A helium balloon ride lifts up passengers in a basket. Assume the density of air
ID: 1480988 • 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 = 5.4 m. The total mass of the empty balloon and basket is mb = 121 kg and the total volume is Vb = 0.061 m3. Assume the average person that gets into the balloon has a mass mp = 72 kg and volume Vp = 0.078 m3.
1)
What is the volume of helium in the balloon when fully inflated?
m3
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.
N
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.
N
4)
What is the magnitude of the force of gravity on each person?
N
5)
What is the magnitude of the buoyant force on each person?
N
6)
How many FULL people can the balloon lift up? (Your answer must be an integer.)
people
Explanation / Answer
1) volume V = 4/3 pi R^3
V = 1.3333 * 3.141592 * 5.4 ^ 3
V = 659.58 m^3
2) Mass balloon = 121 kg
Mass Helium = d_Helium * Volume = 0.18 kg/m^3 * 659.58 = 118.73 kg
Total Mass = 239.73 kg
Force = m*g
m = 239.73
g = 9.81
F = m*g
F = 239.73* 9.81
F = 2351.75 N
3)Mass of displaced volume of air. = d * V
d = 1.28 kg/m^3
V = 659.58 m^3
Mass = 1.28 * 659.58
Mass = 844.26 kg
The volume of the basket = 0.061 m^3
The buoyant mass = the volume of air displaced * density
The buoyant mass = 0.061m^3 * 1.28 kg/m^3 = 0.07808 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 = 844.26 - 239.73+ 0.07808 =604.61
The force =604.61 * 9.81 = 5931.21 N
4) This is really tricky. I think you are intended to use the volume, but you really should not have to.
F person (no buoyancy) = 72 * 9.81 = 706.32 N
Buoyancy on each person = 0.9543
With buoyancy = 706.32 - 0.078 * 1.28 * 9.81 =705.34 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 = 5931.21/705.34 = 8.41 people. In this case you have to round downward, so you could lift 8 people.
5) Magnitude of buoyant force on each person, based upon air displaced by each person. Remember, this assumes that the balloon is tethered to the ground so it is NOT accelerating.
B1 = rho_a*Vp
=1.28*0.078=0.09984 N
6) 8 people
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