A hot air balloon of radius 12 meters has been heated so that the air inside has a density of 1.05 kg/m^3. What can the total load of the balloon be (mass of balloon itself plus cargo) if you need the balloon to accelerate into the air with an acceleration of 4 m/s^2?

Answer 1

bouyancy=(densityair-densityinside)Volume*g

Now for the density of air, we really need temperature, and relative humidity. Assuming 25C, dry air, density air is 1.1839kg/m^3

bouyancy= (1.18-1.05)*9.8*4/3 PI 12^3

net force=mass*acceleration
bouyancy= mass*4 solve for mass