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Submarine (Buoyant Force)

  1. Apr 15, 2008 #1
    1. The problem statement, all variables and given/known data

    William Smith built a small submarine capable of diving as deep as 30.0 m. The submarine's volume can be approximated by that of a cylinder with a length of 3.00 m and a cross-sectional area of 0.500 square meters. Suppose this submarine dives in a freshmwater river and then moves out to sea, which naturally consists of salt water. What mass of fresh water must be added to the ballast to keep the submarine submerged? The density of fresh water is 1000 kg/m3, and the density of sea water is 1025 kg/m3.

    2. Relevant equations

    Cylinder volume = Base area x height
    Buoyant force = Fluid density x Volume x Acceleration due to gravity (9.81 m/s2)

    3. The attempt at a solution

    I found the volume, which is 1.5 cubic meters.
    I then found the buoyant force, which is 15,082.88 N.
    Then I tried to divide the weight of the fluid displaced, which is the buoyant force, by the acceleration due to gravity to try to find the mass...but that didn't seem right.
    I got 1,537.5 kg, but if I try to find the weight, I'll just be back to the buoyant force...and if the buoyant force equals the weight of the object...the object is still floating.
  2. jcsd
  3. Apr 15, 2008 #2


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    Science Advisor
    Homework Helper

    There are two different boyant forces - one for sea water and one for fresh.
    The difference between them is the extra mass you need.
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