Question

An airplane is flying in a horizontal circle at a speed of 440 km/h (see the figure). If its wings are tilted at an angle θ = 37.0° to the horizontal, what is the radius of the circle in which the plane is flying? Assume that the required force is provided entirely by an "aerodynamic lift" that is perpendicular to the wing surface. Use g = 9.81 m/s².

          An airplane is flying in a horizontal circle at a speed of 440 km/h (see the figure). If its wings are tilted at an angle θ = 37.0° to the horizontal, what is the radius of the circle in which the plane is flying? Assume that the required force is provided entirely by an "aerodynamic lift" that is perpendicular to the wing surface. Use g = 9.81 m/s².
        
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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An airplane is flying in a horizontal circle at a speed of 440 km/h (see the figure). If its wings are tilted at an angle θ = 37.0° to the horizontal, what is the radius of the circle in which the plane is flying? Assume that the required force is provided entirely by an "aerodynamic lift" that is perpendicular to the wing surface. Use g = 9.81 m/s².
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Transcript

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00:01 All right, so let's say we have an airplane, and this is our plane.
00:06 It has like propellers or something like this.
00:08 And we're told that it's flying at a speed of 440 kilometers an hour, and its wings are tilted relative to the horizontal at an angle of 37 degrees.
00:20 So we want to know what is the radius of the circle here.
00:24 So the lift force, presumably, we're told, acts perpendicular to the wing.
00:28 So we'll call this fl.
00:29 And then of course the weight acts this way and then our centripetal force acts this way.
00:37 So if we look at it, all right, so the centripetal force times the sine of theta should equal our lift force.
00:51 And then if we also note that the, let's call it's angle phi...
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