Uniform circular motion airplane problem

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SUMMARY

The discussion centers on calculating the radius of a circular path for an airplane flying at a speed of 470 km/h with its wings tilted at 40° to the horizontal. The required centripetal force is provided by aerodynamic lift, which is perpendicular to the wing surface. The initial approach involved using the equation F=mv²/r, but the user encountered difficulties in resolving forces and determining the radius. A free body diagram was suggested to clarify the forces acting on the airplane.

PREREQUISITES
  • Understanding of uniform circular motion principles
  • Familiarity with forces acting on an airplane, including aerodynamic lift
  • Knowledge of basic trigonometry, particularly sine functions
  • Proficiency in applying Newton's second law of motion
NEXT STEPS
  • Study the derivation of the centripetal force equation in circular motion
  • Learn how to construct and analyze free body diagrams for aircraft in flight
  • Explore the relationship between lift, weight, and angle of attack in aviation
  • Investigate the effects of speed and tilt angle on the radius of circular flight paths
USEFUL FOR

Aerospace engineering students, physics enthusiasts, and anyone interested in the dynamics of aircraft motion and circular flight analysis.

snoggerT
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An airplane is flying in a horizontal circle at a speed of 470 km/h (Figure 6-39). If its wings are tilted 40° 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.

m



2. F=mv^2/r



I first tried setting F to mgsin40 and solving for r (thinking the m would cancel from both sides of the equation), but that didn't seem to work. So I'm kind of at a standstill not knowing where to go with this problem
 
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Your diagram isn't visible, but I assume you have a problem resolving forces. Can you post your free body diagram here?
 
maverick280857 said:
Your diagram isn't visible, but I assume you have a problem resolving forces. Can you post your free body diagram here?

- I'm not sure how I could draw one out on here (don't have a scanner to scan it either). I guess I could try describing it.

I have r as my horizontal plane with the airplane set 40 degree's from the horizontal. I have mg (unknown) going toward earth. I have a perpendicular to the plane for my "aerodynamic lift" force. Then a force going towards the center.
 

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