Question

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 960 kg . Neglect the buoyant force on the cargo volume itself. Determine the largest mass of cargo the balloon can lift.

Answer 1

Answer:602.27 kg

Step-by-step explanation:

Given

radius of spherical balloon
`r=6.55\ m`

density of helium
`\rho _(He)=0.179\ kg/m^3`

density of air
`\rho _(air)=1.29\ kg/m^3`

mass of structure
`m=960\ kg`

volume of helium inside balloon

`V=(4)/(3)\pi r^3`

`V=(4)/(3)\pi (6.55)^3`

`V=1406.19\ m^3`

Net upward Thrust on balloon
`F=V* (\rho _(air)-\rho _(He))g`

`F=1406.19* (1.29-0.179)g`

maximum mass cargo can carry

`m=(F-structure\ weight)/(g)`

`m=1562.27-960`

`m=602.27\ kg`