Roadway Banked at Any Angle (advanced)

We will now explore the more difficult case of a car turning a corner that is banked at an angle between 0^o and 90^o Let's begin by recapping what we learned earlier:

1. for a bank angle of 0^o, the Force of Friction provides the inward force needed to push the car around the corner
2. for a bank angle of 90^o the Normal Force provides the inward force

It is reasonable to suspect that for an angle between these two extremes both the Normal Force and the Frictional Force will contribute to the inward force. Let's confirm this by putting the road at an intermediate angle and then toggle free-body diagram and components options. Adjust the angle and notice how the Normal and Frictional Forces and their components behave.

Discussion

Set the bank angle at 45^o , the coefficient of fiction as 0.8 and display the FBD and components. Note carefully what happens to the Frictional force, its direction and the size of its components as you adjust the velocity of the car. Why does it behave this way?