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Application of Archimedes' Principle and Law of Flotation.

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A balloon filled with Helium and air is designed to support a mass of 106kg (payload+ empty balloon) and the mass of gases which fill it.Air density is 1.29kg/m^3, Helium plus air density in the balloon is 0.247kg/m^3, and Helium density is 0.179kg/m^3. Ignoring the volume of the payload, find the volume of the balloon. Answer in units of m^3.

https://brainmass.com/physics/equilibrium/application-archimedes-principle-law-flotation-217340

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Let the volume of the balloon be V m^3
Mass of Helium plus air in balloon 0.247*V Kg
Total mass = (0.247V + 106) Kg
Mass of air displaced by the balloon = 1.29*V Kg
Buoyant force on balloon = 1.29 V Kgf
In equilibrium weight of balloon(entire) = buoyant force
(0.247V + 106) = 1.29 V
1.29 V - 0.247 V = 106
1.043 V = 106
V = 106/1.043
V = 101.629 m^3
V = 101.63 m^3
V = 102 m^3
Density of Helium is not required for this calculation.

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