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Buoyancy and helium balloons

  1. Apr 9, 2015 #1


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    1. The problem statement, all variables and given/known data

    What diameter must a helium filled balloon have to float with neutral buoyancy? The mass of the empty balloon is 2 g.
    2. Relevant equations

    FB = (density)(gravity)(Volume)
    Volume of balloon = 4/3(4.13)r^2
    Density = mass/Volume

    3. The attempt at a solution

    I know that the balloon will float when its weight is equal to the weight of the air displaced.
    Weight of balloon = Weight of air displaced
    Weight of empty balloon = 0.002kg x 9.81 = 0.01962N
    Thus weight of air displaced = 0.01962N
    But this is a far as I am getting as I am very confused with where the density plays a roles since no densities is given in this problem.
  2. jcsd
  3. Apr 9, 2015 #2


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    You've overlooked a contributor to the weight of the balloon.
    You do need facts concerning gas densities. Assume atmospheric pressure.
  4. Apr 9, 2015 #3
    Use the ideal gas law to get the density of air (and helium if you think that will be significant compared to the balloon weight).

  5. Apr 9, 2015 #4


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    Your formula for the volume of the balloon is incorrect.

    V = (4/3)π r3 (yes, r cubed, not r squared)

    and π ≈ 3.14159 ..., not 4.13
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