I was trying to figure out the situation in which energy is conserved and momentum is not and it was quite easy to find out one case which is of a stone tied to a string moving in a uniform circular motion.
Then I thought to consider the reverse situation in which momentum is conserved but energy is not. To me it seems that as soon as we chose a system in which momentum is conserved then it automatically is implied that in such system energy is conserved too. But looking at the case how these two conservations come into existence due to two different symmetries (one related to the invariance in physical laws due to translation in space and the other in time).
So it would be quite helpful
if someone can point out to a case in which momentum is conserved but energy is not.
otherwise if the above is not possible then explain why that is the case?
[Note that I am considering every form of energy of the given system.]
This is to summarise my question so that no further confusion occurs to future visitors. The question in short is:
- can we lose time symmetry and retain translation symmetry? (Give an appropriate example for the case)