Question

A plane is in level flight at constant speed and each of its two wings has an area of $25m^2$. If the speed of the air is 180 km/h over the lower wing and 234 km/h over the upper wing surface, determine the plane’s mass. (Take air density to be $1kg{m}^{–3})$.

Answer 1

The area of the wings of the plane, $A=2\times 25=50m^2$
Speed of air over the lower wing, $V_1$ = 180 km/h = 50 m/s
Speed of air over the upper wing, $V_2$ = 234 km/h = 65 m/s
Density of air, $\rho =1kg{m}^{–3}$
Pressure of air over the lower wing =$P_1$
Pressure of air over the upper wing= $P_2$
The upward force on the plane can be obtained using Bernoulli’s equation as:
$P_1+\frac{1}{2}\rho V_1^2=P_2+\frac{1}{2}\rho V_2^2{P}_1-P_2=\frac{1}{2}\rho (V_2^2-V_1^2)..............\left(i\right)$
The upward force (F) on the plane can be calculated as:
($P_1-P_2$)A
$=\frac{1}{2}\rho (V_2^2-V_1^2)A=\frac{1}{2}\times 1\times \left(\right(65{)}^2-\left(50{)}^2\right)\times 50=43125N$
Using Newton’s force equation, we can obtain the mass (m) of the plane as:
F=mg
$\therefore m=\frac{43125}{9.8}$
=4400.51 kg
$\sim 4400kg$
Hence, the mass of the plane is about 4400 kg.