physics A spherical balloon has a radius of 6.95 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 930 kg. Neglect the buoyant force on the cargo volume itself. Determine the largest mass of cargo the balloon can lift.

volume of balloon

= 4/3 π R³

= 4/3 x 3.14 x 6.95³

= 1405.47 m³

uplift force

= volume of balloon x density of air x 9.8

= 1405.47 x 1.29 x 9.8

= 1813.05 x 9.8 N

weight of helium gas

= volume of balloon x density of helium x 9.8

= 1405.47 x. 179 x 9.8

= 251.58 x 9.8 N

Weight of other mass = 930 x 9.8 N

Total weight acting downwards

= 251.58 x 9.8 + 930 x 9.8

= 1181.58 x 9.8 N

If W be extra weight the uplift can balance

1181.58 x 9.8 + W x 9.8 = 1813.05 x 9.8

1181.58 + W = 1813.05

W = 631.47 kg