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 havinga density such that each square meter has a mass of 5.40 g. We inflate them with a very light gas whose mass we can neglect.
R =1.05 m
m= 7.51 (10^-2) kg
a= 754 m/sec^2

If on Mars these balloons have five times the radius found in part A, how heavy an instrument package could they carry?
? kg

Answer 1

Assuming the radius referred to in part a) is R = 1.05 m, then the balloon would have a surface area of:

A = 4πR2 = 346.36 m2

And volume:

V = 4/3*πR3 = 606.13 m3

Since the mass density of the material is 5.40 g/m2, the total mass of the ballon is:

346.36 m2 * 5.40 g/m2 = 1870.35 g = 1.870 kg

The total density of the ballon + payload (M) must be equal or less than the density of the atmosphere:

(1.870 kg + M)/606.13 m3 = 0.0154 kg/m^3

M/606.13 m3 = -1.870 kg/606.13 m3 + 0.0154 kg/m^3

M = (-1.870 kg/606.13 m3 + 0.0154 kg/m^3)606.13 m3

M = 7.46 kg of payload