Question

Airplanes usually use their wings to turn: When the plane is tilted at an angle \thetaθ, the lift (L) from the wings provides a vertical component and a horizontal component. The direction of the lift is in the plane of symmetry of the plane (up from the wings). Suppose that the plane is tilted at an angle \theta = 29.0^{\circ}θ=29.0∘ and that it is making an exactly horizontal, circular path at a uniform speed of 455 \text{ kph}455 kph. Take g = 9.80 \text{ m.s}^{-2}g=9.80 m.s−2 for three significant figures (the value at Sydney).

What is the radius of its turn? _____ km.

Answer 1

-F Weight of plane In the fig... - O Center of turn R Radius of the turn. L = Lift to the plane fc = centrifugal force on plane weight of plane = mg. mass of the. acceleration due to gravity AB= plane tilted at ange o with respect to horizontala m = plane

Given which plane is tilted with respect to the horizontal 29.0 Speed of the plane, u = 455 kbh Angle at we know; 1000 m 1 km = 1 hour = 3600 S 1 km/hr 1ooo mis. 3600 1 kph. looo mis 3600 455 kph 45 S X 1000 OR . V m/s. 3600 = 126. 389 mis. moz Now, REFER TO THE FIGURE The centrifugal force is given by : Fc = -- (6) R Now, from DCOM CP = Fc = CQ= weight mg sino = MQ Fc E = in fig. Lsine 012 = L mg cQ cos - ² mg = L cosa L см tano Dividing us by is L sino using i muz/R Fc mg Lcoso tano mg .2 tano I tano g Rg

Putting values R = (126. 389) (9.80 ) x tan (29-09) R R = 2940.63 2.94063 x 103 m 2-94