find the density of a balloon to keep it floating near the ground.?

Question

A recreational (open) hot air balloon (i.e., Pinside is approximately Poutside) has a volume of 2339 m3 when fully inflated. The total weight of the balloon, basket, ballast and pilot is 1656.2 N (373 lbs). By how much must the density of the air in the balloon be smaller than that of the surrounding atmosphere in order to keep the balloon floating level near the ground?

Answer 1

assume the density of air inside is ρ, the density of air outside is d and the volume is V

according to Archimedes Principle

buoyant force = Vdg

in this case considering vertical equilibrium
mg = Vdg
m = Vd
Vρ = Vd
ρ = d
density of air inside = density of air outside

Or otherwise we can simply say if density of inside lesser than of outside the balloon moves up, if density of air inside is more than of outside it moves down So for it to float densities should be equal.

all the calculation done by without considering the volumes of other objects as they are quite small.

Answer 2

the density of the air inside of the balloon is required to be 1656.2N per 2339cuM = .7081N per *** less dense than the air in the ballon.