Aspherical balloon has a radius of 8.35 m and is filled with helium. how large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 800 kg? neglect the bouyant force on the cargo volume itself.

Assuming that the densities of the gases are:

density of air, ρ1 = 1.29 kg / m^3

density of helium, ρ2 = 0.179 kg / m^3

Since buoyant force and weight are two forces that are in opposite direction (buoyant force is up while weight is down), therefore equate the two:

buoyant force = weight

m g = (800 + m1) g

where m is the mass of buoyancy, g is gravity and m1 is the maximum mass of the cargo

m = 800 + m1

We know that mass is also expressed as:

m = ρ V

where ρ is density of gas and V is volume of the sphere

Since there are two interacting gases here, therefore m is:

m = (ρ1 – ρ2) V

Therefore:

(ρ1 – ρ2) V = 800 + m1

(1.29 – 0.179) (4π/3) (8.35m)^3 = 800 + m1

2709.33 = 800 + m1

m1 = 1,909.33 kg