An airplane of mass 18700 kg is flying in a straight line at a constant altitude
ID: 1596782 • Letter: A
Question
An airplane of mass 18700 kg is flying in a straight line at a constant altitude and with a speed of 690.0 km/hr. The force that keeps the airplane in the air is provided entirely by the aerodynamic life generated by the wings. The direction of this force is perpendicular to the wing surface. Calculate the magnitude of the life generated by the wings of this airplane. (answer is 1.83 x 10^5 N).
To change the direction of the plan, its wings are banked. If the wings fo the plane are banked 42.5 deg to the horizontal, what is the radius of the circle in which the plane will be flying? Assume that speed remains 690.0 km/hr during the turn and that the magnitude of the lift provided by the wings is unchanged. (answer is 5558 m).
What is the magnitude of the vertical acceleration that the airplane as a result of the turn?
Explanation / Answer
v = 690 km/h = 191.7 m/s
m = 18700 kg
F = mg =18700*9.8
F = 1.83*10^5 N
theta = 42.5 degrees
the life provide a cetripetal force of
Fc =1.83*10^5*sin(42.5) = 123633 N
Fc = mv^2/r
123633 = 18700*191.7^2/r
r =5558 m
a = F/m
a = (1.83*10^5*cos(42.5))/18700
a = 7.215 m/s^2 upward due to the wing lift, but gravity wants to accelerate it downward at 9.81 m/s²
the net acceleration is
9.81 - 7.215 = 2.6 m/s^2 downward