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Homework Help: Balloon buoyancy

  1. Dec 2, 2009 #1
    1. The problem statement, all variables and given/known data
    An empty rubber balloon has a mass of 0.0122 kg. The balloon is filled with helium at a density of 0.179 kg/m3. At this density the balloon has a radius of 0.467 m. The acceleration of gravity is 9.8m/s2. If the filled balloon is fastened to a vertical line, what is the tension in the line? Answer in units of N.

    2. Relevant equations
    V = (4/3) * pi * r3
    Buoyant force B: rhoair * V * g
    Weight of helium wh: rhohelium * V * g
    Weight of balloon wb: m * g

    3. The attempt at a solution
    I think I understand all the concepts, but I'm not coming up with the solution in the book. Book's solution is 4.52537 N.

    I drew a free body diagram to determine the sum of forces:
    B - wh - wb - T = 0

    T = B - wh - wb

    The density of air isn't given, so I went with what the chart in the book listed: 1.20 kg/m3

    V = 0.42662

    B = 1.20 * 0.42662 * 9.8 = 5.01703

    wh = 0.179 * 0.42662 * 9.8 = 0.74838

    wb = 0.0122 * 9.8 = 0.11956

    So I end up with: 4.14909 N.

    So where am I going wrong? Thanks :)
  2. jcsd
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