Vertical circle, miminum radius

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SUMMARY

The discussion centers on calculating the maximum radius of a vertical circle for a fighter pilot diving at a maximum supersonic speed of 2170 km/hr, ensuring that her apparent weight does not exceed six times her actual weight. The key equations involved are the relationship between apparent weight (apparent weight = mg + ma) and centripetal acceleration (a_c = V^2/r). By substituting the expression for centripetal acceleration into the apparent weight equation, one can derive the maximum radius of the circle.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with centripetal acceleration concepts
  • Knowledge of the relationship between weight and apparent weight
  • Basic algebra for solving equations
NEXT STEPS
  • Study the derivation of centripetal acceleration formulas
  • Learn about the effects of gravitational forces on apparent weight
  • Explore the dynamics of vertical circular motion in physics
  • Investigate real-world applications of these principles in aviation
USEFUL FOR

Aerospace engineers, physics students, and anyone interested in the dynamics of high-speed flight and circular motion mechanics.

sunnyorange
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This is my question
A fighter pilot dives her fighter plane toward the ground at maximum supersonic speed of 2170 km/hr. She pulls out of the dive on a vertical circle. What is the maximum radius of the circle, so that her apparent weight is never more than six times her weight?

I have no idea how to approach this. However, I know apparent weight= mg+ma, and a_c= V^2/r

Help needed!:eek:
 
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well solve your second eq for a then sub it into your first and have it equal to 6*w
 
mathmike said:
well solve your second eq for a then sub it into your first and have it equal to 6*w

How do I find the centripetal acceleration? radius?
 

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