a) An airplane of mass 17700 kg is flying in a straight line at a constant altit

Question

a) An airplane of mass 17700 kg is flying in a straight line at a constant altitude and with a speed of 580.0 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.

b) To change the direction of the plane, its wings are banked. If the wings of the plane are banked 25.0° to the horizontal, what is the radius of the circle in which the plane will be flying? Assume that the speed remains 580.0 km/hr during the turn and that the magnitude of the lift provided by the wings is unchanged.

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

Show all calculations. Round to 4 decimal places if possible.

Explanation / Answer

Here ,

mass of airplane , m = 17700 Kg

magnitude of lift force = m* g

magnitude of lift force = 17700 * 9.8

magnitude of lift force = 1.734 *10^5 N

b)

speed of plane , v = 580 km/hr

v = 259.2 m/s

let the radius of plane is r

m *v^2/r = 1.734 *10^5 * cos(25)

17700 * 259.2^2/r = 1.734 *10^5 * cos(25)

solving for r

r = 7567 m

the radius of the circle is 7567 m

c)

let the vertical acceelration is a

m * a = m * g - F * sin(25)

17700 * a= 17700 * 9.8 - 1.734 *10^5 * sin(25)

a = 5.6597 m/s^2 in downawards direction

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