Max Speed to Maintain Road Contact over Bump

AI Thread Summary
The discussion centers on determining the maximum speed a car can travel over a bump without losing road contact. Key factors include the bump's radius of 66.7 meters, the car's speed of 16.4 m/s, and the passenger's weight of 57 kg, which results in an apparent weight of 329.3 N at the bump's peak. The forces acting on the car include gravity and the normal force, with the normal force becoming zero when contact is lost. To maintain contact, the car must adhere to Newton's 2nd law and principles of circular motion, indicating that only gravity would act on the car if it loses contact. Understanding these dynamics is crucial for calculating the safe speed over the bump.
Lnav1982
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I am having a hard time trying to figure out this problem:
What is the max speed that you can drive the car over the top of the bump without losing contact with the road. I have the radius= 66.7 m, constant speed of car = 16.4m/s, and weight of your passenger=57.0kg. With these numbers I was able to find the apparent weight of passenger as you pass over the top of the bump= 329.3 N. I just don't know how to find the speed need to not lose contact. Some one please help. Thanks a lot!
 
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What forces act on the car as it passes the top of the bump? What forces act if it loses contact? Is the car accelerating? How would you apply Newton's 2nd law to the car?
 
The forces are force from the bump? Normal force? If it loses contact wouldn't gravity act on the car? The car is accelerating.
 
There are two forces acting on the car: gravity and the normal force. At the point where the car just loses contact with the road, the normal force goes to zero so only gravity is left to hold the car onto the road. Now apply Newton's 2nd law and what you know about circular motion.
 

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