Question

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.

Answer 1

`6.1* 10^2\ kg`

Step-by-step explanation:

`\rho_a` = Density of air = 1.225 kg/m³

`\rho_h` = 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

`v=(4)/(3)\pi r^3\\\Rightarrow v=(4)/(3)\pi 7.05^3\\\Rightarrow v=1467.76308\ m^3`

Mass the balloon can carry is given by

`M=v(\rho_a-\rho_h)\\\Rightarrow M=1467.76308(1.225-0.1718)\\\Rightarrow M=1545.84807\ kg`

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
`1545.84807-940=605.84807=6.1* 10^2\ kg`