A balloon filled with helium plus air at atmospheric pressure is designed to support a mass of 116 kg (payload + empty balloon). Air density is 1.29 kg/m^3, helium plus air density in the balloon is 0.296 kg/m^3, and helium density is 0.179 kg/m^3. Ignoring the volume of the payload, find the volume of the balloon. Answer in units of m^3.

Question

Brenton Payne

Physics

Today, 16:20

A balloon filled with helium plus air at atmospheric pressure is designed to support a mass of 116 kg (payload + empty balloon). Air density is 1.29 kg/m^3, helium plus air density in the balloon is 0.296 kg/m^3, and helium density is 0.179 kg/m^3. Ignoring the volume of the payload, find the volume of the balloon. Answer in units of m^3.

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Franco · Answer 1

V = 116.70 m^3

Explanation:

let Mb be the mass of the baloon

since air density = 1.29 kg/m^3 and helium plus air density = 0.296kg/m^3

then, the lifting capacity is = (1.29 - 0.296) kg/m^3

then the volume of the baloon is given by:

V = Mb / (lifting capacity)

= 116kg / (0.994 kg/m^3)

= 116.70 m^3

Therefore, the volume of the baloom is 116.70 m^3.