# Is it possible to lift a 5.5 kg load in a 6.5 m3 balloon? The balloon is filled with helium

Is it possible to lift a 5.5 kg load in a 6.5 m3 balloon? The balloon is filled with helium. The force of gravity acting on the shell and devices is 40 N.

At max. ball load: Fa = Fт.
Fa = ρw * g * Vsh, ρw is the air density (ρw = 1.3 kg / m ^ 3), g is the acceleration of gravity (g = 10 m / s ^ 2), Vsh is the volume of the ball (Vsh = 6, 5 m ^ 3).
Ft = m * g, m = m1 + m2 + m3 (m1 is the mass of the shell of the ball and instruments (m1 = P / g, where P is the force of gravity (P = 40 N)), m2 is the mass of helium (m2 = ρg * Vsh, ρg is the density of helium (ρg = 0.18 kg / m ^ 3)), m3 is the maximum weight of the cargo.
ρw * g * Vsh = (P / g + ρg * Vsh + m3) * g
m3 = ρw * Vsh-R / g-ρg * Vsh = 1.3 * 6.5-40 / 10-0.18 * 6.5 = 3.28 kg.
Since the max. the weight of the load is 3.28 kg, then it is impossible to lift a load weighing 5.5 kg.

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