Solving an Archimedes Problem: Air Question Explained

[kindaichi]

I can't really understand Archimedes principle..I mean i know how it works in water but i am totally clueless when it comes to air question.Here is a question:

A balloon having a mass of 120 kg and volume of 400mcube is filled with helium gas of density 0.18kg m to the power of -3.The density of the surrounding air is 1.28kg m to the power of -3.What is the maximum load that can be lifted up by the balloon?Answer:320kg

How do you solve this question?Also can someone please tell me how to count air question..My exam is a few days away

 

[semc]

dude draw the FBD of the balloon the lift force is pgv where p is density of air,g is 9.81 and v is volume of air displaced or u can say volume of balloon. i think u can find the ans from there right?

 

[kindaichi]

I keep getting 392kg whereas the answer is 320kg.I have been spending an hour here

 

[Doc Al]

Don't forget to consider the mass of the helium itself.

 

[kindaichi]

so basically,you count the buoyancy force first and then later subtract the weight of the balloon and helium gas?

 

[semc]

hmm...i got exactly 320kg maybe calculation error?

 

[Doc Al]

so basically,you count the buoyancy force first and then later subtract the weight of the balloon and helium gas?

Right. Whatever is left over is the additional load that can be lifted.

 

[kindaichi]

oh,i see then..thank you everyone.Everyone have been a great help
Just,one last question.The force acting downwards is the buoyancy force right?