Question

A hot-air balloon consists of a basket hanging beneath a large envelope filled with hot air. A typical hot-air balloon has a total mass of 539 kg, including passengers in its basket, and holds 2.62 ✕ 103 m3 of hot air in its envelope. If the ambient air density is 1.27 kg/m3, determine the density (in kg/m3) of hot air inside the envelope when the balloon is neutrally buoyant. Neglect the volume of air displaced by the basket and passengers. HINT kg/m3

Answer 1

1.05045 kg/m³

Step-by-step explanation:

`\rho_a` = Density of air = 1.26 kg/m³

`\rho_(ha)` = Density of hot air

`m_a` = Mass of balloon = 539 kg

g = Acceleration due to gravity = 9.81 m/s²

v = Volume of air in balloon =
`2.62* 10^3\ m^3`

The net force on the balloon will be

`F_n=(\rho_a-\rho_(ha))vg`

Also

`F_n=m_ag`

`\\\Rightarrow 549g=(\rho_a-\rho_(ha))vg\\\Rightarrow 549=(1.26-\rho_(ha))2.62* 10^3\\\Rightarrow -\rho_(ha)=(549)/(2.62* 10^3)-1.26\\\Rightarrow \rho_(ha)=1.05045\ kg/m^3`

The density of hot air inside the envelope is 1.05045 kg/m³