Max Velocity for a Car over a Speed Bump in Uniform Circular Motion

AI Thread Summary
The discussion focuses on determining the maximum speed a car can maintain while passing over a speed bump without losing contact with the road. The key point is that sufficient force is needed to provide the necessary centripetal acceleration at the highest point of the bump. The only downward force acting on the car is gravity, which must be greater than the required centripetal force for the car to stay in contact with the road. The participant concludes that by calculating the maximum velocity where gravitational force exceeds centripetal acceleration, they can solve the problem. This understanding is crucial for modeling particles in uniform circular motion effectively.
astrokat11
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I'm doing problems modeling particles in uniform circular motion and one is about a car going over a speed bump. I figured out the problem, but then it asks "What is the max speed the car can have as it passes this highest point without losing contact with the road?" I'm not sure what this part of the question is asking. Can anyone rephrase it for me or lead me in the right direction? I don't think it's a friction thing since it's not sliding, would this be over coming the maximum radial force?
Thank you
 
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In order to maintain contact with the road as the car goes over the bump there must be enough force to provide the needed centripetal acceleration. The faster you go, the greater the centripetal acceleration and thus the greater force required. What forces act on the car as it goes over the bump? What's the maximum net downward force on the car?
 
Ah, well the only downward force is gravity, so I just need to find the max velocity while mg is greater than the centripetal accel. I think I can figure that out then. Thanks
 

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