Final answer:
The frictional force between the car's tires and the road provides the necessary centripetal force to keep a car in circular motion on an un-banked road. In the case of a frictionless banked curve, the normal force can provide the centripetal component.
Step-by-step explanation:
The force that keeps a car in circular motion while traveling an un-banked curved road at a constant speed is the frictional force between the car's tires and the road. This force acts horizontally toward the center of the circular path, providing the necessary centripetal force that allows the car to stay on the curved path. In the context of a frictionless banked curve, the normal force exerted by the road has a component that provides the centripetal force for circular motion. However, in a usual real-world scenario on a flat road, friction is the primary source of the centripetal force.
When analyzing such a scenario using a free-body diagram, only the frictional force (or in the special case of a banked curve, the horizontal component of the normal force) has a horizontal component which equals the centripetal force required for circular motion, as represented by the equation mv²/r, where 'm' is the mass of the car, 'v' is its speed, and 'r' is the radius of the circular path.