A helium balloon (in the shape of a sphere) has radius 7.00 m. For the density o

Question

A helium balloon (in the shape of a sphere) has radius 7.00 m. For the density of air, please use 1.29 kg/m^3, and for Helium, use. 179 kg/m^3 Part A How much additional mass (payload) could this balloon lift? You should assume the balloon's skin, plus other parts of the balloon's structure have a total mass of 900 kg. however that this number does NOT yet include the mass of the helium filling the balloon, which you will need to account for! Express your answer using two significant figures. m = kg

Explanation / Answer

volume of balloon = (4/3)*pi*r^3 = (4/3)*(22/7)*(7)^3 = 1437.33 m^3

The maximum mass that a balloon can lift will cause it to have the same density as air. Therefore, the balloon must displace a volume of air with an equal mass.

Mass of air displaced by balloon = 1437.33 m^3 * 1.29kg/m^3 = 1854.15kg = Mass of loaded balloon

Mass of unloaded balloon = 900kg + 1437.33m^3 * 0.179kg/m^3 = 1157.28 kg

Mass that balloon can lift = Mass of loaded balloon - Mass of unloaded balloon = 1854.15kg - 1157.28kg = 696.87kg

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