A hot-air balloon has a mass of 520 kg and carries a cargo of 1500 kg. The volum
ID: 2256465 • Letter: A
Question
A hot-air balloon has a mass of 520 kg and carries a cargo of 1500 kg. The volume of the balloon is 12,300 m^3. The balloon is floating close to the ground. What are (A) the density and (B) the mass of the hot air in the balloon? (C) If the entire volume of the balloon would be filled with helium instead of hot air, what would be the maximum mass of the load that the balloon can carry right above the ground? (Rho of cold air = 1.29 kg/m^3, Rho of Helium = 0.18 kg/m^3)
Please write clearly and show all steps; Thanks.
Explanation / Answer
since it is floating
buyoant force = weight of ballon and cargo
=> 12,300 * (rho of cold air - rho)*9.81 = 2020*9.81
=> (1.29 - rho) = 0.164
a) => rho =1.126 kg/m^3
b) mass = 1.126*12300 =13849.8 kg
c)let carrying mass = x
12,300 * (rho of cold air - rho)*9.81 = (x+520)*9.81
12300*(1.29-0.18) = x+520
=>x = 13133 kg
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