Question

A modern-day zeppelin holds 9,650 m3 of helium. Compute its maximum payload at sea level. (Assume the helium and air to be at 0°C and 1 atm.)

Answer 1

Answer:

10809.93 kg

Explanation:

$\rho_a$ = Density of air = 1.292 kg/m³

$\rho_{He}$ = Density of air = 0.1718 kg/m³

V = Volume of Helium = 9650 m³

g = Acceleration due to gravity = 9.81 m/s²

Net force on the zeppelin is given by

$F_n=\rho_aVg-\rho_{He}Vg-mg\\\Rightarrow 0=\rho_aVg-\rho_{He}Vg-mg\\\Rightarrow mg=(\rho_a-\rho_{He})Vg\\\Rightarrow W=(1.292-0.1718)9650\times 9.81\\\Rightarrow W=106045.4133\ N$

The maximum payload will be $\frac{106045.4133}{9.81}=10809.93\ kg$