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 = 5.2 m. The total mass of the empty balloon and basket is m_b = 126 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 = 73 kg and volume V_p = 0.078 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

Answer 1

1). Radius of the balloon, R= 5.2m

Then Volume of helium in the balloon when fully inflated,

  (ANS)

2). Density of Helium gas,

then Mass of Helium,

Mass of empty balloon and basket,

Then force due to gravity on the entire system will be

(ANS)

3). Buoyancy force is the force exerted by the weight of the displaced air in upward direction.

Now density of air,

Then Mass of the displaced air will be

And Buoyancy force on the entire system will be

4). Mass of each person, m_p= 73 kg

then Force of gravity on each person will be

5). Again the Buoyancy force on each person will be the weight of the displaced air.

Given volume of each person, V_p= 0.078m³

then Mass of displaced air,

then Buoyancy force on each person will be

6). Let the number of people which can the balloon can lift be "n" then we'll have

using all calculated values from above,

  

  

  (ANS)