Question

12) Consider a party balloon filled with helium with a small mass m hanging from it, as depicted in Figure 2. The balloon can be approximated as a sphere with volume V = 0.035 m. The mass of the rubber and string (i.e. the balloon's mass when it is not filled with helium) is 0.0025 kg. a) If the balloon with the mass hanging is floating in equilibrium, what is the value of the hanging mass? Suggestion: Write Newton's Second Law for the system as a whole, rather than for the balloon and the mass separately. The mass of the system is the sum of three parts: the unknown mass m, the mass of the rubber and string, and the mass of the helium inside the balloon. The buoyancy force can be computed using only the volume of the balloon (the volumes of the mass and string are negligible) but remember it depends on the density of the surrounding fluid, which in this case is air, not water! b) Now that you know how much mass a balloon can keep floating, make an order-of- magnitude estimate of the mass of a house (don't think about it too much, it doesn't need to be very accurate) and based on this, make an oder-of-magnitude estimate for how many balloons would be needed to lift the house as seen in the movie Up.

Answer 1

V=0.035 o3, M=0.0025Kg 6) Pars = 1.275 kglrm3 %3D Srte = 0.1 66u kglm3 dorm FBD : v Bning I mg Vfais 9 = VPHe g +mg+ng %3D 0•035x 1•275= 0.035% 0•1664+ 0•0025+m m= 0.038 01 - 0.0025 m = Ov036301 kG | g Unknocon mao P) Let mass of howe be m = 40000 kg ballon: . Lel N be no N Všar - VBuc -M]=m N= 4bo00 0. 036301 = !•l02x106 N= 1•102x106