
An airplane flies on a level path. There is a pressure difference of 606 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 plane, we can use Bernoulli’s principle and the lift equation. Bernoulli's principle tells us that the pressure difference between the upper and lower surfaces of the wings is due to the difference in airspeed on each side. The lift generated by the wings must balance the weight of the airplane for it to maintain level flight.

### Step-by-step solution:

1. **Given dataTo estimate the weight of the plane, we can use Bernoulli’s principle and the lift equation. Bernoulli's principle tells us that the pressure difference between the upper and lower surfaces of the wings is due to the difference in airspeed on each side. The lift generated by the wings must balance the weight of the airplane for it to maintain level flight.

### Step-by-step solution:

1. **Given **
   - Pressure difference between lower and upper surfaces: \(\Delta P = 606 \, \text{Pa}\)
   - Area of each wing: \(A = 100 \, \text{m}^2\)
   - Speed of air below the wings: \(v_\text{lower} = 80.5 \, \text{m/s}\)

2. **Formula for lift force:**
   The lift force (\(F_{\text{lift}}\)) is given by:
   \[
   F_{\text{lift}} = \Delta P \cdot A
   \]
   where:
   - \(\Delta P\) is the pressure difference.
   - \(A\) is the area of the wings (for both wings, we will double the area since both contribute to lift).

3. **Calculate the lift force:**
   Since both wings contribute equally to lift, we multiply the area by 2:
   \[
   F_{\text{lift}} = \Delta P \cdot (2 \cdot A)
   \]
   Substituting the values:
   \[
   F_{\text{lift}} = 606 \, \text{Pa} \times (2 \times 100 \, \text{m}^2) = 606 \times 200 = 121200 \, \text{N}
   \]

4. **Weight of the airplane:**
   In level flight, the lift force equals the weight of the airplane (\(W = F_{\text{lift}}\)):
   \[
   W = 121200 \, \text{N}
   \]

Thus, the estimated weight of the airplane is **121,200 N**.

### Conclusion:
The weight of the airplane is approximately **121,200 N**.

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Would you like more details on the principles behind this calculation or any other clarifications?

Here are 5 follow-up questions that you might find helpful:
1. How does Bernoulli's principle explain the lift in an airplane wing?
2. What happens if the airspeed below and above the wing becomes equal?
3. How would the weight of the plane change if the pressure difference increased?
4. Why is the pressure lower on the upper surface of the wing than on the lower surface?
5. How do other factors like wing shape or angle of attack affect lift?

**Tip:** In aviation, the weight of an airplane is often measured in newtons (N), which directly reflects the force of gravity acting on the plane. To convert this to mass (in kilograms), you can divide the weight by the acceleration due to gravity (9.8 m/s²).

An airplane flies on a level path. There is a pressure difference of 606 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 Bernoulli's principle, given a pressure difference of 606 Pa, wing area of 100 m², and airspeed below the wings at 80.5 m/s. This detailed solution walks through the lift force calculation step-by-step. Suitable for students in Grades 11-12.

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