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 = 4.8 m. The total mass of the empty balloon and basket is m_b = 129 kg and the total volume is V_b = 0.066 m³. Assume the average person that gets into the balloon has a mass m_p = 70 kg and volume V_p = 0.079 m³.

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

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.

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.)

Please include the process!!!!!

Answer 1

Given :

• The density of air is 1.28 kg/m^3 and the density of helium in the balloon is 0.18 kg/m^3.
• The radius of the balloon (when filled) is R = 4.8 m.
• The total mass of the empty balloon and basket is m_b = 129 kg
• Total volume is V_b = 0.066 m^3
• The average person that gets into the balloon has a mass m_p = 70 kg and volume V_p = 0.079 m³.

1 ) The volume of helium in the balloon when fully inflated,

= 4/3 π R^3

= 4/3 x 3.14 x (4.8)^3

=> 463.24 m^3 = 463 m^3 _Ans.

2 ) Force of gravity on the entire system ,but with no people;

= (mass of the empty balloon and basket + mass of helium )x g

=( 129kg + 463.24 m^3 x 0.18kg/m^3 )x 9.8

=> 2081.35 N = 2081 N _Ans.

3.) Magnitude of the buoyant force on the entire system (but with no people )

( Volume of empty balloon + basket + volume of helium ) density of air x g

( 0.066 m^3 + 463.24 m^3 ) x 1.28 x 9.8

=> 5811.71 N = 5812 N _Ans.

4 ) Magnitude of the force of gravity on each person=

Mass of each person(m_{​​​​​​p}) × g

= 70 x 9.8

= 686 N _Ans.