Driving the Perfect Curve: Maximum Speed on a Hilltop

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SUMMARY

The discussion centers on calculating the maximum speed a car can achieve while driving over the top of a hill modeled as a circular arc with a radius of 250 meters. The critical formula established is vmax = √(rg), where g represents the acceleration due to gravity. The conclusion is that the maximum speed occurs when the normal force equals zero, indicating that the car is on the verge of losing contact with the road. No additional factors or considerations were identified as necessary for this calculation.

PREREQUISITES
  • Understanding of basic physics concepts, particularly forces and motion.
  • Familiarity with circular motion dynamics.
  • Knowledge of the formula for centripetal acceleration.
  • Basic algebra for manipulating equations.
NEXT STEPS
  • Explore the implications of varying the radius on maximum speed in circular motion.
  • Study the effects of friction and incline on vehicle dynamics.
  • Learn about the role of centripetal force in maintaining vehicle stability on curves.
  • Investigate real-world applications of these principles in automotive engineering.
USEFUL FOR

Physics students, automotive engineers, and anyone interested in vehicle dynamics and safety on curved roads.

DBaima22
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A person drives a car over the top of a hill, the cross section of which can be approximated by a circle of radius r=250m. What is the greatest speed at which he can drive without the car leaving the road at the top of the hill?

I know that the maximum speed occurs when the normal force= zero. And by my calculations vmax=√rg (where r is the radius and g is the acceleration of gravity)

Is this all I need? Am I missing anything?
 
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Seems ok to me. What to you think you might be missing?
 
I didn't think there was anything missing, this is just me being paranoid I guess. Thank you
 

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