An empty spherical weather balloon with a mass of 5.00 kg has a radius of 2.879
ID: 1469942 • Letter: A
Question
An empty spherical weather balloon with a mass of 5.00 kg has a radius of 2.879 m when fully inflated with helium. It is supposed to carry a small load of instruments having a mass of 10.0 kg. Taking air and helium to have densities of 1.16 kg/m3 and 0.160 kg/m3, respectively, will the balloon get off the ground? An empty spherical weather balloon with a mass of 5.00 kg has a radius of 2.879 m when fully inflated with helium. It is supposed to carry a small load of instruments having a mass of 10.0 kg. Taking air and helium to have densities of 1.16 kg/m3 and 0.160 kg/m3, respectively, will the balloon get off the ground? An empty spherical weather balloon with a mass of 5.00 kg has a radius of 2.879 m when fully inflated with helium. It is supposed to carry a small load of instruments having a mass of 10.0 kg. Taking air and helium to have densities of 1.16 kg/m3 and 0.160 kg/m3, respectively, will the balloon get off the ground?Explanation / Answer
Mass of Helium = Density of Helium * Volume of Ballon
Mass of Helium = 0.160 kg/m^3 * 4/3 * pi * r^3 m^3
Mass of Helium = 15.99 Kg
Total Mass of Ballon Acting Downwards = Empty Mass of Ballon + Mass of Helium Filled + Mass of Instruments
Total Mass of Ballon Acting Downwards = 15.99 + 5.00 + 10.0 = 30.99 Kg
Mass of Displaced Air = Density of Air * Volume of Ballon
Mass of Displaced Air = 1.16 kg/m^3 * 4/3 * pi * r^3 m^3
Mass of Displaced Air = 1.16 * 4/3 * 3.14 * 2.879^3 Kg
Mass of Displaced Air = 115.89 Kg
Fb = Mass of Displaced Air * 9.8 = 115.89 * 9.8 N
Net Weight of the Ballon acting downwards = 30.99 * 9.8 N
The net force on the balloon will be equal to the buoyant force minus the balloon’s weight
So we can clearly see, Buoyant force > Net Weight of the Ballon acting downwards.
Therefore it will get off the ground.
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