Question

A spherical balloon has a radius of 7.15 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 900 kg . Neglect the buoyant force on the cargo volume itself. Part A Determine the largest mass of cargo the balloon can lift.

Answer 1

Using Force balance on the balloon:

Weight of Cargo + Structure = Buoyant Force

Suppose mass of cargo = M,

mass of structure = 900 kg

then

Weight of Cargo = M*g

Weight of structure = 900*g

Buoyant Force = Weight of air - Weight of helium inside balloon

Mass = Volume*density

Using above relation

Fb = rho_air*V*g - rho_He*V*g = (rho_air - rho_He)*V*g

rho_air = density of air = 1.29 kg/m^3

rho_He = density of Helium = 0.179 kg/m^3

V = Volume of balloon = 4*pi*R^3/3 = 4*pi*7.15^3/3 = 1531.11 m^3

So, Now

M*g + 900*g = (1.29 - 0.179)*1531.11*g

M + 900 = (1.29 - 0.179)*1531.11

M = (1.29 - 0.179)*1531.11 - 900

M = mass of cargo balloon can lift = 801.1 kg

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