Question

Find the minimum radius of a helium balloon that will lift her off the ground. the density of helium gas is 0.178 kg/m3, and the density of air is 1.29 kg/m3. neglect the weight of the deflated balloon itself (but not the weight of the helium). assume that the shape of the balloon is a sphere. neglect the buoyant force of the air on the woman.

Answer 1

$Volume of balloon = \frac{4}{3} \pi r^{3}$

Where r is the radius of balloon.

Here mass of woman = 68 kg

Mass of air displaced by a balloon with volume V = 1.29*V

Mass of helium inside balloon = 0.178*V

Total mass to be lifted by balloon = 68 +0.178*V

Buoyant force = 1.29V-0.178V=1.112V

So we have 1.112 V =  68+ 0.178*V

   0.934 V = 68

     V = 72.81 $m^3$

    \frac{4}{3} \pi r^{3}[/tex]= 72.81

     r = 2.59 m

So radius of helium balloon = 2.59 m