An airplane of mass \( m \) is flying in a horizontal circle at an altitude \( h \) above the ground. The point on the ground located directly below the center of the circle is considered the origin of a 3D coordinate system, where the \( +z \)-axis is the line passing through the origin to the center of the circle. The angle between the \( z \)-axis and the dotted line in the figure is \( \alpha \). The airplane experiences a lift force \( \left(\overrightarrow{F_{L}}\right) \) from the air that acts in a direction perpendicular to the dotted line and a downward gravitational force \( (\vec{W}) \). a) Find the radius \( r \) of the horizontal circular path of the object in terms of \( h \) and \( \alpha \). b) Draw the two forces acting on the airplane in the diagram below: c) Using cylindrical coordinates, find the net force \( \overrightarrow{F_{n e t}} \) on the object (with components along \( \widehat{e_{r}}, \widehat{e_{\phi}}, \widehat{e_{z}} \) ).
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We can form a right triangle with \( h \), \( r \), and the hypotenuse (the dotted line in the figure). The angle \( \alpha \) is between the hypotenuse and the vertical side (\( h \)). Show more…
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