A helium balloon ride lifts up passengers in a basket. Assume the density of air
ID: 1413974 • 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 = 126 kg and the total volume is Vb = 0.066 m3. Assume the average person that gets into the balloon has a mass mp = 72 kg and volume Vp = 0.077 m3.
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 = 126 kg and the total volume is b = 0.066 m3. Assume the average person that gets into the balloon has a mass mp = 72 kg and volume Vp = 0.077 m3. 1) What is the volume of helium in the balloon when fully inflated? m3 m Submit 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 Submit 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 Submit 4) What is the magnitude of the force of gravity on each person? N Submit 5) What is the magnitude of the buoyant force on each person? N Submit 6) How many FULL people can the balloon lift up? (Your answer must be an integer.) people SubmitExplanation / Answer
(1) Volume, V = 4/3 pi r^3
V = 1.3333 * 3.141592 * 5.1 ^ 3
V = 554.15 m^3
(2) Mass balloon = 126 kg
Mass Helium = d_Helium * Volume = 0.18 kg/m^3 * 554.15 = 99.75 kg
Total Mass = 126+99.75 = 225.75 kg
Now, F = m*g
F = 225.75 * 9.81
F = 2214.61 N
(3) Mass of displaced volume of air. = d * V
d = 1.28 kg/m^3
V = 554.15 m^3
Mass = 1.28 * 554.15
Mass = 709.31 kg
The volume of the basket = 0.066 m^3
The buoyant mass = the volume of air displaced * density
The buoyant mass = 0.066 m^3 * 1.28 kg/m^3 = 0.08448 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 = 709.31 - 225.75 + 0.08448 = 483.64
The force = 483.64 * 9.81 = 4744.51 N
(4) Magnitude of force of gravity on each person = mg = 72 * 9.81 = 706.32 N
(5) Magnitude of buoyant force on each person = 0.077*1.28*9.81 = 0.9669 N
(6) With buoyancy total force = 706.32 - 0.9669 =705.35 N
The number of people who could be lifted by the system = 4744.51/705.35 = 6.72 people.
So, the total persons, that can be lifted by balloon = 6
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