Minimum coefficient of friction to keep cars from sliding off the road

AI Thread Summary
To determine the minimum coefficient of friction required to prevent cars from sliding off a banked curve designed for 61 km/h while traveling at 44 km/h, the relevant equations include the frictional force and centripetal force. The angle of the banked curve is calculated using the formula tan(θ) = v²/(gR), resulting in an angle of approximately 4.32°. A diagram illustrating the forces acting on the car is essential for visualizing the problem. The discussion emphasizes the importance of understanding the forces at play and applying the correct physics principles to find the solution. Calculating the minimum coefficient of friction is crucial for safe driving conditions on wet roads.
rockchalk1312
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A banked circular highway curve is designed for traffic moving at 61 km/h. The radius of the curve is 201 m. Traffic is moving along the highway at 44 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to take the turn without sliding off the road? (Assume the cars do not have negative lift.)


Fk=ukFn
Fs, max=usFn
F=mv^2/R


Honestly no idea at how to attempt it. Although I did find that θ needed to be:
tanθ=v^2/gR
tanθ=12.2^2/(9.8)(201)
θ=4.32°

Thank you for any help!
 
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As always, the first step is to draw a diagram showing all the forces acting on the car.
 
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