Final answer:
In a car coasting at a constant speed over a circular hill, the weight and normal force exerted by the road combine to provide the necessary centripetal force for circular motion, given by mv²/r, ensuring the car follows the curved path.
Step-by-step explanation:
A car coasting at a constant speed over a circular hill is subject to various forces. The forces acting on the car in such a scenario are its weight, directed towards the center of the Earth, and the normal force from the surface of the hill, which is perpendicular to the surface.
In the scenario of a car coasting at a constant speed over a circular hill, several forces are acting on the car. Weight: The force of gravity acting downward on the car's mass. Normal force: The force exerted by the road perpendicular to the car's motion, which counters the weight. Friction force: The force opposing the car's motion, which comes mainly from the tires interacting with the road surface. Centripetal force: The force pointing towards the center of the car's circular path, necessary to keep the car moving in a curved trajectory.
On a frictionless banked curve, these two forces combine to provide the necessary centripetal force for the car to move in a circular path without slipping or losing traction. This centripetal force is horizontal and points toward the center of the circular path, which is required for maintaining the car's circular motion at a constant speed. The magnitude of this force can be represented by the formula mv²/r, where 'm' is the mass of the car, 'v' is its velocity, and 'r' is the radius of the circular path.