Chapter 20, Problem 65A

How many newtons of lift are exerted on the wings of an airplane that have a total area of $100m^2$ when the difference in air pressure below and above the wings is 5% of atmospheric pressure?

To determine

Force exerted on the wings of airplane.

Answer to Problem 65A

Force exerted on the wings, $F=5\times {10}^5\text{N}$

Explanation of Solution

Given:

Area of wing, $A=100{\text{m}}^2$

Difference in air pressure below and above wings is 5% of atmospheric pressure.

Formula Used:

The pressure is given as,

  $P=\frac{F}{A}$

Where, $F$ is force and $A$ is area in contact.

Calculation:

Since the atmospheric pressure is ${10}^5{\text{N/m}}^2$

So, the pressure on the wing is

  $P=\left(0.05\times {10}^5\right){\text{N/m}}^2$

Putting the values in formula,

  $\begin{array}{l}\left(0.05\times {10}^5\right){\text{N/m}}^2=\frac{F}{100{\text{m}}^2}\\ \Rightarrow F=5\times {10}^5\text{N}\end{array}$

Conclusion:

Therefore, the lift exerted on the wings of an airplane is $F=5\times {10}^5\text{N}$ .