Roads are banked to allow cars to safely follow curves at high speed without slipping, even if the static friction of the tires is reduced (due to water, ice, or oil on the road surface). A free-body diagram of a car moving along a banked curve is shown at left (the car is coming toward us). Suppose a car with mass 1250 kg is driven on a road banked at angle theta space equals 30.0 degrees as the road curves with a radius of curvature of 149 m. The acceleration due to gravity is 9.80 N/kg. Neglecting friction, the vertical component of the normal force balances the car's weight M g so the normal force N space equals space fraction numerator M g over denominator cos space theta end fraction. Also, again neglecting friction, the horizontal component of the normal force provides a centripetal force of N sin space theta for the car. Combining these ideas gives us a way to calculate the maximum centripetal force and acceleration (without friction), so we can estimate a maximum rated speed (given in m/s with appropriate signficant figures) for the curve of:
