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Unformatted text preview: 2.25 PROBLEM 1.9: DICUSSION AND SOLUTION Ain Sonin, MIT The net upward lift force on a helium-filled balloon under quasi-static conditions is L = ( He ) gV mg (1) air where air is the density of the ambient air around the balloon, He is the density of the helium inside the balloon, V is the balloons volume, and m is the total mass associated with the balloon, cargo, personnel, equipment, etc. In what follows, we assume that the atmosphere and balloon are at constant absolute temperature T , which is given, and the gases are perfect. Pressure and density are then related by pM = (2) RT where R is the universal gas constant (8.31 J/mol K) and M is the molar mass of the gas being referred to (0.029 kg/mol for air, 0.004 for helium). The hole at the bottom of the balloon prevents balloon rupture by ensuring that the helium pressure inside is the same as the air pressure just outside. Using (2) and pressure equality, we find the density of the helium inside the balloon as M He = M air air...
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- Fall '05