Problem 15.34 A 3.5kg balloon is filled with helium ( density = 0.179 kg/m3). Pa

Question

Problem 15.34

A 3.5kg balloon is filled with helium ( density = 0.179 kg/m3).

Part A

If the balloon is a sphere with a radius of 5.4m , what is the maximum weight it can lift?

Express your answer using two significant figures.

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Problem 15.34

A 3.5kg balloon is filled with helium ( density = 0.179 kg/m3).

Part A

If the balloon is a sphere with a radius of 5.4m , what is the maximum weight it can lift?

Express your answer using two significant figures.

SubmitMy AnswersGive Up

Explanation / Answer

Volume of a sphere = (4/3) * pi * r^3
Using r = 5.4m this gives a volume = 659.24928 m^3
This is therefore the volume of surrounding air that is displaced.

If the balloon is in air with a density of 1.2 kg/m^3 it will therefore displace a mass of :
659.24928 m^3 * 1.2 kg/m^3 = 791.099136 kg
The upthrust on the balloon due to this displaced air =mg
Taking g as 9.8 m/s^2

Upthrust = 7752.7715328 N
This upthrust must support the weight of the helium and the weight of the balloon fabric itself.

Mass of helium = 659.24928 m^3 * 0.179 kg/m^3 = 118.00562112 kg
Mass of balloon = 3.5 kg
Downward weight force due to balloon plus helium
= (3.5 + 118.00562112) * 9.8 = 1190.755086976 N

Net upward force = upthrust - weight = 6562.016445824 N

So it can lift a weight of 6562 N

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