Cute.
If there were no friction, then the equation for the angle of banking needed is given by:
g tan@ = V^2 / R
where:
g is the local gravitational constant
V is the velocity
R is it the curve radius
http://www.batesville.k12.in.us/Physics/...
Once we have friction, some of the centripetal force can be provided by the geometry, but some can be provided by friction. Once you have the banking angle, this site gives the equations for the maximum speed (when the car is about to slide up the incline):
http://hyperphysics.phy-astr.gsu.edu/hba...
For the minimum safe speed we have to go slow enough so the car is at the threshold of sliding down the incline. Since the friction is acting in the opposite direction it is as if the sign of coefficient of static friction has changed; so the equations just have two sign reversals:
M V^2 / R = N sin @ - Ks N cos @
0 = N cos @ - Mg + Ks N sin @
So the results for the minimum safe speed can be easily derived from those of the maximum safe speed.
