Question

A spherical balloon has a radius of 6.55 m and is filled with helium. The density of helium is 0.179 kg/m3, and the density of air is 1.29 kg/m3. The skin and structure of the balloon has a mass of 990 kg . Neglect the buoyant force on the cargo volume itself. Part A Determine the largest mass of cargo the balloon can lift. Express your answer to two significant figures and include the appropriate units.

Answer 1

`M_1 = 317.7 kg`

Step-by-step explanation:

Mass of the helium gas filled inside the volume of balloon is given as

`m = \rho V`

`m = 0.179((4)/(3)\pi R^3)`

`m = 0.179((4)/(3)\pi 6.55^3)`

`m = 210.7 kg`

now total mass of balloon + helium inside balloon is given as

`M = 210.7 + 990`

`M = 1200.7 kg`

now we know that total weight of balloon + cargo = buoyancy force on the balloon

so we will have

`(M + M_1)g = \rho_(air) V g`

`(1200.7 + M_1) = ((4)/(3)\pi 6.55^3) (1.29)`

`1200.7 + M_1 = 1518.4`

`M_1 = 317.7 kg`