A helium balloon ride lifts up passengers in a basket. Assume the density of air
ID: 1918736 • Letter: A
Question
A helium balloon ride lifts up passengers in a basket. Assume the density of air is 1.28 kg/m3 and the density of helium in the balloon is 0.18 kg/m3. The radius of the balloon (when filled) is R = 4.9 m. The total mass of the empty balloon and basket is mb = 122.0 kg and the total volume is Vb = 0.074 m3. Assume the average person that gets into the balloon has a mass mp = 73.0 kg and volume Vp = 0.077 m3. My question is for: 6) How many FULL people can the balloon lift up? (Your answer must be an integer.)Explanation / Answer
V = 4/3 pi r^3
V = 1.3333 * 3.141592 * 4.9 ^ 3
V = 492.8 m^3
Mass balloon = 122 kg
Mass Helium = d_Helium * Volume = 0.18 kg/m^3 * 492.8 = 88.71 kg
Total Mass = 210.71 kg
Force = m*g
m = 210.71
g = 9.81
F = m*g
F = 210.71 * 9.81
F = 2067.06 N
Mass of displaced volume of air. = d * V
d = 1.28 kg/m^3
V = 492.8 m^3
Mass = 1.28 * 492.8
Mass = 630.78 kg
The volume of the basket = 0.074 m^3
The buoyant mass = the volume of air displaced * density
The buoyant mass = 0.074m^3 * 1.28 kg/m^3 = 0.09472 kg
The buoyant mass is the difference between the balloon full of helium that displaces the air and the helium mass and the basket mass.
m = 630.78 - 210.71+ 0.09472 = 420.165
The force = 420.165 * 9.81 = 4121.81 N
F person (no buoyancy) = 73 * 9.81 = 715.4 N
Buoyancy on each person = 0.9543
With buoyancy = 715.4 - 0.077 * 1.28 * 9.81 =714.4 N
The number of people who could be lifted by the system = 4121.81/714.4 = 5 people.
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