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Homework Statement:

a balloon is filled with helium. Volume of the balloon is 1000m^3 and the density of helium is 0.1785kg/m^3. The balloon will be released. the air pressure at the bottom is 1013hPa and the density of the air is 1.21kg/m^3.
a) what mass can the balloon can carry at the maximum?
b) to what height can the balloon reach, if its volume remains constant and the mass it is carrying is 500kg?
Homework Equations:

Fbouyancy= mg = density air * volume air *g
P0= p0 e ^ (p0gh/p0)
In a I used F_{Bouyancy}  F_{Balloon} F _{mass} = 0
rewrote mass as a product of density and volume to obtain;
m= v(density_{air}  density_{He})
m= 1031.5kg.
I am stuck in part b. I have this formula called Barometric formula which ı should use;
P = P_{0} * e^{((P0*g*h)/ P0}
So what I understood is that this formula would give me the pressure at a particular height but I am not sure about how to apply this on what is asked ie not sure about how to find how high the balloon can go up. can you give me any tips please?
rewrote mass as a product of density and volume to obtain;
m= v(density_{air}  density_{He})
m= 1031.5kg.
I am stuck in part b. I have this formula called Barometric formula which ı should use;
P = P_{0} * e^{((P0*g*h)/ P0}
So what I understood is that this formula would give me the pressure at a particular height but I am not sure about how to apply this on what is asked ie not sure about how to find how high the balloon can go up. can you give me any tips please?