A plane is in level flight at constant speed and each of its wings has an area of \( 25 m^2\). 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 \( 1 kg/m^3\)), g = \( 9.8 m/s^2\)

Asked by Abhisek | 1 year ago |  160

1 Answer

Solution :-

Area of the wings of the plane, A=2×25=50 m2
Speed of air over the lower wing, V1
​=180km/h= 180 x (\( \dfrac{5}{18}\)) = 50 m/s

Speed of air over the upper wing, V2
=234km/h= 234 x (\( \dfrac{5}{18}\)) = 65 m/s

Density of air, =1kg/m3
Pressure of air over the lower wing =P1
​Pressure of air over the upper wing =P2
​Pressure difference,ΔP = P1​−P2 

= (\( \dfrac{1}{2}\)) ρ (V22 – V12)

= (\( \dfrac{1}{2}\)) x 1 x (652 – 502) = 862.5 Pa

​The net upward force F=ΔP x A
The upward forces balances the weight of the plane

mg = ΔP x A

m = \( \dfrac{(ΔP \times A)}{g}\)

\( \dfrac{(862.5 \times 50)}{9.8​}\)
=4400kg

The mass of the plane is 4400kg

Answered by Abhisek | 1 year ago

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