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A Helium Balloon and Buoyancy

  1. Dec 20, 2011 #1

    TMO

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

    A helium balloon ride lifts up passengers in a basket. Assume the density of air is 1.28 kg1m-3 and the density of helium in the balloon is 0.18 kg1m-3. The radius of the balloon (when filled) is R = 5 m. The total mass of the empty balloon and basket is mb = 123 kg and the total volume is Vb = 0.066 m3. Assume the average person that gets into the balloon has a mass mp = 73 kg and volume Vp = 0.076 m3. What is the magnitude of the buoyant force on the entire system (but with no people)? Include the volume of the balloon, basket, and helium.

    2. Relevant equations

    [tex]V_{sph} = \frac{4}{3} \cdot \pi \cdot r^3[/tex]
    [tex] F_b = \rho_{fluid} \cdot V \cdot g [/tex]

    3. The attempt at a solution

    Since the volume of the balloon and basket is given by [tex]V_b[/tex] and the volume of the balloon is given by [tex]\frac{4}{3} \cdot \pi \cdot R^3,[/tex] it seems natural to conclude that the magnitude of the buoyancy force is [tex](1.28 \cdot V_b + 0.18 \cdot \frac{4}{3} \cdot \pi \cdot R^3) \cdot g,[/tex] but this does not seem to provide the correct answer. Any advice?

    Thank you for your time. :)
     
    Last edited: Dec 20, 2011
  2. jcsd
  3. Dec 20, 2011 #2

    BruceW

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    Homework Helper

    This is the correct equation for the buoyant force. But you need to be careful about what density to use.

    First think of a simple example, like a solid object immersed in water. Would the buoyant force be calculated using the density of the object, or the water?
     
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