Question

It has been proposed that we could explore Mars using inflated balloons to hover just above the surface. The buoyancy of the atmosphere would keep the balloon aloft. The density of the Martian atmosphere is 0.0154 kg/m^3 (although this varies with temperature). Suppose we construct these balloons of a thin but tough plastic having a density such that each square meter has a mass of 4.50 g . We inflate them with a very light gas whose mass we can neglect.

a. What should be the radius and mass of these balloons so they just hover above the surface of Mars?
b. If we released one of the balloons from part (a) on earth, where the atmospheric density is 1.20kg/m^3, what would be its initial acceleration assuming it was the same size as on Mars? Would it go up or down?
c. If on Mars these balloons have five times the radius found in part (a), how heavy an instrument package could they carry?

Answer 1

a) 0.0537 kg, 0.877 m

b) 609 m/s²

c) 4.35 kg

Step-by-step explanation:

B = ρ(air).V(g)

Assuming g(m) is the "g" for Mars.

For a sphere, V = 4/3πR³.

Surface area of a sphere is A = 4πR²

Thus, the mass of the balloon is (4.5*10^-3 kg/m²) (4πR²)

See the attachment for the calculations