Uniform Circular Motion Problem

AI Thread Summary
The discussion centers on solving a uniform circular motion problem involving a banked highway curve designed for vehicles traveling at 93 km/h with a radius of 210 m. The first part of the problem requires determining the correct angle of banking, while the second part seeks the minimum coefficient of friction needed to prevent skidding if the curve is not banked. Participants emphasize understanding the forces acting on a car in motion on a banked curve, particularly the relationship between centripetal acceleration and gravitational forces. There is confusion regarding the use of multiple angles in the equations, specifically the roles of sine and cosine in calculating the forces. Clarifying these concepts is essential for accurately solving the problem.
Gattz
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Homework Statement


A circular curve of highway is designed for traffic moving at 93 km/h. Assume the traffic consists of cars without negative lift. (a) If the radius of the curve is 210 m, what is the correct angle of banking of the road? (b) If the curve were not banked, what would be the minimum coefficient of friction between tires and road that would keep traffic from skidding out of the turn when traveling at 93 km/h?


Homework Equations



a=v2/r

The Attempt at a Solution


I found acceleration to be 3.177 m/s2. Then I tried setting ma to Fnradial, which I got to be mgcostheta * mgsintheta. But there are two thetas.
 
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Wheres the cosine coming from? I think the correct equation should be ma=mgsin(theta)
 
Before trying to directly calculate centripetal acceleration, ask yourself about the forces that act on a car in motion on a banked curve.
 

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