Buoyant force problem

  1. Hi, I am having some trouble with the following question:

    You (mass 70.1 kg) decide to take off--literally--with a helium balloon of mass 31.6 kg. The densities of air and helium are air = 1.321 kg/m3 and helium = 0.179 kg/m3. What volume of helium is needed to levitate you and the balloon?

    I think that you use the buoyant force equations, but I am not sure how. I tried doing it like this:
    F(buoy)=density(fluid)*V'*g or
    (101.7*9.81)=(1.321*V'*9.81) and solved for V' and got
    V'=76.987 m^3
    but this is not correct.

    I cannot figure out how to do this problem, any help would be appreciated.

    Thanks!!
     
  2. jcsd
  3. Hootenanny

    Hootenanny 9,678
    Staff Emeritus
    Science Advisor
    Gold Member

    If we take the equation which you stated;

    [tex]F_{b} = \rho V g[/tex]

    The 'thing' that is creating the bouyant force is the difference between the relative densities of the fluids hence in your case;

    [tex]F_{b} = ( \rho_{air} - \rho_{helium} )Vg[/tex]

    -Hoot
     
  4. arildno

    arildno 12,015
    Science Advisor
    Homework Helper
    Gold Member

    First, you must state the total weight of your system:
    [tex]W=W_{person}+W_{balloon}+W_{helium}[/tex]
    Note that your unknown volume appears in [itex]W_{helium}[/tex]
    Assuming that you and the balloon material contributes only negligibly to the total volume of the system, you can now find what the volume must be by equating this total weight with the buoyant force (which is the net pressure force needed to keep a volume V of air floating in..the air).
     
    Last edited: Apr 9, 2006
  5. andrevdh

    andrevdh 1,723
    Homework Helper

    Try adding the weight of the helium in the balloon to the lefthand of your equation, the mass of the balloon probably do not include this additional weight
    [tex]m_{helium}g=\rho_{helium} Vg[/tex]
     
    Last edited: Apr 9, 2006
  6. so the volume must be 89.05 m^3, thanks everyone!
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?