It has been proposed that we couldexplore Mars using inflated balloons to hover just above the surface. Thebuoyancy of the atmosphere would keep the balloon aloft. The density ofthe Martian atmosphere is 0.0154 kg/m3 (although this varies with temperature).Suppose we construct these balloons of a thin but tough plastichaving a density such that each square meter has a mass of 5.00 g. Weinflate them with a very light gas whose mass we can ignore. (a) Whatshould be the radius and mass of these balloons so they just hoverabove the surface of Mars? (b) If we released one of the balloons frompart (a) on earth, where the atmospheric density is 1.20 kg/m3, whatwould be its initial acceleration assuming it was the same size as onMars? Would it go up or down? (c) If on Mars these balloons have fivetimes the radius found in part (a), how heavy an instrument packagecould they carry?
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/m3 (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 5.00 g. We
inflate them with a very light gas whose mass we can ignore. (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 1.20 kg/m3, 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?
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