Question

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 vertical component, FNcosθ of the normal force.
2. The horizontal component, FNsinθ of the normal force.
3. Both the normal force, FN, and the weight, mg, of the car.
4. The normal force, FN.
5. The weight, mg, of the car.
6. The horizontal component, FNsinθ of the norma.l

Answer 1

The horizontal component of the normal force, represented as FNsinθ, provides the centripetal force necessary for a car to round a circular curve on a banked turn without friction.

Step-by-step explanation:

When a car is rounding a circular curve on a banked turn, the force that provides the centripetal force necessary to keep the car moving on the circular path is the horizontal component of the normal force exerted on it by the road. This can be represented as FNsinθ, where θ is the banking angle. The weight of the car, mg, acts vertically downwards and does not contribute to the centripetal force in this ideal frictionless scenario. For ideal banking, where the angle is perfect for the speed and radius of the turn, the net external force equals the horizontal centripetal force required for circular motion. Therefore, the horizontal component of the normal force is the only force component that acts towards the center of the curvature, providing the centripetal acceleration.