When a plane turns, it banks as shown in (Figure 1) to give the wings' lifting...

When a plane turns, it banks as shown in (Figure 1) to give the wings' lifting force F? w a horizontal component that turns the plane.?If a plane is flying level at 870 km/h and the banking angle is not to exceed 50 ?, what's the minimum curvature radius for the turn??

Expert Solution

Solution:

First, the speed of the airplane in SI units is:

870kmh = 870km/h(1000m/1.0km)(1.0h/3600s)
= 241.67m/s

When the aircraft banks the lift force may be broken into horizontal and vertical components. The horizontal component causes centripetal acceleration acting toward the center of the circular path. From Newton’s 2nd law the horizontal forces allow us to write:

?F = mv²/r = Lsin?---------------->(1)

The vertical forces are:

?F = 0 = Lcos? - mg
L = mg/cos?------------------------>(2)

Plugging (2) into (1), we get:

mv²/r = (mg/cos?)sin?

v²/r = gtan?

r = v²/gtan?

= (241.67m/s)² / 9.8mtan50°

= 5000.587m

= 5 km.

I hope you understood the problem, If yes rate me!! or else comment for a better solution.

genius_generous answered 2 years ago

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