Creating Weightlessness in an Airplane: Calculating Flight Path Radius

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SUMMARY

To achieve weightlessness inside an airplane during a wide "outside" loop, the radius of curvature must be calculated based on the aircraft's speed of 749 km/h and the acceleration due to gravity of 9.8 m/s². The necessary radius can be determined using the formula for centripetal acceleration, which equates the gravitational force to the required centripetal force for the given speed. The resulting radius of curvature is approximately 28.5 meters.

PREREQUISITES
  • Understanding of centripetal acceleration
  • Familiarity with basic physics equations
  • Knowledge of units of measurement (meters, seconds)
  • Ability to convert speed from km/h to m/s
NEXT STEPS
  • Learn how to derive the centripetal acceleration formula
  • Study the effects of gravitational force on objects in circular motion
  • Explore the principles of flight dynamics in aviation
  • Investigate the relationship between speed and radius in circular paths
USEFUL FOR

Aerospace engineers, physics students, and aviation enthusiasts interested in the dynamics of flight and the conditions for achieving weightlessness in aircraft.

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Homework Statement


An airplane in a wide "outside" loop can create an apparent zero eight inside the aircraft cabin. What must be the radius of curvature of the flight path for an aircraft moving at 749 km/h to create a condition of weightlessness inside the aircraft? Assume the acceleration of gravity is 9.8 m/s/s. Answer in units of m.


Homework Equations





The Attempt at a Solution

 
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