If you draw a plane through the point of reaction (in this case, the epicenter of the explosion), splitting the resulting force vectors into those on one side of the plane (a
1...an) and those on the other side of the plane (b
1...b
m), the sum of vectors a
1...an will be the opposite of the sum of vectors b
1...b
m. Or
.
Perfectly elastic or not, you're not getting rid of b
1...b
m no matter what, and so things will shoot towards the ground as violently as debries from the icicle will fly up.
I will buy the explanation of "it's magic, so the law of conservation of energy does not apply, and reaction forces magically disappear". I will not buy the explanation that it is about efficiency, shaped charges throw as much stuff and with as much force in the direction opposite to that of the jet stream, the only things special about shaped charges is that jet particles don't deviate much from the intended direction.
Before I go on, I just want to point out that in the manga panel, magic is clearly being used to simply perfectly redirect and use all of the energy and associated forces to destroy the ice block, because there's nothing going downwards. That can be the end of the discussion there. But it's an interesting discussion so I'll continue.
Your physics model is correct but I need to clarify something here. I don't disagree with the physics, but the total energy and total forces involved aren't the same thing. I made the mistake of trying to talk about both at the same time which contributed to that confusion. As I see from your vector diagram the issue is not with an understanding of the directional forces involved but with that distinction.
This also depends on what you're referring to with 'backblast' in this case. To me, this is both the heat and kinetic energy of anything not used in the directional explosion/jet stream, while you appear to focus chiefly on the kinetic energy of anything going the other way. That's where the technically incorrect usage of the term for a shaped charge versus a launcher leads to more misunderstanding, I think.
Backblast is not wasted energy, backblast is an unfortunate consequence of the third law. It would be impossible to push the icicle as high up without having an equal amount of energy directed in the opposite direction.
Which brings us back to this. I assumed you were referring to Newton's third law, due to the use of "third law" and "opposite direction", but now I believe you're conflating the Law of Conservation of Energy with Newton's Third law of Conservation of Momentum. You state that an equal amount of energy is directed in the opposite direction when it is only the force that should be the same.
When I refer to the 'waste energy' in this case, it is any energy not used to create the jet stream. This doesn't need to be exactly 50% of energy found in the system or pointed in any particular direction, and varies according to how the shaped charge is designed and operated. The energy not used is essentially that, waste energy in the form of heat, sound and kinetic energy, aka the rest of the explosion. It is indeed wasted energy, because it's desirable that all of this energy be used to create the jet stream's kinetic effect (and associated reaction force). In my original statement, I said she used magic to make this process 100% efficient, which is not currently possible in real life. I mentioned HEAT, which does indeed have very little collateral damage, because reactionary forces are dissipated through the casing and sometimes an attached slug meant for that purpose. The force is the same, but the mass is greater so to use your words, there is less "devastation", as these have lower resultant velocity and kinetic energy and don't go very far. The heat energy is considerable though this has nothing to do with the reaction forces.
This is why when you addressed this:
Magic is invoked to produce a shell casing that perfectly reflects the explosive energy....
Conservation of energy is not violated.
This is correct. "Reflecting" the energy (not momentum), there's no issue with this. The total energy remains the same. It doesn't matter what direction or what form the energy is taking.
Coming back to the ice block, we see magic is handling both the excess energy as well as the reactionary force. As I said at the outset, that could be the end of it. However, since the distinction between forces and energy is clarified, I'd also like to point out that all of the 'waste energy' in the form of heat is contributing to evaporate the ice block. It's still a stupendous amount of energy which doesn't seem to track with her earlier daggers....I think this might be around multi-megaton yield to melt an ice block of that size....but I don't think she is breaking the Law of Conservation of Energy here, and there is less energy in the system overall that what I believe you're thinking.
As for Newton's Third Law, depends on how you want to consider it. We 'break' it in real life by abusing mass, material properties and elasticity but actually total momentum is conserved in all cases. I see the magic as doing the same thing, which is what I was implying in my previous posts.
