1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: A Helium Balloon and Buoyancy

  1. Dec 20, 2011 #1


    User Avatar

    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


    User Avatar
    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook