An airplane flies on a level path. There is a pressure difference of 513 Pa between the lower and upper surfaces of the wings. The area of each wing surface is about 100 m2. The air moves below the wings at a speed of 80.5 m/s.

 


Estimate the weight of the plane.

To estimate the weight of the airplane, we can use the concept of lift, which is generated by the pressure difference between the upper and lower surfaces of the wings.

1. **Identify Given Information**:
   - Pressure difference, \( \Delta P = 513 \ \text{Pa} \)
   - Wing area (for each wing surface), \( A = 100 \ \text{m}^2 \)
   - Air speed below wings, \( v_{\text{below}} = 80.5 \ \text{m/s} \)

2. **Calculate Total Lift Force (Using Pressure Difference)**:
   The lift force, \( F_{\text{lift}} \), generated by the pressure difference can be calculated as:
   \[
   F_{\text{lift}} = \Delta P \times A
   \]
   Since there are two wings, the effective area is doubled:
   \[
   F_{\text{lift}} = \Delta P \times (2 \times A)
   \]

   Substituting values:
   \[
   F_{\text{lift}} = 513 \ \text{Pa} \times (2 \times 100 \ \text{m}^2)
   \]
   \[
   F_{\text{lift}} = 513 \times 200 = 102,600 \ \text{N}
   \]

3. **Interpret Lift Force as Weight**:
   For the airplane to maintain a level path, the lift force must equal the airplane's weight. Therefore, the weight \( W \) of the plane is:
   \[
   W = F_{\text{lift}} = 102,600 \ \text{N}
   \]

4. **Final Answer**:
   The estimated weight of the airplane is **102,600 N**.

Would you like further details on this solution, or do you have any questions? Here are some related questions you might find helpful:

1. How is lift calculated in different flying conditions?
2. What happens if the speed below the wings changes?
3. How would varying the wing area affect the airplane's lift?
4. Why does the pressure difference contribute to lift?
5. How can Bernoulli's principle be applied to wing lift?

**Tip:** Lift depends heavily on both wing shape and airspeed – higher speeds generally increase lift for the same pressure difference.

An airplane flies on a level path. There is a pressure difference of 513 Pa between the lower and upper surfaces of the wings. The area of each wing surface is about 100 m2. The air moves below the wings at a speed of 80.5 m/s. Estimate the weight of the plane.

Learn how to estimate the weight of an airplane using pressure difference and wing area. This problem covers key concepts in physics and fluid dynamics, including Bernoulli's Principle and lift force calculations. Suitable for high school students in Grades 10-12.

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