Maximum Speed and Banked Turns in Circular Motion

AI Thread Summary
A car driving over a circular hill has a maximum speed determined by the balance of gravitational and centripetal forces, which ensures it remains in contact with the road. For part A, the maximum speed can be derived from the equation a = mv^2 / r, indicating that a larger radius allows for a higher maximum speed. In part B, the car must maintain a specific speed range while navigating a banked turn, factoring in the angle of the bank and the coefficients of friction. The wet road conditions complicate the calculations, requiring consideration of both static and kinetic friction. Understanding the forces at play is crucial for solving these problems effectively.
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Homework Statement



Part A) A car drives over a circular hill (hill radius is r). Is there a maximum speed that the car can have and still remain in contact with the road? If not, why not. If so, find an expression for the maximum speed.

Part B) Now, the car (with mass = 1000kg) enters a circular turn of radius, r=50m. The road is inwardly banked at an angle of 15 degrees. The road is wet so the coefficients of friction are: static u_s = 0.15, kinetic u_k = 0.08, rolling u_r = 0.02. Determine the range for the speed (v_min < v < v_max) that the car must maintain to stay on the circular turn.

Homework Equations



a = mv^2 / r
v = wr

The Attempt at a Solution



Very lost with this problem. I am assuming for part a that there is a maximum speed (this makes sense just thinking about it physically) but I don't know how to find this. I also can deduce that the greater the radius is, the greater the max speed will become. For part b, I tried drawing a free body diagram, but it seems to be in three dimensions because of the bank in the curve and I'm not sure how to account for that. Any help would be appreciated. Thanks.
 
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Please? I could really use some help.
 
Even if it's just A or B?
 

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