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/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 5.10 g . We inflate them with a very light gas whose mass we can neglect.

Part A What should be the radius of these balloons so they just hover above the surface of Mars? Submit My Answers Give Up Part B What should be the mass of these balloons so they just hover above the surface of Mars? kg Submit My Answers Give U Part C 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? Submit My Answers Give U

Answer 1

IDENTIFY: The buoyant force B equals the weight of the air displaced by the balloon SET UP: B-2airTg . Let Su be the value of g for Mars. For a sphere V = πR3 . The surface area of a sphere is given by A = 4nK . The mass of the balloon is (5.00 x 10-3 kg/m2)ATR"). Main 3(5.00x10 kg/m2) 0.974 m. (5.00x10-3 kg/m2)(4TR2 0.0596 kg 4π (D) F. B-mg ma. B-Pa Rg (1.20 k/(0.974 m (9.80 m/s) 45.5 N. B-mg 45.5 N (0.0596 kg)(9.80 m/s2) , = 754 m/s upward. 0.0596 m med0.0154 kg/m0.974 m (5.00x10 kg/m)(47)(5[0.974 m] me7.45 kg-1.49 kg 5.96 kg EvALUaTE: The buoyant force is proportional to R and the mass of the balloon is proportional to R, so the load that can be carried increases when the radius of the balloon increases. We calculated the mass of the load. To find the weight of the load we would need to know the value of g for Mars