Question

A spherical balloon has a radius of 6.35 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 970 kg . Neglect the buoyant force on the cargo volume itself.

Determine the largest mass of cargo the balloon can lift.

Answer 1

Solution:-

Given –

Radius – 6.35 m

Density of helium – 0.179 kg/m³

Density of air – 1.29 kg/m³

Mass of balloon – 970kg

Weight of (structure) balloon W1 = 970*g, where g = 9.8 m/s²

Weight of (structure) balloon W1 = 970*g

Weight of helium W2,

Volume*density of helium*g

4π/3*r³ *0.179*g

Weight of helium W2 = 191.88*g

Buyout force on balloon W’

= volume*density of air*g = 4π/3*r³ *1.29*g

Buyout force on balloon W’ = 1382.8628*g

Down force = up force

W1+W2+weight of additional cargo = W’

Mg = W’-W1-W2

Mg = 1382.8628*g – 970*g – 191.88*g

M = 220.98 kg

​Largest mass of cargo the balloon can lift is = 220.98 kg.