91影视

The given information can be listed below,

• The density of the air is, ${蚁}_{air}=1.20鈥�kg/m^3.$.
• The density of helium is, ${蚁}_{gas}=0.166鈥�kg/m^3$.
• The density of Hydrogen is,${蚁}_H=0.0899鈥�kg/m^3$ .
• The lift in hydrogen-filled airship is,$\mathrm{l}=90鈥�\mathrm{kN}\frac{1000鈥�\mathrm{N}}{1\mathrm{KN}}=90脳{10}^3鈥�\mathrm{N}$ .

When immersed in a liquid, the net force on an object could be positive, negative, or zero, with a buoyant force acting on it, meaning that the object could rise or sink depending on the magnitude. If zero, the object will stay stationary - that is, it will neither rise nor sink.

The fluid that exerts buoyant force here is air; the lift corresponds to a mass which is calculated as,

${\mathrm{m}}_{\mathrm{gas}}=\frac{\mathrm{l}}{\mathrm{g}}$

Here, l is the lift in the airship, and g is the acceleration due to gravity whose value is $9.8鈥�\mathrm{m}/{\mathrm{s}}^2$.

Substitute all the values in the above equation.

$$\begin{gathered} {\mathrm{m}}_{\mathrm{lift}}=\frac{90脳{10}^3\mathrm{N}}{9.8\mathrm{m}/{\mathrm{s}}^2}\left(\frac{1\mathrm{kg}.\mathrm{m}/{\mathrm{s}}^2}{1\mathrm{N}}\right) \\ =9.184脳{10}^3\mathrm{kg} \end{gathered}$$

The buoyant force exerted by air is given by,

$B={蚁}_{air}Vg$

Here, ${蚁}_{air}$ is the density of air, V is the volume of the airship, and g is the acceleration due to gravity.

According to Newton鈥檚 law, the force acting on the airship is expressed as,

$鈭�F=ma$

So, the net force can be given by,

$B-m_{tot}g=0$

Here,$m_{tot}$is the total mass of the airship.

And total mass of airship can be calculated as,

${\mathrm{m}}_{\mathrm{tot}}={\mathrm{m}}_{\mathrm{lift}}+{\mathrm{m}}_{\mathrm{gas}}$

Here, ${\mathrm{m}}_{\mathrm{lift}}$is the mass corresponding to the lift and$m_{gas}$is the mass of hydrogen gas.

The free-body diagram is given by,

Substitute the value of total mass. The net force equation can be written as,

localid="1656496391340" $B-\left(m_{lift}+m_{gas}\right)g=0$

The volume displaced by hydrogen-filled airship can be expressed as,

localid="1656496399634" $$\begin{gathered} B=\left(m_{lift}+m_{gas}\right)g \\ {蚁}_{air}Vg=\left(m_{lift}+{蚁}_{gas}V\right)g \\ {蚁}_{air}V-{蚁}_{gas}V=m_{lift} \\ v=\frac{m_{lift}}{{蚁}_{air}-{蚁}_{gas}} \end{gathered}$$

Substitute all the values in the above equation.

localid="1656496408216" $$\begin{gathered} \mathrm{V}=\frac{9.184脳{10}^3\mathrm{kg}}{1.20\mathrm{kg}/{\mathrm{m}}^3-0.0899\mathrm{kg}/{\mathrm{m}}^3} \\ =8.27脳{10}^3鈥�{\mathrm{m}}^3 \end{gathered}$$

Thus, the total volume displaced by Hydrogen-filled airship is localid="1656496417486" $8.27脳{10}^3鈥�m^3$.

The mass of lift observed can be given by,

$m_{lift}={蚁}_{air}V-{}_{蚁H}V$

Substitute all values in the above equation.

$$\begin{gathered} {\mathrm{m}}_{\mathrm{lift}}=\left(1.20\mathrm{kg}/{\mathrm{m}}^3-0.166\mathrm{kg}/{\mathrm{m}}^3\right)\left(8.27脳{10}^3{\mathrm{m}}^3\right) \\ =8550\mathrm{kg} \end{gathered}$$

So, the lift force can be calculated as,

$$\begin{gathered} {\mathrm{m}}_{\mathrm{lift}}\mathrm{g}=8550\mathrm{kg}\left(9.8\mathrm{m}/{\mathrm{s}}^2\right)\left(\frac{1\mathrm{N}}{1\mathrm{kg}.\mathrm{m}/{\mathrm{s}}^2}\right)\left(\frac{1\mathrm{KN}}{1000\mathrm{N}}\right) \\ =83.8\mathrm{KN} \end{gathered}$$

Thus, the lift in the airship when helium was used instead of hydrogen is 83.8 KN .

Here, the density of helium is less than that of air but greater than that of hydrogen. Helium provides lift but less than hydrogen. Hydrogen is not used because it is highly explosive in the air.

That is why helium is used in modern airships like advertising blimps.