A spherical balloon has a radius of 12.0 m, and is filled with helium. How large a cargo can it lift, assuming

This is what AP physics is like


!!!!!!A spherical balloon has a radius of 12.0 m, and is filled with helium. How large a cargo can it lift, assuming
AP Physics is phun, dont let anyone tell you otherwise.





First, find the volume of the balloon.


The volume of a sphere = 4/3 pi * r^3


you are given the radius, so this should be no problem.





Once you know the volume of the balloon, find how much Helium and air it would take to fill it.


You could do this two ways, (the Physics way or the Chemistry way) either by using the molar masses of the gasses....or using the densities of the gasses, the density way is probably easier, but you either need to have those given to you or you can look them up and assume what temperature the experiement is taking place at.


You need to find the masses of each of the gasses.





The lifting force of the balloon will equal the difference in the upward and downward forces acting on it. The downward force is the force of the Helium's weight, the upward for is the weight of the air that the balloon is displacing (we ignore the weight of the ballooon).





If you want to believe wikipedia,


the density of air at 20 degrees C = 1.204 kg/m^3,





one mole of Helium = 4.00 grams.


At STP 1 mole of Helium would have a volume of about 22.4 Liters.A spherical balloon has a radius of 12.0 m, and is filled with helium. How large a cargo can it lift, assuming
What is wrong with that? The lift of the balloon is just the buoyant force, minus the weight of the balloon.





Wb=weight of balloon


V=volume of balloon (4/3)*pi*R^3


DHe=density of helium


Da=density of air


g=acceleration of gravity


B=buoyant force


L=lifting capacity of balloon





From Archimedes, you know the buoyant force is the same as the weight of the material displaced so,


B=Da*V*g





The weight of the balloon plus the weight of the helium is


Wb + DHe*V*g





The lifting capacity is of course the difference





L=B - Wb -DHe*V*g = Da*V*g - Wb -DHe*V*g


=(Da-DHe)*V*g -Wb





That is so hard? Come on now!