Question

A jet airplane is in level flight. The mass of the airplane is m = 8930 kg. The airplane travels at a constant speed around a

circular path of radius R = 8.01 mi and makes one revolution every T = 0.106 h. Given that the lift force acts perpendicularly
upward from the plane defined by the wings, what is the magnitude of the lift force acting on the airplane?
At what angle is the airplane banked?

Answer 1

Step-by-step explanation:

The lift force will have a vertical component equal to the weight of the plane and a horizontal component sufficient to supply the needed centripetal accleration.

R = 8.01 mi = 12891 m

ω = 2π/T = 2π/(0.106(3600)) = 0.016465 rad/s

F = m√(g² + (ω²R)²)

F = 8930√(9.81² + (0.016465²(12891))²)

F = 8930√(9.81² + 3.49²)

F = 92,996.480...

F = 93.0 kN

θ = arctan(3.49/9.81) = 19.6°