Question

Balloons are sometimes filled with helium gas because it has a mass only about one-seventh that of air under identical conditions. The buoyancy force, which may be expressed as Fb = ????air g Vballoon, will push the balloon upward. If the balloon has a diameter of 10 m and carries two people having a mass of 70 kg each and the mass of the gondola is 64 kg, determine the acceleration of the balloon when it is first released. Assume that the density of the air is ????air = 1.16 kg/m3 , and neglect the weight of the ropes and balloon envelope fab

Answer 1

Answer:

10.1 m /s²

Explanation:

Let m₁ be the mass of the helium gas inside balloon. Mass of air displaced  is m₂

m₁ = volume x density

= 4/3 x 3.14 x 5³ x .179

= 93.67  kg

mass of displaced air

= 4/3 x 3.14 x 5³ x 1.16

= 607.06 kg

Net buoyant force in upward direction

(607.06 - 93.67 ) x g

= 5031.22 N

weight of people and gondola

= (2 x 70 + 64 ) x 9.8

= 1999.2 N

Net force in upward direction

= 5031.22 - 1999.2

= 3032.02 N

Acceleration produced

= 3032.02 / total mass

= 3032.02 / ( 93.67 +204 )

= 3032.02 / 297.67

= 10.1 m /s²