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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 1kgm3).


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=1kgm3
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+12ρV22P1P2=12ρ(V22V21)..............(i)
The upward force (F) on the plane can be calculated as:
(P1P2)A
=12ρ(V22V21)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.


Physics
NCERT Textbook
Standard XI

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