Applied force vs Frictional Force Graph

Question

Now I understand the concept of friction.

But I just wanted to clear a confusion. As we keep increasing applied force, static friction acts till its maximum limit. After that the body comes in motion and kinetic friction starts acting which is less than static friction.

At the limiting point, will there be a sudden break in continuity of graph or will it just continuously decrease till kinetic friction.

I have read several books and articles and some do this and some don't.

Is it that in reality it should be like this-

but for simplification for high school students they tell this-

Answer 1

According to the simplified friction model of static vs. kinetic friction, you can only have one type or the other. So as soon as the static friction limit is met and the object starts moving, by the definition of kinetic friction according to the model, the friction that is present will be kinetic friction right at that instant.

Of course the above is a simplified model. A more accurate model might be to think of static friction as a bunch of small interactions between the object and the surface. Right near when the limit is past these interactions start failing one by one as the object eventually begins accelerating, and thus the resistive force of friction during motion then arises from interactions that are not as "fully formed" as before. This picture might give a little more continuity as opposed to the simplified model above.

However, if you want to have a more continuous picture you need to give more detail to the model. Just having $f_s\leq\mu_sN$ and $f_k=\mu_kN$ for no relative motion and relative motion respectively isn't going to cut it.