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?
1.The horizontal component, FNsinθ of the normal force.
2.The vertical component, FNcosθ of the normal force.
3.The weight, mg, of the car.
4.Both the normal force, FN, and the weight, mg, of the car.
5. The normal force, FN.
2. the vertical component
The force that provides the centripetal force keeping the car moving on the circular path is the horizontal component of the normal force, FNsinθ.
To understand why, we need to consider the forces acting on the car. In this situation, there are two forces: the weight of the car, mg, acting vertically downwards, and the normal force, FN, exerted by the road perpendicular to the surface.
When a car is on a banked turn, the road is angled or banked, typically at an angle θ, to help with the turning motion. In this case, the normal force can be resolved into two components: the vertical component, FNcosθ, and the horizontal component, FNsinθ.
The weight of the car, mg, acts vertically downward and is balanced by the vertical component of the normal force, FNcosθ.
However, to keep the car moving in a circular path, a centripetal force is required. The centripetal force is directed towards the center of the circular path and is responsible for the car's inward acceleration.
In this case, the horizontal component of the normal force, FNsinθ, provides the centripetal force. It acts inward, towards the center of the circular path, and balances the car's outward force caused by its inertia.
Therefore, the correct answer is 1. The horizontal component, FNsinθ, of the normal force.