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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?

Respuesta :

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

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

here radius R = 16 cm

[tex]V = \frac{4}{3}*\pi*0.16^3[/tex]

V = 0.0172 m^3

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

[tex]F_b = \rho * V * g[/tex]

[tex]F_b = 1.2 * 0.0172 * 9.8[/tex]

[tex]F_b = 0.202 N[/tex]

Now weight of the person that we have to counter balance

[tex]W = 75*9.8 = 735 N[/tex]

Now by force balance

[tex] N*F_b = W[/tex]

[tex] N*0.202 = 735[/tex]

[tex] N = 3639[/tex]

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

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