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A spherical balloon has a radius of 6.55 m and is filled with helium. The density of helium is 0.179 kg/m3, and the density of air is 1.29 kg/m3. The skin and structure of the balloon has a mass of 990 kg . Neglect the buoyant force on the cargo volume itself. Part A Determine the largest mass of cargo the balloon can lift. Express your answer to two significant figures and include the appropriate units.

Respuesta :

Answer:

[tex]M_1 = 317.7 kg[/tex]

Explanation:

Mass of the helium gas filled inside the volume of balloon is given as

[tex]m = \rho V[/tex]

[tex]m = 0.179(\frac{4}{3}\pi R^3)[/tex]

[tex]m = 0.179(\frac{4}{3}\pi 6.55^3)[/tex]

[tex]m = 210.7 kg[/tex]

now total mass of balloon + helium inside balloon is given as

[tex]M = 210.7 + 990[/tex]

[tex]M = 1200.7 kg[/tex]

now we know that total weight of balloon + cargo = buoyancy force on the balloon

so we will have

[tex](M + M_1)g = \rho_{air} V g[/tex]

[tex](1200.7 + M_1) = (\frac{4}{3}\pi 6.55^3) (1.29)[/tex]

[tex]1200.7 + M_1 = 1518.4[/tex]

[tex]M_1 = 317.7 kg[/tex]

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