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## Homework Statement

I don't know if I am posting in the wrong thread. This is not a question for solving a homework, but a question to help me write some homework students will have to solve.

I teach algorythmics to mechanics students. The program they are developing is about driving a car along a street. As they are mechanics students, the program will tell them when active driving aids are activated (ABS, traction control and stability control systems). The street has curves and slopes. In curves I have already stated that the maximum speed takes into account the MU friction constant of the surface and the radius of the curve. When braking, if they brake too hard, ABS will start to activate. In fact I would like that the ABS activation were dependent on the speed and surface of the street but well, but I haven't found how. This doubt is related to the one I am asking. I want that when the car accelerates, the traction control activates when the acceleration is too heavy and some tire looses traction, that is, it starts slipping on the surface. I think it is most important if they accelerate in an ascending slope. Let's see if someone can help me.

## Homework Equations

A slope has a % increase, from 5% to 10%. The car has a mass. I have seen in some tutorials that in this case, the sin and cos of the angle play some part. But there is also the surface of the road. If it is wet the MU friction constant is lower and it is easier to slip. When running horizontally, the weight of the car is ignored (simplification) because friction and innertia both depend on the weight. But in slopes there is an angle and then the weight is relevant.

## The Attempt at a Solution

No idea. I would like a very simplified formula so that I can say, when this happens, the driving simulator will show a message of Traction Control System activation. This condition could be immediate or it could have to take into account what has been done in previous actions.

Any help? I can add any info you need