A car is rounding a circular curve of radius r on a banked turn. As the drawing indicates, there are two forces acting on the car, its weight mg and the normal force FN exerted on it by the road. Which force, or force component, provides the centripetal force that keeps the car moving on the circular path?
Horizontal component of the normal force.
Yes
The force that provides the centripetal force to keep the car moving on the circular path is the friction force between the tires of the car and the road surface.
The force that provides the centripetal force to keep the car moving on the circular path is the frictional force acting on the car. To understand why, let's break down the forces acting on the car.
In a banked turn, the road is inclined at an angle θ with respect to the horizontal. The two forces acting on the car are the weight force (mg) and the normal force (FN) exerted by the road. The weight force is always directed vertically downward, while the normal force is perpendicular to the incline of the road.
To determine which force provides the centripetal force, let's consider the horizontal forces acting on the car. There are two components of the normal force: one that acts perpendicular to the incline (FN⊥) and one that acts parallel to the incline (FN∥). Only the parallel component of the normal force can provide the centripetal force.
Using trigonometry, we can decompose the weight force into two components: one that acts perpendicular to the incline (mg⊥) and one that acts parallel to the incline (mg∥). The component mg⊥ is balanced by the perpendicular component of the normal force (FN⊥), which cancels out the weight's effect in the perpendicular direction.
The remaining force in the horizontal direction is the frictional force (f). The frictional force opposes the motion of the car and provides the necessary centripetal force to keep the car moving on the circular path. The frictional force arises due to the contact between the car's tires and the road surface.
In summary, it is the frictional force acting parallel to the incline (mg∥ - FN∥) that provides the centripetal force, allowing the car to successfully navigate the banked turn.