A 2.8kg balloon is filled with helium ( density = 0.179 kg/m 3 ). Part A If the...

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Physics

A 2.8kg balloon is filled with helium ( density = 0.179 kg/m 3).
Part A
If the balloon is a sphere with a radius of 5.1m , what is themaximum weight it can lift? (N)

Answer & Explanation Solved by verified expert

4.5 Ratings (964 Votes)

Volume of the balloon is

V = 4?r³/3

Â Â = (4)(?)(5.1 m)³ / 3

Â Â = 555.36552 m³
The density of helium,?_helium = 0.179 kg/m³
The density of airm, ?_air = 1.29 kg/m³
The mass of the balloon, m = 2.8 kg

The air's weight equal to mg
Â Â W_air = ?_air V g
Â Â Â Â Â Â Â Â Â Â = (1.29 kg/m³)(555.36552 m³)(9.8 m/s²)
Â Â Â Â Â Â Â Â Â Â = 7020.93 N

The weight of balloon including helium is
Â Â W_helium = mg+?_helium V gÂ Â Â Â Â Â Â Â Â
Â Â Â Â Â Â Â Â Â Â Â Â Â = (2.8 kg)(9.8 m/s²) + (0.179 kg/m³)(555.36552 m³)(9.8 m/s²)
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 1001.66 N

Therefore maximum weight it can lift is

maximum weight lift = W_air -W_helium
Â Â Â Â Â Â Â Â Â Â Â = 7020.93 N - 1001.66 N
Â Â Â Â Â Â Â Â Â = 6019.27 N

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