Need Help- Centripetal plane problem

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    Centripetal Plane
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SUMMARY

An airplane flying in a horizontal circle at a speed of 420 km/h with wings tilted at 35° requires a radius of 2421.59 meters for its circular path. The calculations utilize the equations of motion, specifically a = v²/r and the force components of lift, where Fc = Fnsin35°. The conversion of speed from km/h to m/s is essential, resulting in 116.67 m/s for accurate calculations.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Familiarity with forces acting on an airplane
  • Knowledge of trigonometric functions, particularly sine
  • Ability to convert units from km/h to m/s
NEXT STEPS
  • Study the principles of centripetal acceleration in circular motion
  • Learn about aerodynamic lift and its role in flight mechanics
  • Explore the application of free body diagrams in physics problems
  • Investigate the effects of wing tilt on flight dynamics
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Aerospace engineers, physics students, and anyone interested in understanding the mechanics of flight and circular motion dynamics.

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Homework Statement


An airplane is flying in a horizontal circle at a speed of 420 km/h. If the wings of the plane are tilted 35° 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.



Homework Equations



a=v^2/r
Fc = Fnsin35°

The Attempt at a Solution


So first i looked at what was given:
V= 420 km/h = 116.67 m/s
r= ?

Since i know that the plane wings are tilted 35° to the horizontal, i broke the Fn into two parts the Fn pointing towards the centre of the circle being Fnsin35°

So:
Fc= Fnsin35°
ma=mgsin35°
a=gsin35°
(v^2/r) = gsin35°
(116.67m/s^2)^2/(9.8m/s^2)(sin35°)=r
r=2421.59 m
 
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Lolagoeslala said:

Homework Statement


An airplane is flying in a horizontal circle at a speed of 420 km/h. If the wings of the plane are tilted 35° 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.

Homework Equations



a=v^2/r
Fc = Fnsin35°

The Attempt at a Solution


So first i looked at what was given:
V= 420 km/h = 116.67 m/s
r= ?

Since i know that the plane wings are tilted 35° to the horizontal, i broke the Fn into two parts the Fn pointing towards the centre of the circle being Fnsin35°

So:
Fc= Fnsin35°
ma=mgsin35°
a=gsin35°
(v^2/r) = gsin35°
(116.67m/s^2)^2/(9.8m/s^2)(sin35°)=r
r=2421.59 m
Start by drawing a free body diagram for the airplane.
 
SammyS said:
Start by drawing a free body diagram for the airplane.

i did this is it...

http://s1176.beta.photobucket.com/user/LolaGoesLala/media/fff.jpg.html
 

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