Tuner,
Respectfully, I think you're really over-thinking it (or thinking about it in the wrong way).
If you have to do all of this imagining and use analogies, but cannot find dynamic equations to describe them, the equations probably don't exist. Notice no one seems to have an equations for the 'broken force vectors'? We can all agree, I think, and calculate, slide-barrel velocity as the bullet leaves the system using m(bullet)v(bullet) = -(m(barrel-slide)v(barrel-slide)), and if we assume constant acceleration for the bullet, we can even predict the amount of slide-barrel movement. I think that's about it.
There should be a calulatable "thrust vector" once the bullet leaves the system - From the escaping gasses, but not from the bullet.
I fully agree there's significant friction as the bullet moves through the barrel (but remember that it will be different than pushing a bullet through the barrel at almost zero velocity - I suspect the frictional coefficient changes with velocity and the heat created), but your hypothetical 'pulling' the bullet analogy is seriously flawed.
--The bullet and pistol aren't being pulled from forces from outside the system, creating 'broken force vectors' like snapping cables --
--It's being pushed from
within the system.--
In your tug-o-war example, the pistol is being pulled from EXTERNAL forces, that's not what's happening. The forces are internal, and that's an important difference. The barrel is getting stretched and deforming slightly, like a spring. The only rope cutting analogy when the bullet leaves would be the barrel returing to it's original length and diameter as the pressure drops.
Maybe think of your rope as a rigid pipe, closed on one end, filled with, let's say concrete. A charge is ignited at the closed end. Is there friction between the pipe and concrete? Sure. But if the friction is less than the strength of the materials, that's were the movement (the break) will occur. Assuming the pipe is much less massive than the concrete, the pipe will go one direction, and, regardless of the friction, the concrete will move a bit in the other. The pipe, won't, indeed can't, drag the concrete around from internal pressue and friction in the system. The pipe and concrete will heat up as they're -"pushed apart"- The friction will reduce the final velocity of the pipe and concrete due to this energy loss, which produced heat. But momentum will be conserved. All of the 'tugging' is producing -
internal- strain on the pipe and concrete, stretching and compressing both to some extent, especially the pipe, but nothing gets dragged anywhere from the friction (other than some atoms at the interface of the pipe and concrete); the friction creates heat and robs velocity through (energy stealing) to some extent.
Rather than thinking about pulling the pistol with cables, think about a really strong spring being released between the breech and bullet - what happens in that analogy? Regardless of the frictional resitance, the gun goes in one direction and the bullet the other, right? The friction between the bullet and the barrel heats the barrel, but doesn't drag it along by its nose. The barrel stretches behind the bullet due to internal strain in the system, but the bullet can't drag the gun along by it's nose, as it's being pushed forward! Conservation of momentum is what moves the system.
Does this change you mind? If not, give me some numbers on those "broken vectors", and explain where they're coming from (no cables pulling things around
)