First of all, you might want to rephrase your question. You seem to be placing science and logical evidence on one side, and empirical evidence on the other. This is a false dichotomy. There is only a dichotomy between logic and empirical evidence. Where science stands with regards to those two is another question. In fact the logical positivists defined science as exactly the set of facts that can be described using a combination of true empirical statements and valid logical propositions. Put more simply: science = logic + empirical evidence.
The conservation of momentum law in Physics is a widely accepted, heavily used, empirical law (or charge, energy or any other basic conservation laws). There is no fundamental proof as to its validity. We accept it since no contradictions have been observed so far.
From the text of your question, you seems to be asking about the problem of induction. This is indeed a major problem in the philosophy of science. Several authors have tried to address it.
One example is Karl Popper, who proposed the idea of falsificationism: no science theory can ever be definitively proven, instead the most successful theories in science (i.e. those backed by empirical evidence) will only be the best for now, until the day they are falsified (i.e. proven wrong by new evidence).
He proposed that the criteria for what constitutes a scientific statement should thus not be whether the statement can be verified or not. Instead it should be whether a statement can be falsified or not.
Falsification is a stronger criteria than verification. It is no longer enough to provide empirical evidence for statement, one must provide a way of proving the statement false. The statement is considered a valid scientific result when one has tried to prove it false and failed.
In your example, one must design an experiment to prove that momentum isn't conserved and then run it and show that the experiment failed. Of course someone else in the future might succeed, hence the principle that theories are just the best we have so far, never definitely proven.
Others besides Popper have discussed the problem of induction. I'll leave it to you to look them up.