Buoyancy and Archimedes' Principle (Helium ballon and cargo problem)

AI Thread Summary
The discussion revolves around calculating the cargo capacity of a helium balloon with a radius of 7.35 m and a mass of 930 kg. The buoyant force equation is established, relating the mass of helium and cargo to the density of air and the balloon's volume. A calculation attempt yields an incorrect mass of 1847.8 kg, with confusion arising over the need to include the balloon's mass in the total lift equation. Participants emphasize that the balloon must first lift its own weight before carrying additional cargo. Clarification is sought on how to properly incorporate the balloon's mass into the calculations.
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Homework Statement



" A spherical balloon has a radius of 7.35 m and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 930 kg? Neglect the buoyant force on the cargo volume itself."

Homework Equations



So F(b) = (mass of helium + mass of cargo) X 9.8

F(b) = Density of air X volume X 9.8

9.8 cancels out on both sides.

Density of air is 1.29 kg/m^3 so
1.29V = (mass of helium + mass of cargo)

mass of helium = density of helium (.179) X volume

so 1.29V - .179(V) = mass of cargo
V for a sphere = 4/3 (pi) (r)^3 = 1663.2


The Attempt at a Solution



plug that in and I get 1847.8 for the mass, which is WRONG
strangely if I divide that by 2 I get the right answer though... 924, which rounded down would be 920, but I have no idea why id divide it by 2.

I do not know what thing is wrong, and please explain detail. I am an international student.
 
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You forgot to include mass of the balloon in your calculations.
 
hmm... I don't know what you mean. Could you explain more easier to me?
Well.. Actually, I don't know where should I put mass of the balloon.

Could you write a equation exactly include mass of the balloon?
 
Before balloon can lift anything else, it has to lift itself.
 
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