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Hot air balloon - Archimedes Principle

  1. Feb 26, 2014 #1
    1. The problem statement, all variables and given/known data

    A hot air balloon with V = 500 m^3 is floating in the air without moving. The air outside the balloon has a density of 1,20 kg/m^3, and the hot air inside the balloon has a density of 0,75 kg/m^3. Calculate the total mass of the hot air balloon.

    2. Relevant equations

    Archimedes Principle F0 = ρVg

    3. The attempt at a solution

    I googled the answer to this question, so I already know how to solve it:
    F0 = (1,20 -0,75) * 500 = 225 kg

    What I don´t understand is why g wasn´t integrated into this answer? How come the answer isn´t (1,20-0,75)*500 * 9,82 =2210 kg?
     
  2. jcsd
  3. Feb 26, 2014 #2

    ehild

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    The buoyant force is ρVg, but you made it equal with mass, which is wrong.

    Fo has to be equal to the weight, that is, ρ(outside)Vg=ρ(inside)Vg+Mg where M is the mass of the balloon and cargo, without the air inside the balloon.
    You can divide the whole equation with g.

    ehild
     
  4. Feb 26, 2014 #3
    I do not think you described the problem as stated. Because as stated, the answer is simply ## m = \rho V##, where ##\rho## is the hot air density, by definition of density.

    The answer that you think should be true is not a correct answer to a question about mass, simply because that answer gives some force.
     
  5. Feb 26, 2014 #4

    ehild

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    The total mass of the hot-air balloon was asked. It is not the mass of the air only, but includes both the balloon material and the cargo.


    ehild
     
  6. Feb 27, 2014 #5
    Then the answer is wrong. Just the air in the balloon is 375 kg.
     
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