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 of air, but the balloon only weighs , then the balloon can lift . Airships have sometimes been filled with hydrogen (), but hydrogen is very flammable, and after the Hindenburg caught fire and crashed in with serious loss of life airships have nearly always been filled with helium () instead. gas density air Suppose a new airship Star of Balogna will have the shape of a cylinder long, with a radius of , and will weigh without any gas inside it. Suppose also the average passenger weighs . Calculate how many passengers the Balogna could carry if it were filled with hydrogen, and also if it were filled with helium.

With H2 = 860 persons

With He = 783 persons

Explanation:

the volume of the balloon is equal to:

V = π*r^2*h = π*(15^2)*100 = 70685.83 m^3

For the ballon with H2, we have:

mH2 = mass of H2 = V*ρ = 70685.83 * 0.09 = 6361.72 kg

mtotal = total mass of ballon with H2 = 9200 + 6361.72 = 15561.72 kg

mairdis = mass of air displaced = V* ρ = 70685.83 * 1.23 = 86943.57 kg

The maximum weight that the balloon loaded with H2 can lift is equal to:

Wmax = 86943.57 - 15561.72 = 71381.85 kg

the number of people is equal to:

No of persons = 71381.85/83 = 860.02 = 860 persons

For the ballon with He, we have:

mHe = mass of He = V*ρ = 70685.83 * 0.18 = 12723.45 kg

mtotal = total mass of ballon with He = 9200 + 12723.45 = 21923.45 kg

mairdis = mass of air displaced = V* ρ = 70685.83 * 1.23 = 86943.57 kg

The maximum weight that the balloon loaded with He can lift is equal to:

Wmax = 86943.57 - 21923.45 = 65020.12 kg

the number of people is equal to:

No of persons = 65020.12/83 = 783.4 = 783 persons

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