# Banked Frictionless Curve with Friction

A car of mass M traveling at speed v enters a banked turn covered with ice. The road is banked at an angle theta, and there is no friction between the road and the car's tires. What is the radius r of the turn (assuming the car continues in uniform circular motion around the turn)? Express the radius in terms of the given quantities and g, the magnitude of the acceleration due to gravity.

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#### Solution Preview

Since the car does not move up or down on the incline, the total force parallel to the incline must be ...

#### Solution Summary

The answer expresses the parameters of the radius r of a banked turn, given the angle theta and the fact there is no friction between the road and the car's tires. Using the magnitude of the acceleration due to gravity, and trigonometry (properties of cosine and tan), the r radius is calculated in terms of the parameters given.