a balloon filled with helium can carry 2 people each of a mass of 85 kg. the bal

Question

a balloon filled with helium can carry 2 people each of a mass of 85 kg. the balloon materials and the carriage weigh 980 N. if the acceleration when the balloon is first released is 16.40 ft/s^2, calculate the volume of the balloon in m^3. The buoyancy force is defined as the weight of the fluid displaced. It is given in this situation as FB= Pair x Vballoon x g. Apply Newton's second law of motion and solve for the unknown volume after some algebra.

Use for the density of air Pair=1.16 kg/m^3 and for Phe=0.166 kg/m^3

Explanation / Answer

Weight of balloon materials and the carriage = 980 N

Weight of 2 persons = 85*2*9.8 = 1666 N

Total Weight = 2646 N

Pair=1.16 kg/m^3 ; Phe=0.166 kg/m^3

acceleration (a)= (16.4/32.2)*9.8 = 5.8114 m/s2

Buoyancy Force (FB) = (Pair - Phe) x Vballoonx g

Buoyancy force - Weight = mass*acceleration of balloon

(1.16-0.166) *Vballoon*9.8 - 2646 = (2646/9.81)*(5.8114)

9.7412*Vballoon = 1569.078+2646 = 4215.078 N

Vballoon = 432.71 m3

The volume of the balloon is 432.71 m3

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