How Do You Calculate the Minimum Coefficient of Friction for a Banked Curve?

[nickmai123]

"A banked circular highway curve is designed for traffic moving at 70 km/h. The radius of the curve is 186 m. Traffic is moving along the highway at 35 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to negotiate the turn without sliding off the road?"


$$F_{c}=\frac{mv^{2}}{r}$$

$$v_{unbanked}=\sqrt{ru_{k}g}$$

$$v_{banked}=\sqrt{rgtan\theta}$$


I'm lost. I don't know where to start with this problem. I know how to work the typical banked and unbanked curves, but I don't get how to draw the free-body diagram here.

Thanks.

 

[jgens]

Well, a good place to start this problem is finding an expression for the banking angle (the case without friction). Draw the freebody diagram for this simplified problem and obtain an expression for the banking angle.

Once you've done that, draw the freebody diagram including friction. Note that the only new force acting in this picture is the frictional force and that it acts parallel to the banked surface.