What is the Radius of a Helium Balloon Needed to Lift 180 kg?

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SUMMARY

The radius of a helium balloon required to lift a total weight of 180 kg, including the balloon's own weight, can be estimated using the formula F = ρgV, where ρ is the density of helium (0.179 kg/m³) and g is the acceleration due to gravity. The calculated radius is approximately 3.22 meters. However, it is crucial to consider the density of the surrounding air, as this affects buoyancy. Without accounting for air density, the calculation is incomplete, as a balloon in a vacuum would not achieve lift regardless of its size.

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  • Understanding of buoyancy principles
  • Familiarity with the formula F = ρgV
  • Knowledge of the density of helium (0.179 kg/m³)
  • Basic physics concepts related to weight and lift
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  • Learn about the principles of buoyancy in different fluids
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Homework Statement


Estimate the radius of a helium filled balloon if a load of 180 kg (including the weight of the empty balloon) is to be lifted. Density of helium is 0.179 kg/m^3


Homework Equations



F=rho*g*V

The Attempt at a Solution



F=\rhogV

r=3.22m
 
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I don't think it's that simple.
Don't you also need to know the density of air?

If this was done in a vacuum then no matter how big your radius was it would not float.

Also, from the way the problem is worded it doesn't sound like the weight of the helium is incorporated in the 180kg.
You can solve this if you are given the density of the surrounding fluid in which the balloon is to float (most likely normal air).
 

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