Solving a Balloon Mass Calculation: Find Minimum Gas Mass Needed

[etothey]

Homework Statement

A balloon contains gas of density pg and is to lift a mass M, including the balloon but not the gas. Show that the minimum mass of gas required is m= Mp / (pa - pg). Where pa is Atmospheric density

Homework Equations

I assume fluid motion so
P= Po + p*h*g
Also archimedes principle Vair=Vgas could come in handy?

The Attempt at a Solution

I managed to rearrange into mpa-mpg = Mpg and then i am so stuck.

Help is needed so I can solve a question that is related to this!

 

[issacnewton]

Hi
Buoyancy force has to be , at least

F_B=Mg+M_{gas}g

where M_gas is the mass of the gas in the balloon. If V is the volume occupied
by the gas and if \rho_g is the density of the gas,

M_{gas} = \rho_g V

Now apply Archimedes principle

 

[etothey]

Hi
Buoyancy force has to be , at least

F_B=Mg+M_{gas}g

where M_gas is the mass of the gas in the balloon. If V is the volume occupied
by the gas and if \rho_g is the density of the gas,

M_{gas} = \rho_g V

Now apply Archimedes principle

I keep walking around in a circle. I convert Fb into mass atmosphere times gravity, i convert that into mass of gas times density of atmosphere over density off gas times gravity. I cancel gravity on both sides but still don't manage to get the equation needed.

 

[etothey]

Managed to solve it. Thanks!