Circular turns of radius r in a race track are often banked at an angle to allow the cars to achieve higher speeds around the turns. Assume friction is not present, and use the coordinate system specified.

A)

Find the x component of the normal force F_N on a car going around the turn in terms of the angle and the magnitude of the normal vector F_N.

B)

Now write the magnitude of the normal force again, this time in terms of the gravitational force F_g, g, , the radius of the track r, and the velocity that the car is traveling v.