Question

current attempt in progress
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 (f_n) exerted on it by the road. which force, or force component, provides the centripetal force that keeps the car moving on the circular path?

the weight, mg, of the car.
the vertical component, (f_ncos\theta) of the normal force.
the normal force, (f_n).
the horizontal component, (f_nsin\theta) of the normal force.
both the normal force, (f_n), and the weight, mg, of the car.

Explanation:

Centripetal force acts towards the center of the circular path. The weight \(mg\) acts vertically downwards and has no horizontal - component towards the center in this case. The normal force \(F_N\) on a banked turn has a horizontal component \(F_N\sin\theta\) which is directed towards the center of the circular path and provides the centripetal force for the car's circular motion.

Answer:

The horizontal component, \(F_N\sin\theta\) of the normal force.