Question

The velocity of air over the upper surface of the wing of an airplane is $40m/s$ and that on the lower surface is $30m/s$. If the area of the wing is $5m^2$ and the mass of the wing is $300kg$, the net force acting on the wing is (Density of air $=1.3kg/m^3$ and $g=10m/s^2$)

• A. $725N$ downward
• B. $725N$ upward
• C. $2275N$ upward
• D. $2275N$ downward

Answer 1

The correct option is A $725N$ downward

REF.Image

Consider the wing be of negligible height.

From Bernoulli's equation;

pressure develop across top & bottom of the wing is:

$P=\frac{1}{2}P(V_1^2-V_2^2)$

$=\frac{1}{2}\times 1.3\times ({40}^2-{30}^2)=455$ Pa

This pressure provides an upthrust F of:

$F=P\times A=455\times 5=2275N$ [A: Area of wing]

Thus Net force on the wing.

$N=Mg-F$

$=300\times 10-2275$

$\Rightarrow N=725N$ (Ans)

[Downward]