Curved portions of highways are always banked (tilted) to prevent cars from sliding off the highway. When a highway is dry, the frictional force between the tires and the road surface may be enough to prevent sliding. When the high- way is wet, however, the frictional force may be negligible, and banking is then essential. Figure 6-1la represents a car of mass m as it moves at a constant speed v of 20 m/s around a banked circular track of radius R 190 m. (It is a normal car, rather than a race car, which means any verti- cal force from the passing air is negligible.) If the frictional force from the track is negligible, what bank angle o pre- vents sliding? The toward-the- center force is due to the tilted track. (a) Tited normal force supports car and provides the toward the-center force. KEY IDEAS Here the track is banked so as to tilt the normal force Fy on the car toward the center of the circle (Fig, 6-11b). Thus, F now has a centripetal component of magnitude F inward along a radial axis r. We want to find the value of the bank angle @ such that this centripetal component keeps the car on the circular track without need of friction. Car directed Track-level view of the forces The gravitational force pula car downward

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