A plane is in level flight at constant speed and each of its two wings has an area of 40 m². If the speed of the air is 180 km / h over the lower wing surface and 252 km / h over the upper wing surface, the mass of the plane is ___________ kg.
(Take air density to be 1 kg m⁻³ and g=10 ms⁻² )

Solution

Physics sir · 4 steps

Faster air on top means lower pressure there; that pressure gap times the total wing area holds the plane up.

1. Convert speeds. Multiply km/h by 5/18 to get m/s. Below the wing: 180 × 5/18 = 50 m s⁻¹. Above the wing: 252 × 5/18 = 70 m s⁻¹.
2. Pressure difference. The two surfaces are at almost the same height, so Bernoulli's theorem links pressure and speed only. Faster air above the wing means lower pressure above it.

   P_(lower) - Pᵤₚₚₑᵣ = 1/2ρ(vᵤₚₚₑᵣ² - v_(lower)²) = 1/2(1)(70² - 50²) = 1200 Pa

3. Lift equals weight. There are two wings, so the total area is 2 × 40 = 80 m². Lift is 1200 × 80 = 96000 N. In level flight at constant speed, lift balances the weight mg.
4. So. m = 96000/10 = 9600 kg, so the mass of the plane is 9600.

The common slip: 4800. Using the area of only one wing, 40 m², gives 4800 kg. The question gives the area of each of the two wings, so the total is 80 m².

The idea to keep. For lift problems, find the pressure gap from 1/2ρ(v₁² - v₂²), multiply by the full wing area, and set it equal to mg. Convert speeds to m/s first.

Answer from the NTA final answer key. Solution by PrepWiser.