Uniform Circular Motion A Jet Pilot

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SUMMARY

The discussion focuses on calculating the minimum radius of a vertical loop for a jet pilot flying at a speed of 840 km/h (233.33 m/s) while ensuring that the centripetal acceleration does not exceed 6.0 g's (58.8 m/s²). The correct formula for centripetal acceleration, a = (v²)/r, is applied to derive the radius. The accurate calculation yields a radius of 925.90 m, confirming that this value is significantly more plausible than the alternative calculation of 14.82 m, which is incorrect.

PREREQUISITES
  • Understanding of uniform circular motion principles
  • Knowledge of centripetal acceleration and its formula
  • Familiarity with unit conversions (km/h to m/s)
  • Basic algebra for solving equations
NEXT STEPS
  • Study the physics of centripetal force in circular motion
  • Learn about the effects of gravitational acceleration on motion
  • Explore advanced topics in dynamics related to aircraft maneuvers
  • Investigate the implications of g-forces on pilot health and performance
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Aerospace engineers, physics students, and aviation professionals interested in the dynamics of flight and the effects of acceleration on aircraft performance.

Brenwells
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Uniform Circular Motion "A Jet Pilot"

Hi, my apologies if this has been posted before. I was just wondering if someone could help look over this question for me and confirm if I did it correct or not. It is a written homework rather than online so I can't check my answer to see if I did it correctly.

A jet pilot takes his aircraft in a vertical loop. (a) If the jet is moving at a speed of 840km/h at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g's.

840km/h = 233.33 m/s
6g = (6*9.80) = 58.8m/s^2

Equation used a=(v^2)/r

but I continue to get confused between which is velocity and acceleration.

Would I have

r=(233.33^2)/58.8
r=925.90m

or

r=(58.8^2)/233.33
r=14.82m

which the first answer of 925.90m sounds a lot more correct than 14.82 but I just wanted to make sure. If someone could please confirm that would be great.

Thank you
 
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Velocity has units of m/s

Acceleration has units of m/s^2
 

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