Driving the Perfect Curve: Maximum Speed on a Hilltop

AI Thread Summary
The discussion focuses on determining the maximum speed a car can maintain while driving over the top of a hill modeled as a circular arc with a radius of 250 meters. The key point is that the maximum speed occurs when the normal force equals zero, leading to the formula vmax = √(rg), where g represents the acceleration due to gravity. Participants express confidence in this calculation but also reflect on potential oversights or additional considerations. The conversation highlights the importance of understanding the physics involved in maintaining traction and safety at high speeds. Overall, the calculations and reasoning presented appear sound for the scenario described.
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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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