NASA is experimenting with balloons for use on ultralong duration (100 days) flight around the Earth. Consider a balloon that has the shape of a cylindrical chamber which is 35 m tall with 30 m radius, and is made of extremely light plastic. If our model cylindrical balloon is filled with helium gas, what is the mass of the maximum payload it could lift from the Earth's surface? (Given `rho_(air)=1.29(kg)/(m^3)`. `rho_He)=0.18(kg)/(m^3)`. Why would NASA design the balloon so large?

Explanation

As `F_B=rho_(air)V_g=m_(He)g+m_(P)g=rho_(He)V_g+m_(P)g`
`m_(P)g=rho_(air)V_g-rho_(He)Vg`
or `m_(P)=(rho_(air)-rho_(He))V=(rho_(air)-rho_(He))(pir^2h)`
`=(1.29-0.18)((kg)/(m^3))(3.14)(30m)^2(35m)`
`=1.1xx10^5kg`
This payload is quite large, most scientific payloads would have a much smaller mass, density of decrease as the balloon moves up in the atmosphere and the lower density at high altitudes decreases Lifting capability of the balloon will need to have a much greater lift force at ground level.