Questions: An airplane flies on a level path. There is a pressure difference of 581 Pa between the lower and upper surfaces of the wings. The area of each wing surface is about 100 m^2. The air moves below the wings at a speed of 80.5 m / s. Estimate the weight of the plane.

Solution Steps

We need to estimate the weight of the airplane using the given pressure difference between the lower and upper surfaces of the wings, the area of each wing, and the speed of air below the wings. The pressure difference provides the lift force per unit area, and the total lift force can be used to estimate the weight of the airplane.

The lift force \( F_L \) can be calculated using the pressure difference \( \Delta P \) and the area \( A \) of the wings. The formula for lift force is:

\[ F_L = \Delta P \times A \]

Given:

• Pressure difference, \( \Delta P = 581 \, \text{Pa} \)
• Area of each wing, \( A = 100 \, \text{m}^2 \)

The total area for both wings is \( 2 \times 100 = 200 \, \text{m}^2 \).

Substituting the values:

\[ F_L = 581 \, \text{Pa} \times 200 \, \text{m}^2 = 116200 \, \text{N} \]

The lift force \( F_L \) is equal to the weight of the airplane when it is flying on a level path. Therefore, the weight \( W \) of the airplane is:

\[ W = F_L = 116200 \, \text{N} \]

Final Answer