A helium balloon ride lifts up passengers in a basket. Assume the density of air
ID: 1796587 • 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 = 5.1 m. The total mass of the empty balloon and basket is mb = 125 kg and the total volume is Vb = 0.064 m3. Assume the average person that gets into the balloon has a mass mp = 71 kg and volume Vp = 0.077 m3.
What is the magnitude of the force of gravity on the entire system (but with no people)? Include the mass of the balloon, basket, and helium.
What is the magnitude of the buoyant force on the entire system (but with no people)? Include the volume of the balloon, basket, and helium.
What is the magnitude of the force of gravity on each person?
What is the magnitude of the buoyant force on each person?
Explanation / Answer
Mass balloon = 125 kg
Mass Helium = d_Helium * Volume = 0.18 kg/m^3 *555.365 =99.965 kg
Total Mass = 224.9657 kg
Force = m*g
m = 224.9657
g = 9.81
F = m*g
F = 224.9657 * 9.8
F = 2204.66477 N
Mass of displaced volume of air. = d * V
d = 1.28 kg/m^3
V = 555.365 m^3
Mass = 1.28 * 555.365
Mass = 710.8672 kg
The volume of the basket = 0.064 m^3
The buoyant mass = the volume of air displaced * density
The buoyant mass = 0.064m^3 * 1.28 kg/m^3 = 0.08192 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 = 710.8672 - 224.9657+ 0.08192 = 485.98342
The force = 485.98342 * 9.81 = 4767.49735 N
F person (no buoyancy) = 71 * 9.81 = 696.51 N
Buoyancy on each person = 0.96687
With buoyancy = 706.32 - 0.077 * 1.28 * 9.81 =705.3531 N
the actual force is close enough without the buoyancy, but I gave you both.
The number of people who could be lifted by the system = 4767.49735/705.3531 = 6.759 people. In this case you have to round downward, so you could lift 6 people.
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