  Question

A plane is in level flight at constant speed and each of its two wings has an area of 25m2. If the speed of the air is 180 km/h over the lower wing and 234 km/h over the upper wing surface, determine the plane’s mass. (Take air density to be 1kgm–3).

Solution

The area of the wings of the plane, A=2×25=50m2 Speed of air over the lower wing, V1 = 180 km/h = 50 m/s Speed of air over the upper wing, V2 = 234 km/h = 65 m/s Density of air, ρ=1kgm–3 Pressure of air over the lower wing =P1 Pressure of air over the upper wing= P2 The upward force on the plane can be obtained using Bernoulli’s equation as: P1+12ρV21=P2+12ρV22P1−P2=12ρ(V22−V21)..............(i) The upward force (F) on the plane can be calculated as: (P1−P2)A =12ρ(V22−V21)A=12×1×((65)2−(50)2)×50=43125N Using Newton’s force equation, we can obtain the mass (m) of the plane as: F=mg ∴m=431259.8 =4400.51 kg ∼4400kg Hence, the mass of the plane is about 4400 kg. PhysicsNCERT TextbookStandard XI

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