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Question
On October $15,2009,$ a homemade helium balloon was released, and for a while authorities were led to believe that a 6-year-old boy had been carried away in the balloon. (The incident was later revealed to be a hoax.) The balloon traveled more than $50 \mathrm{mi}$ and reached a height of $7000 \mathrm{ft}$. The shape and span of the balloon are shown in the figure. How much weight could this balloon lift? (A helium balloon can lift a mass equal to the difference in the mass of air and the mass of helium that would be contained in the balloon.) Could it actually lift a 6 -year-old boy?
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We need to find out how much weight this balloon can lift. Remember that a helium balloon can lift a mass equal to the difference in the mass of air and the mass of helium that would be contained in the balloon. Show more…
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Going Over Like a Myth buster Lead Balloon On one episode of $M y t h b u$ sters, Jamie and Adam try to make a lead balloon that will float when filled with helium. The balloon they constructed was approximately cubical in shape, and 10 feet on a side. They used a thin lead foil, which gave the finished balloon a mass of $11 \mathrm{kg}$. (a) What was the thickness of the foil? (b) Would the lead balloon float if filled with helium? (c) If the balloon does float, what would be the most mass it could lift in addition to its own mass?
Archimedes tells us the lifting power of a balloon (how much mass it can lift) is equal to the difference between the mass of the balloon and the mass of the air it displaces. That is, if the balloon occupies the same volume as 10 kg of air, but the balloon only weighs 2 kg, then the balloon can lift 8 kg. Airships have sometimes been filled with hydrogen (H2), but hydrogen is very flammable, and after the Hindenburg caught fire and crashed in 1937 with serious loss of life, airships have nearly always been filled with helium (He) instead. Gas density: H2: 0.090 kg/m^3 He: 0.18 kg/m^3 Air: 1.23 kg/m^3 Suppose a new airship, Star of Balogna, will have the shape of a cylinder 100 m long, with a radius of 15.0 m, and will weigh 9100 kg without any gas inside it. Suppose also the average passenger weighs 81 kg. Calculate how many passengers the Balogna could carry if it were filled with hydrogen, and also if it were filled with helium.
Consider an ordinary, helium-filled party balloon with a volume of $2.2 \mathrm{ft}^{3}$. The lifting force on the balloon due to the outside air is the net resultant of the pressure distribution exerted on the exterior surface of the balloon. Using this fact, we can derive Archimedes' principle, namely that the upward force on the balloon is equal to the weight of the air displaced by the balloon. Assuming that the balloon is at sea level, where the air density is $0.002377$ slug/ft $^{3}$, calculate the maximum weight that can be lifted by the balloon. Note: The molecular weight of air is $28.8$ and that of helium is 4 .
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