Question

A modern-day zeppelin holds 9,130 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

For this problem we are given the volume in cubic meters, therefore we will use the fact that the weight density of a substance can be represented as the mass density of the substance times the acceleration due to gravity:

$Dw = Dg$

Step 1:

Volume:

V = 9130 $m^{3}$

Mass Density of air:

D(air) = 1.29 $( \tfrac{m}{m^{3}})$

Mass Density of helium:

D(helium) = 0.18 $( \tfrac{m}{m^{3}})$

Step 2:

Weight of helium:

W = ?

Buoyant force:

F_(buoyant) = ?

Maximum payload or Net Force:

F_net = ?

Step 3:

Weight of helium:

$W = D_{helium}\cdot g \cdot V_{helium}$

Buoyant force:

$F_{buoyant} = D_{air} \cdot g \cdot V_{air}$

In this case $V_{helium} = V_{air} = V$

Net Force:

$F_{net} = F_{buoyant} - W$

Step 4:

Net Force:

$F_{net} = F_{buoyant} - W=D_{air} \cdot g \cdot V-D_{helium}\cdot g \cdot V=[D_{air} -D_{helium}]\cdot g \cdot V$

Step 5:

Final Answer:

$F_{net} =$ $(1.29 - 0.18) \cdot g \cdot 9130 = 99,417.4 N$

$F_{net} =$ $99,417.4 N$