Uniform Circular Motion: banked race track circular path

[cle102]

Homework Statement

On a banked race track, the smallest circular path on which cars can move has a radius of 108 m, while the largest has a radius 169 m, as the drawing illustrates (image below). The height of the outer wall is 18 m.

(a) Find the smallest speed at which cars can move on this track without relying on friction.
_____ m/s

(b) Find the largest speed at which cars can move on this track without relying on friction.
______ m/s

Relevant Equations

a=v^2/R
F꜀=(mv^2)/R
μg = v^2/R

Basically, I need help to continue on this question. This is what I have now:

Angle of the race track (angle of the grey part):
tan(18/(169-108)) = 0.30396
Not sure how to continue?? What am I supposed to do and find next?

Thank you in advance!

 

[kuruman]

Assume that the track is frictionless because the problem says "without relying on friction."
Draw a free body diagram (FBD).
Get a relation between the speed and the radius assuming that the car goes around on a horizontal circle.
Solve for v and substitute numbers.

 

[Lnewqban]

Welcome, cle102!
Do you understand all the relevant questions that the problem provides?
What suggests you that the angle that you have calculated is important?

While traveling on a flat curve, some force must make a car turn; otherwise, it would move following a straight line (think of Newton's first law of motion).
That force is normally friction that develops among the road and the tires.

Your problem is telling you that you don't have that friction force in this case (think of a road that is covered by ice).
Since the car is still turning, what other force is producing the same result?
Since the car turns at a constant rate, some balance of forces must be maintained during the time the turning lasts.