A helium balloon ride lifts up passengers in a basket. Assume the density of air

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 = 4.7 m. The total mass of the empty balloon and basket is mb = 128 kg and the total volume is Vb = 0.061 m3. Assume the average person that gets into the balloon has a mass mp = 74 kg and volume Vp = 0.077 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

PLEASE, CLEARLY WORK IT OUT CORRECTLY..THNKS

Explanation / Answer

1) Vhe = 4 * 4.73 / 3 = 434.9 m3

2) Fg,sys = (mb + Vhehe)g = [128 + (434.9 * 0.18)] * 9.81 = 2023.6 N

3) Fbuo,sys = (Vb + Vhe)airg = (0.061 + 434.9) * 1.28 * 9.81 = 5461.7 N

4) Fg,p = mpg = 74 * 9.81 = 725.9 N

5) Fbuo,p = Vpairg = 0.077 * 1.28 * 9.81 = 0.97 N

6) Let the ballon lift 'n' people.

Fbuo = Fg

=> Fbuo,sys + nFbuo,p = Fg,sys + nFg,p

=> 5461.7 + 0.97n = 2023.6 + 725.9n

=> n = 4.74

So, balloon can lift 4 people.

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