s2
    TF=?
    BF= (from above)
    3. The attempt at a solution
    A) P=(1.01E+5) + [(1.025E+3)*(9.81)*(800m)]
    =8.145E+6Pa

    B) 8.145E+6Pa = BF / (pi * 3.5)2
    BF=3.135E+8N

    C) WF=150000*9.81
    WF=1471500
    TF=313500000-1471500
    TF=3.120E+8N

    Is this correct? The numbers seem very high...
     
    Last edited: Apr 25, 2015
  2. jcsd
  3. Apr 25, 2015 #2

    TSny

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    Hello and welcome to PF!

    Is the depth .8000 hm or .8000 km?

    Your method for part (a) is correct. For part (b) you have not calculated the BF correctly. Consider Archimedes' principle.

    Your approach to part (c) looks correct.
     
  4. Apr 25, 2015 #3

    km, I have corrected the typo.

    for part (b) density=mass/displaced volume
    so displaced volume = mass/density
    so displaced volume = 150,000/1025
    so displaced volume = 146.341
    BF = density * displace volume * gravity
    BF=1025 * 146.341 * 9.81
    =1.471E+6
    ???
     
  5. Apr 25, 2015 #4

    TSny

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    No, this isn't correct. 150,000 kg is the mass of the diving sphere, but 1025 kg/m3 is the density of sea water.

    Try to think of another way to get the displaced volume. Hint: geometry.
     
    Last edited: Apr 25, 2015
  6. Apr 25, 2015 #5

    SteamKing

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    Your calculations become a lot more intelligible if you state the units after each result. It's a habit you should cultivate now.
     
  7. Apr 25, 2015 #6
    What is the volume of a sphere 7 m in diameter?

    Chet
     
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