Question

Suppose that a party balloon is spherical, has a radius of 16 centimetres and is filled with helium. furthermore suppose that we do our experiment under standard atmospheric conditions, when the air density is . how many of these balloons should a 75 kilogram human carry in order to become airborne?

Answer 1

Let N number of balloons are used to pull the person upwards

So there would be buoyancy force due to air on balloons which will be counterbalanced by the weight of a person.

Volume of one balloon is given by

`V = (4)/(3)\pi r^3`

here radius R = 16 cm

`V = (4)/(3)*\pi*0.16^3`

V = 0.0172 m^3

Now the buoyancy force of air on each balloon is given by

`F_b = \rho * V * g`

`F_b = 1.2 * 0.0172 * 9.8`

`F_b = 0.202 N`

Now weight of the person that we have to counter balance

`W = 75*9.8 = 735 N`

Now by force balance

`N*F_b = W`

`N*0.202 = 735`

`N = 3639`

So we require 3639 balloons to hold the person of mass 75 Kg