An airplane of mass 17000 kg is flying in a straight line at a constant altitude

Question

An airplane of mass 17000 kg is flying in a straight line at a constant altitude and with a speed of 700.0 km/hr. The force that keeps the airplane in the air is provided entirely by the aerodynamic lift generated by the wings. The direction of this force is perpendicular to the wing surface. Calculate the magnitude of the lift generated by the wings of this airplane.

To change the direction of the plane, its wings are banked. If the wings of the plane are banked 30.0° to the horizontal, what is the radius of the circle in which the plane will be flying? Assume that the speed remains 700.0 km/hr during the turn and that the magnitude of the lift provided by the wings is unchanged.

What is the magnitude of the vertical acceleration that the airplane experiences as a result of the turn?

Explanation / Answer

goven,

mass = 17000 kg

velocity = 700 km/h

magnitude of lift generated = weight of the plane

magnitude of lift generated = 17000 * 9.8

magnitude of lift generated = 166600 N

when the plane is turning centripetal force = 166600 * cos(60)

also,

centripetal force = mv^2/r

so,

mv^2 / r = 166600 * cos(60)

17000 * 700^2 / r = 166600 * cos(60)

r = 100000 m

vertical acceleration = 166600 * sin(60) / mass

vertical acceleration = 166600 * sin(60) / 17000

vertical acceleration = 8.487 m/s^2

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