EPT
1) Now apparently, the strong interaction doesn't diminish in strength as distance increases? What how? How can that be, please somebody explain. The force will be as strong if they are 1m apart as if they are 1 angstrom apart? How?
The quantum mechanics of the strong force are a bitch. Since you have taken classical mechanics 2, i will assume that you know what a Hamiltonian is, and what a phase diagram is. So here's the problem: we do not know a simple way to write the potential energy for the strong force. We can make simple aproximations, but you can't write the Hamiltonian and solve Shroedinger's equation for a nucleus the way you can for an atom. All we can do is use aproximation (for example, the strong force remains constant). It obviously isn't always true, but within certain limits it's a good enough aproximation. There's examples of this in classical physics too: an infinite plane with a uniform charge distrubution will generate an electric field that's constant; this aproximation in fact is used in real life in calculating the capacity of condensators for example.
2) The way I understand it, is if you have a strong interaction, you cannot actually exist, because you will be too attracted to things, therefore free quarks don't exist, and if you somehow split a baryon, it'd combine again almost instantaneously.
It's not that quarks don't exist on their own. Simply, to this day they have never been seen in a free state, unbound from other quarks. We haven't created an experiment capable of separating quarks, but they are there anyway. Imagine having an atom that for some odd reason can't be ionized. The electrons are there and you can measure things on them, they exist but they will always be in that atom.
3) I'm going to exclude the weak interaction as frankly it doesn't appear too significant in what I'm curious about, and well, it's not well understood by the scientific community either.
I'm not sure what you mean here. The weak interaction is just another kind of nuclear interaction, and in fact at short range it's stronger than the electromagnetic force (which is why it occurs at nuclear scales like the strong force, and not atomic scales). I'm not sure what you mean by not well understood by the scientific community, i'm not aware of any uncertainty on its origins or behaviour (even though it does wierd shit like violating symmetries and other things that an actual praticle physicist will be able to explain much better than me).
4) At short distances the strong force is super powerful, why don't the two protons collapse into each other, is there something I am not considering? If the strong force is the one doing the most work, why wouldn't the protons be infinitely close together? Is there something keeping them at a safe distance?
The force between nucleons includes a repulsive term that forces the nucleons to be separated. I'm not sure where this term comes from, but if you think about it the same exact thing happens with the electromagnetic force as well as gravitational force: there is something (in the case of em and gravitational forces, that's angular momentum) which keeps things apart and balances things out. Normally an attractive potential looks something like this:
+ Show Spoiler +
![[image loading]](http://thynnine.github.io/pysic/plot_directive/inline/da638a9740.hires.png)
Two terms "fight" against each other, one being repulsive and one being attractive. Depending on the range you are at, one of the two will dominate. A good way of writing the Coulomb potential for electrons in a hydrogen atom, for instance, is -1/r + 1/r^2 (without constants). At short range the 1/r^2 term dominates and the two particles actually push each other away, at long range both go to zero, and in between there is a minimum of the function where the particle tends to stay (things like staying at the lowest possible potential energy of course).
5) Why do you need neutrons and protons in a nucleus to make it stable?
Going back to point 1), you can not write the EXACT potential energy for a nucleon in a nucleus (as far as i'm awae). At best, we come up with our own, more or less complicated, phenomenological potentials to explain the nuclear properties. These potentials need to predict what actually happens in nature, ie, that you need both protons and neutrons in a stable nucleus. Once you have found a satisfactory form for these potentials, you can then give them (sometimes) an interpretation that resembles what happens at a macroscopic scale (ie, our own world). In fact, often times the point to start writing these potentials is a real world effect or force that we can experience in every day life. Essentially, you build a theoretical model around the empirical data. The nice thing is, these potentials are also able to predict other properties of nuclear behaviour (like multipole momentums, magic numbers and whatnot).
