Question

The velocities of air above and below the surfaces of a flying aeroplane wing are 50 m/s and 40 m/s respectively. If the area of the wing is 10 m² and the mass of the aeroplane is 500 kg, then as time passes by (density of air = 1.3 kg/m³), the aeroplane will: 

• A. the aeroplane will gain altitude
• B. the aeroplane will experience weightlessness
• C. the aeroplane will fly horizontally
• D. the aeroplane will lose altitude

Hint:

For aerodynamics problems, Bernoulli’s principle can be used to determine lift force. If lift force exceeds the weight of an object, it gains altitude.

Answer 1

The Correct Option is A

Step 1: Applying Bernoulli’s Theorem According to Bernoulli’s principle, the pressure difference between the upper and lower surfaces of the wing is given by: \[ P_{\text{lower}} - P_{\text{upper}} = \frac{1}{2} \rho \left( v_{\text{upper}}^2 - v_{\text{lower}}^2 \right) \] where: - \( \rho = 1.3 \) kg/m³ (density of air), - \( v_{\text{upper}} = 50 \) m/s, - \( v_{\text{lower}} = 40 \) m/s. 

Step 2: Calculating the Lift Force The lift force \( F_L \) is given by: \[ F_L = (P_{\text{lower}} - P_{\text{upper}}) A \] \[ = \frac{1}{2} \times 1.3 \times (50^2 - 40^2) \times 10 \] \[ = \frac{1}{2} \times 1.3 \times (2500 - 1600) \times 10 \] \[ = \frac{1}{2} \times 1.3 \times 900 \times 10 \] \[ = \frac{1}{2} \times 1.3 \times 9000 \] \[ = 5850 \text{ N} \] 

Step 3: Comparing with the Weight of the Aeroplane The weight of the aeroplane: \[ W = mg = 500 \times 9.8 = 4900 \text{ N} \] Since \( F_L>W \), the lift force is greater than the weight, meaning the aeroplane will gain altitude. Thus, the correct answer is: \[ \mathbf{the\ aeroplane\ will\ gain\ altitude} \]