Banked Curve Problem: Find Radius with Friction Coefficients

[M1ZeN]

Homework Statement

A car approaches a curve that is banked at 20 degrees. The minimum speed for the curve is 20 m/s. The car's mass is 1000 kg. What is the radius of the curve if the coefficient of kinetic friction is 0.5 and the coefficient of static friction is 1.0?

Homework Equations

I really don't know how to set up an equation for this problem. I understand that there are three forces acting upon the car, static friction, kinetic friction and force of gravity.

The Attempt at a Solution

I understand that the coefficients both are interpreted to be:

(vector)fk = u(k)N
(vector)fs = u(s)N
(vector)Fg = mg

 

[Delphi51]

There are a couple of ways of looking at a banked curve problem, one using centripetal force and one using centrifugal force. I prefer the latter. Sketch your car on the slope and show the centrifugal force horizontally and outward. Gravity downward. Write expressions for the components of each that are parallel to the slope and straight into the slope. Then you can calculate the friction force.

 

[M1ZeN]

There are a couple of ways of looking at a banked curve problem, one using centripetal force and one using centrifugal force. I prefer the latter. Sketch your car on the slope and show the centrifugal force horizontally and outward. Gravity downward. Write expressions for the components of each that are parallel to the slope and straight into the slope. Then you can calculate the friction force.

I graphed everything out and fully understand where all the friction forces are. I'm still confused on how to interpret the coefficients in with a working mathematical equation.

 

[Delphi51]

At the "minimum speed" the parallel component of centrifugal force + friction just prevent the parallel gravity component from making the car slide down the slope.
At the "maximum speed" gravity + friction just prevent the centrifugal force from making the car slide up the slope.

The kinetic friction only comes into play when the car starts to slip. And it is less than the static friction so once it starts to slip, it will slip right off the road.