Why are corners such a problem when driving?

    As I'm sure you are all aware, corners present a large problem when driving in a car. Why is this you might be wondering? There are a few different things that we can look at to analyze why corners are such pain to deal with while driving, especially when you are driving fast. In this section, we are going to discuss some of the ideas and equations behind why a car has more potential to lose control on corners.
            One of the biggest problems with going around a corner is the idea of inertia. The easiest way to rationalize the basic idea of forces while taking a corner is to look at Newtons first law of motion. According to the Physics Classroom website, the simplest way to put Newtons first law is that an object will stay at rest will stay at rest, and one in motion will stay in motion, unless acted upon by an outside force. You can apply this to a corner by saying that a car will want to go straight, but the turning of the tires on the corner cause it to change direction, which means that they have to exert a force to overcome newtons first law.

            Based off of Newtons first law, the car is going to want to keep going in a straight line, but when it turns, it puts more force on the outermost side of the car, putting uneven force on the car. Now, there can be two outcomes to a situation like this one. The first situation is that the car could tip. For example, in the picture above, the semi going around the corner is starting to tip over. This is because his center of mass is further off the ground, which, combined with the increase in outside wheel pressure, causes him to tip.

            Another thing to look at is the radial acceleration of a car, ar. This is the acceleration inward, which is what determines how much stress and force there is on the car as you are turning. The equation for radial acceleration is (ar)=(v2)/r. From this equation, you can see that the faster you are going, the greater your radial acceleration will be. Along with that, the smaller the radius of your turn is, the greater your radial acceleration will be. On to the next step, we look at the forces that hold the car on the road. These forces can be calculated as Fc which is the centrifugal force of the car. You can determine the Fc value by computing the mass (M) of the car times acceleration due to gravity (9.8m/s2) and then multiply that by the coefficient of  static friction (us). You can then set that equal to the (v2)/r to find out the maximum speed the car can travel so as to not slide off the road.