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 = 4.5 m. The total mass of the empty balloon and basket is m_b = 123 kg and the total volume is V_b = 0.068 m³. Assume the average person that gets into the balloon has a mass m_p = 70 kg and volume V_p = 0.077 m³.

1. 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. I got 487 but its wrong.
2. What is the magnitude of the force of gravity on each person?
3. What is the magnitude of the buoyant force on each person?
4. How many FULL people can the balloon lift up? (Your answer must be an integer.)

Answer 1

1.

Buoynat force = weight of the displced air

B = rho V g

where rho is density of air

V is Volume of displaced air

g is accleration due to gravity

so

volume of dispalced air = volume of the balloon, basket, and helium.

V = 0.18 + 0.068 + (4/3)*pi*4.5^3

V = 381.95 m^3

thus B = 1.28* 381.95 *9.8

B = 4791.18 N

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part B :

mass of balloon = 123 kg

mass of helium = Density of He * Volume

Mass of He = 0.18 * (4/3)*pi*4.5^3 = 68.7 kg

total mass = 123 + 68.7 = 191.7 kg

FOrce F = mg

F = 191.7 * 9.81

F = 1880.577 N

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Mass of displaced volume of air. = d * V

d = 1.28 kg/m^3

Mass = 1.28 * (4/3)*pi*4.5^3

M = 488.58 kg

The buoyant mass = the volume of air displaced * density

The buoyant mass = 0.077 * 1.28 = 0.0985 kg

The buoyant mass m = 488.58 - 191.7 + 0.0985 = 297 kg

The force = 297 * 9.81 = 2913.57 N

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3. F person (no buoyancy) = 70 * 9.81 = 686.7 N

Buoyancy on each person = 0.0985 * 9.81 = 0.966 N

4. )

With buoyancy = 686.7 - 0.068 * 1.28 * 9.81 = 685.84 N

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5. The number of people who could be lifted by the system

N = 2913.57/685.84

N = 4 people