Question

A plane is in level flight at constant speed and each of its two wings has an area of 25 m2. 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 1 kg m–3).

Answer 1

Here,
area of each wing( A) = 25m²
speed of air over the wing ( V1) = 180km/h = 180 × 5/18 m/s
= 50 m/s

speed of air below the wing ( V2) = 234 km/h = 234× 5/18 m/s
= 65 km/h
density of air ( d ) = 1 kg/m³

Use Bernoulli's theorem ,
P1 + 1/2dV1² = P2 + 1/2dV2²
( P1 - P2) = 1/2 d ( V2² - V1²)
= 1/2 × 1 × { ( 65)² - (50)²}
= 1/2 × 1 × 1725
= 862.5 Pa

So, lifting force = pressure change × area of wings
= ( P1 - P2)× ( A + A) [ two wings in plane ]
= 862.5 × 50

Let m is the mass of the plane ,
Then,
a/c to Newton's 2nd law
mg = 862.5 × 50 [ g = 9.8 m/s²
m = 862.5 × 50 /9.8
= 4400 Kg

Answer 2

Answer:

Explanation:

Hope it help u