11.2 Worked Example - Car on a Banked Turn
Let's consider the motion of a car on a circular track, and the track is frictionless. And it's also banked. So this is the overhead view of our circular track. It has radius, r. And here's our car moving at a constant velocity. Now, from the side view when we want to look at that bank turn-- let's draw a side view. So here's our side view, and the car is moving with a velocity into the plane of the figure. Now this surface here is frictionless. And what we'd like to do is find out what speed the car can move such that it doesn't slide up or down the inclined plane. So how should we analyze that? Well our approach will be to apply Newton's second laws. Now what's very important to realize is this is circular motion. And for circular motion we know that the car is accelerating towards the center of the circle. Now from the side view, towards the center of the circle is in this direction. So the car is accelerating radially inward. And th...