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

Area of the wings of the plane, A=2×25=50 m^{2}

Speed of air over the lower wing, V_{1}

=180km/h= 180 x (\( \dfrac{5}{18}\)) = 50 m/s

Speed of air over the upper wing, V_{2}

=234km/h= 234 x (\( \dfrac{5}{18}\)) = 65 m/s

Density of air, =1kg/m^{3}

Pressure of air over the lower wing =P_{1}

Pressure of air over the upper wing =P_{2}

Pressure difference,ΔP = P_{1}−P_{2}

= (\( \dfrac{1}{2}\)) ρ (V_{2}^{2} – V_{1}^{2})

= (\( \dfrac{1}{2}\)) x 1 x (65^{2} – 50^{2}) = 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

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