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Buoyancy and Archimedes' Principle (Helium ballon and cargo problem)

  1. Sep 8, 2009 #1
    1. The problem statement, all variables and given/known data

    " A spherical balloon has a radius of 7.35 m and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 930 kg? Neglect the buoyant force on the cargo volume itself."

    2. Relevant equations

    So F(b) = (mass of helium + mass of cargo) X 9.8

    F(b) = Density of air X volume X 9.8

    9.8 cancels out on both sides.

    Density of air is 1.29 kg/m^3 so
    1.29V = (mass of helium + mass of cargo)

    mass of helium = density of helium (.179) X volume

    so 1.29V - .179(V) = mass of cargo
    V for a sphere = 4/3 (pi) (r)^3 = 1663.2


    3. The attempt at a solution

    plug that in and I get 1847.8 for the mass, which is WRONG
    strangely if I divide that by 2 I get the right answer though... 924, which rounded down would be 920, but I have no idea why id divide it by 2.

    I do not know what thing is wrong, and please explain detail. I am an international student.
     
  2. jcsd
  3. Sep 8, 2009 #2

    Borek

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    Staff: Mentor

    You forgot to include mass of the balloon in your calculations.
     
  4. Sep 8, 2009 #3
    hmm... I don't know what you mean. Could you explain more easier to me?
    Well.. Actually, I don't know where should I put mass of the balloon.

    Could you write a equation exactly include mass of the balloon?
     
  5. Sep 8, 2009 #4

    Borek

    User Avatar

    Staff: Mentor

    Before balloon can lift anything else, it has to lift itself.
     
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