Question

A spherically shaped balloon has a radius of 8.14m, and is filled with helium. How large a mass of cargo can it lift, assuming that the skin and structure of the balloon have a mass of 872kg? Neglect the bouyant force on the cargo volume itself. The density of air is 1.29 kg/m3 and the density of helium is 0.179 kg/m3.

Answer 1

Radius of balloon = 8.14 m

Therefore volume of the balloon =

Volume of balloon = volume of air displaced = 2259.24 m²

Boyuant force = density of air displaced * volume of air displaced * acceleration due to gravity =

Mass of the balloon + mass helium gas in it =Mass of the balloon + volume of balloon * density of helium

Let the maximum mass of cargo lifted be m Kg

So net mass of the balloon system + cargo = (1276.4 + m ) Kg

Net downward force by this system = net mass * g = (1276.4 + m ) g N

So for maximum mass lifted, the downward force and the bouyant force will become equal

=> (1276.4 + m ) g = 2914.4g

=> (1276.4 + m ) = 2914.4

=> m = 1638 Kg

So the maximum mass of cargo that can be lifted = 1638 Kg