Mechanics

# Car on a sloping track

In some car races the tracks differ only by their slope, that is, most of the time we see horizontal tracks, although some races are carried out on raised tracks. The figure above shows an example of a raised track, that is, an inclined track.

In this type of situation, in which we have the movement of a car on an elevated curved track, so that the resultant of the forces points to the center of the curve, it is necessary that this resultant obeys the diagram of forces. The diagram of the force diagram can be seen in the figure below.

Determination of the centripetal force on the car

In a curvilinear motion on an inclined road, regardless of friction, it is not necessary for the driver to turn the steering wheel to change the direction of motion if he maintains the same speed. According to the composition of the forces acting on the car in the figure above, we have:

We know that for a flat and horizontal curve the speed of the car can be determined through the following equation  :

If you are on an elevated lane and want to overtake another vehicle on the outside of the curve, simply accelerate the vehicle without turning the steering wheel. But if you want to increase the speed and stay on the same horizontal level, it is enough that, simultaneously, you increase the vehicle speed and turn the car’s steering wheel into the curve. By doing so, the use of frictional force will prevent the car from driving out of the turn.

It should be noted that if you reduce the car’s speed, the car will tend to fall towards the center of the curve, however, to compensate for this fall towards the center of the curve, you must turn the steering wheel out of the corner.

In order to simplify what has been mentioned we can do a very simple experiment. If we take a funnel and we put a marble inside and we start to make it rotate, we will notice that it will describe a horizontal curve. Now if we increase the speed of the marble we will see that it tends to “go up” to the side of the funnel. If the speed of the ball decreases, it tends to “fall” towards the center of the funnel.