2. 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 p = 0.0154 kg/m³ (although this varies with temperature). Suppose we construct these balloons of a thin but tough plastic having an area density = 5.10 g/m2 (i.e., each square meter has a mass of 5.10 g). We inflate the balloons with a very light gas whose mass we can neglect. a) If such a balloon were floating just above the surface of Mars, what forces would be acting on it? Express each force in terms of the balloon's radius along with the parameters given above, and calculate the necessary radius for the balloon to be in equilibrium. b) Calculate the mass of a balloon with the radius you found in part (a). c) Suppose we release a balloon of this size on Earth, where the density of the atmosphere is 1.3 kg/m³. Would it go up, go down, or hover in place? Calculate its initial acceleration. d) Back to Mars: if we make a balloon with 5 times the radius you found in part (a), it should be able to carry a package of instruments in addition to its own weight. How heavy can the instrument package be?
2. 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 p = 0.0154 kg/m³ (although this varies with temperature). Suppose we construct these balloons of a thin but tough plastic having an area density = 5.10 g/m2 (i.e., each square meter has a mass of 5.10 g). We inflate the balloons with a very light gas whose mass we can neglect. a) If such a balloon were floating just above the surface of Mars, what forces would be acting on it? Express each force in terms of the balloon's radius along with the parameters given above, and calculate the necessary radius for the balloon to be in equilibrium. b) Calculate the mass of a balloon with the radius you found in part (a). c) Suppose we release a balloon of this size on Earth, where the density of the atmosphere is 1.3 kg/m³. Would it go up, go down, or hover in place? Calculate its initial acceleration. d) Back to Mars: if we make a balloon with 5 times the radius you found in part (a), it should be able to carry a package of instruments in addition to its own weight. How heavy can the instrument package be?
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Transcribed Image Text:2. 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 p = 0.0154
kg/m³ (although this varies with temperature). Suppose we construct these balloons of a thin but tough plastic
having an area density = 5.10 g/m² (i.e., each square meter has a mass of 5.10 g). We inflate the balloons
with a very light gas whose mass we can neglect.
a) If such a balloon were floating just above the surface of Mars, what forces would be acting on it? Express
each force in terms of the balloon's radius along with the parameters given above, and calculate the necessary
radius for the balloon to be in equilibrium.
b) Calculate the mass of a balloon with the radius you found in part (a).
c) Suppose we release a balloon of this size on Earth, where the density of the atmosphere is 1.3 kg/m³.
Would it go up, go down, or hover in place? Calculate its initial acceleration.
d) Back to Mars: if we make a balloon with 5 times the radius you found in part (a), it should be able to
carry a package of instruments in addition to its own weight. How heavy can the instrument package be?
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