Solved: Three forces act significantly on a freely
Chapter , Problem 101(choose chapter or problem)
Three forces act significantly on a freely floating heliumfilledballoon: gravity, air resistance (or drag force), and abuoyant force. Consider a spherical helium-filled balloonof radius r = 15 cm rising upward through 0C air,and m = 2.8 g is the mass of the (deflated) balloon itself.For all speeds v, except the very slowest ones, the flow ofair past a rising balloon is turbulent, and the drag force FDis given by the relationFd = \C v Pairirr2v2where the constant CD = 0.47 is the drag coefficient fora smooth sphere of radius r. If this balloon is released fromrest, it will accelerate very quickly (in a few tenths of a second)to its terminal velocity Vj, where the buoyant force iscancelled by the drag force and the balloons total weight.Assuming the balloons acceleration takes place over anegligible time and distance, how long does it take thereleased balloon to rise a distance h = 12 m?
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