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 = 4.6 m. The total mass of the empty balloon and basket is mb = 126 kg and the total volume is Vb = 0.056 m3. Assume the average person that gets into the balloon has a mass mp = 72 kg and volume Vp = 0.079 m3.

1) What is the volume of helium in the balloon when fully inflated? m3 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

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?

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.) people Submit

Answer 1

V = 4/3 pi r³

= 1.3333 * pi * 4.6³

= 407.7 m³

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mass of balloon = 126 kg

mass of helium = d_helium * Volume = 0.18 * 407.7 = 73.39 kg

Total Mass = 199.4 kg

F = m g = 199.4 * 9.81

F = 1956 N

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mass of displaced volume of air = d * V

= 1.28 * 407.7 = 521.9 kg

Volume of the basket = 0.056 m³

Buoyant mass = volume of air displaced * density = 0.056 * 1.28 = 0.07168 kg

The buoyant mass = balloon full of helium that displaces the air - helium mass and the basket mass

m = 521.9 - 199.4 + 0.07168 = 322.6

Force = 322.6 * 9.81 = 3164 N

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F_person = 72 * 9.81 = 706.32 N

With buoyancy = 706.32 - 0.07168 * 1.28 * 9.81 = 705.4 N

The number of people who could be lifted by the system = 3164 / 705.4 = 4.48 people