Balloons are often filled with helium gas because it weighs only about one-seventh of what air weighs under identical conditions. The buoyancy force which can be expressed as Fb = ρairgVballoon, will push the balloon upward. If the balloon has a diameter of 12 m and carries two people 85 kg each determine the acceleration of the balloon when it is first released. Assume the density of air is ρ = 1 16 kg/m3, and neglect the weight of the ropes and the cage. Answer: 22.4 m/s2
The acceleration of the balloon when it is first released.
Answer to Problem 101RP
The acceleration of the balloon when it is first released is
Explanation of Solution
Show the free body diagram of the balloon.
Write the expression of volume of sphere of a balloon.
Write the expression of the buoyancy force acting on the balloon.
Here, the density of air is
Write the expression of the mass of helium.
Here, the density of the helium is
Write the expression of the total mass can carried by balloon.
Here, the total mass of a people is
Write the expression of the total weight.
Write the expression of net force acting on the balloon.
Write the expression of acceleration.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the acceleration of the balloon when it is first released is
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