A helium balloon ride lifts up passengers in a basket. Assume the density of air
ID: 1484777 • 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 = 5.2 m. The total mass of the empty balloon and basket is mb = 128 kg and the total volume is Vb = 0.072 m3. Assume the average person that gets into the balloon has a mass mp = 74 kg and volume Vp = 0.079 m3.
1) What is the volume of helium in the balloon when fully inflated?
2) 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.
3) 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.
4) What is the magnitude of the force of gravity on each person?
5) What is the magnitude of the buoyant force on each person?
6) How many FULL people can the balloon lift up? (Your answer must be an integer.)
PLEASE SHOW STEPS
Explanation / Answer
R = 5.2m
1) V = 4/3 pi R^3
V = 1.3333 * 3.141592 * 5.2 ^ 3
V = 588.96 m^3
2) Mass balloon = 128 kg
MHe = dHe * V =0.18*588.96 = 106.123 kg
Total Mass = 106.123+ 128 = 234.123 kg
Force = m*g = 234.123*9.81
F = 2296.75 N
3) Mass of displaced volume of air. = d * V
d = 1.28 kg/m^3, V = 588.96 m^3
Mass = 1.26 * 588.96
Mass = 742.1 kg
The volume of the basket = 0.072 m^3
The buoyant mass = the volume of air displaced * density
The buoyant mass = (588.96+ 0.072)* 1.28 = 753.96 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 = 742.1 - 234.123+ 753.96 = 1261.94 kg
The force = 1261.94 * 9.81 = 12379.6 N
4) F person (no buoyancy) = 74 * 9.81 = 725.94 N
5)
Buoyancy on each person =0.079 * 1.28 * 9.81 = 0.99199 N
6) With buoyancy = 725.94 - 0.079 * 1.28 * 9.81 =724.95 N
The number of people who could be lifted by the system = 12379.6/724.95 = 17.07 people.
The number of people can lift the ballon is 17.07
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