first of all, it is not the momentum that goes to infinity, but rather the uncertainty in the momentum. so if you make an exact measurement of the position, you cannot say anything about the momentum. it is completely unknown, and could have any value. energy conservation and momentum conservation still apply, so the particle doesn t get energy for free. i will necessarily have to impart some energy to the particle to make this kind off measurement. i don t know how much energy i might have to impart, but it might be a lot. it could be arbitrarily large.