### Banked With No Friction

At the Indianapolis Motor Speedway there are 4 turns that have the tracked banked at nine and twelve degrees. Compared to a flat track, inclined edges add an additional force that keeps the cars on their path. This force prevents the cars from being pulled towards the center or pushed out.

#### Why It Matters

- When a car is driving on a flat surface in a straight line, the following 4 forces are acting on it:
- The weight of the car.
- The normal force.
- The force applied by the tires.
- The frictional force.

- These 4 forces keep the car moving in a straight line. There are no forces that are perpendicular to the other two forces that would allow the car to turn in a circular path.
- If a car is on a banked turn, centripetal force is an additional force on the car. Usually the normal force just has a vertical component, but in the case of a banked curve it has both a vertical and a horizontal component. In the case where friction exists, it must be added to the horizontal normal component since the frictional force points towards the center of the arc.
- Watch what happens when friction does not exist:

http://www.youtube.com/watch?v=ZwqLLpNuAQU

#### What Do You Think?

Using the information provided above, answer the following questions.

- The equation for the maximum velocity of a car on a banked curve is given as: \begin{align*}v=\sqrt{\frac{rg(\tan \theta - \mu_{s})}{1+\mu_{s} \tan \theta}}\end{align*}
v=rg(tanθ−μs)1+μstanθ−−−−−−−−−−−−√ . What does this equation simplify to when there is no banked corner? - Why does the normal force have a horizontal component when the car is on a banked curve?
- What does the equation for the maximum velocity of a car on a banked curve simplify to when there is no friction?