Question

A jet airplane is in level flight. The mass of the airplane is m=8950 kg. The airplane travels at a constant speed around a circular path of radius R=9.33 mi and makes one revolution every T=0.123 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?

Answer 1

Answer:

The net force is 91780.8 N.

Explanation:

mass, m = 8950 kg

Radius, R = 9.33 miles = 15015.2 m

Time, T = 0.123 h = 442.8 s

There are two forces acting on the plane.

Horizontal force is the centripetal force and the vertical force is the weight.

$Fx =m R w^2\\\\Fx = m R \frac{4\pi^2}{T^2}\\\\Fx = 8950\times 15015.2\times \frac{4\times 3.14\times 3.14}{442.8\times 442.8}\\\\Fx = 27030.8 N \\\\Fy = m g \\\\ Fy = 8950\times 9.8 \\\\Fy = 87710 N$

The net force is

$F = \sqrt{Fx^2 + Fy^2}\\\\F = \sqrt {27030.8^2 + 87710^2}\\\\F = 91780.8 N$