A highway curves to the left with radius of curvature of 26m and is banked at 17

Question

A highway curves to the left with radius of curvature of 26m and is banked at 17 degrees so that cars can take this curve at higher speeds. Consider a car of mass 1151 kg whose tires have a static friction coefficient 0.37 against the pavement. How fast can the car take this curve without skidding to the outside of the curve? The acceleration of gravity is 9.8 m/s^2. U (mu )= 0.37 theta = 17 degrees. Answer in units of m/s

Explanation / Answer

v = [r * g * (sin ? + µ * cos ?) ÷ (cos ? – µ * sin ?)]^0.5 =>(sin ? + µ * cos ?) ÷ (cos ? – µ * sin ?) = (sin(Radians(17))+(0.37*cos(Radians(17))))/(cos(Radians(17))-(0.37*sin(Radians(17)))) = 0.761919256 =>v = sqrt(26*9.81*0.761919256) = 13.9404 m/s

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