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A spherical balloon has a radius of 7.05 m and is filled with helium. Part A How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 940 kg ? Neglect the buoyant force on the cargo volume itself. Express your answer using two significant figures.

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Answer:

[tex]6.1\times 10^2\ kg[/tex]

Explanation:

[tex]\rho_a[/tex] = Density of air = 1.225 kg/m³

[tex]\rho_h[/tex] = Density of helium = 0.1718 kg/m³

r = Radius balloon = 7.05 m

Mass of skin and structure of the balloon = 940 kg

Volume of balloon

[tex]v=\frac{4}{3}\pi r^3\\\Rightarrow v=\frac{4}{3}\pi 7.05^3\\\Rightarrow v=1467.76308\ m^3[/tex]

Mass the balloon can carry is given by

[tex]M=v(\rho_a-\rho_h)\\\Rightarrow M=1467.76308(1.225-0.1718)\\\Rightarrow M=1545.84807\ kg[/tex]

The mass the balloon can carry including the weight of the balloon itself is 1545.84807 kg

The mass of cargo it can lift is [tex]1545.84807-940=605.84807=6.1\times 10^2\ kg[/tex]

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