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 = 0.062 m3. Assume the average person that gets into the balloon has a mass mp = 72 kg and volume Vp = 0.079 m3.

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.)

Answer 1

volume of helium, V = 659.58 m³

force of gravity on the system

F = m_bg + _HeVg

F = 121 * 9.8 + 0.18 * 659.58 * 9.8

F = 2349.3 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.

F_b = (V + V_b ) _air g

F_b = (659.58 + 0.062) * 1.28 * 9.8

F_b = 8274.5 N

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4)

What is the magnitude of the force of gravity on each person

F = mg

F = 72 * 9.8

F = 705.6 N

_________________

5)

What is the magnitude of the buoyant force on each person

F = 1.28 * 9.8 * 0.079

F = 0.99097 N

________________

6)

How many FULL people can the balloon lift up

N = 8274.5 - 2349.3 / 705.6

N = 8 persons