A speed of wind over the wings of a small aeroplane is 70 m/s and below the wings is 60 m/s. If the mass of the aeroplane is 1000 kg and the area of wing is 14 m 2 , then the net vertical force on the

Question

A speed of wind over the wings of a small aeroplane is 70 m/s and below the wings is 60 m/s. If the mass of the aeroplane is 1000 kg and the area of wing is 14 m 2 , then the net vertical force on the aeroplane will be (density of air = 1.2 kg/m 3 and g = 10 m/s 2 )

TestHub · Accepted Answer

Using Bernoulli's principle, the pressure difference between the lower and upper surfaces of the wings is given by

$Δ P = \frac{1}{2} ρ (v_{1}^{2} - v_{2}^{2})$

The upward lift force on the aeroplane is

$F_{L} = Δ P \times A = \frac{1}{2} ρ A (v_{1}^{2} - v_{2}^{2})$

Substituting the given values:

$F_{L} = \frac{1}{2} \times 1.2 \times 14 \times (7 0^{2} - 6 0^{2})$

$F_{L} = 8.4 \times (4900 - 3600) = 8.4 \times 1300 = 10920$ N

The downward gravitational force (weight) on the aeroplane is

$W = m g = 1000 \times 10 = 10000$ N

The net vertical force on the aeroplane is

$F_{n e t} = F_{L} - W = 10920 - 10000 = 920$ N

Since the lift force is greater than the weight, the net force is $920$ N upwards.

Answer: $920$ N upwards

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