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Problem

The density of air is $ 1.29 \: kg/m^3 $ and the density of helium is $ 0.18 \: kg/m^3 $. The mass of the balloon is $ 20 \: kg $.

What volume of helium would a hot air balloon needed to lift a $ 180 \: kg $ crate?
Hot-air-balloon

Solution

The balloon must be able to lift the crate and its own mass.

$ F_B = ({m}_{He} + 180 + 20)g $
$ {\rho}_{air} Vg = \left({\rho}_{He} V + 200 \right) g $
$ V = \frac{200}{{\rho}_{air} - {\rho}_{He}} $
$ V = \frac{200}{1.29 - 0.18} $
$ V = 180 \: m^3 $
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