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 = 4.5 m. The total mass of theempty balloon and basket is mb = 123 kg and the total volume is Vb = 0.068 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

Explanation / Answer

1) volume of helium ballon is (4/3)*pi*R^3 = (4/3)*3.142*4.5^3 = 380.8 m^3...

2) Force of gravity Fg = mb*g + mH*g...

mH is mass of helium = Density*volume = 0.18*380.8 = 68.54 Kg..

Fg = (123+68.54)*9.8 = 1877.13 N....

3) Buoyancy Force Fb = 1877.13 N..
4) Fg on each person is Fg = mp*g=74*9.8= 725.2 N...

5) Fb on each person = 725.2 N..

6) Eac person has a weight 725.2 N....
no.of people can the ballon lift up is 1877.13/725.2 = 2.58 = 3 people(ROUND OFf)

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