# Total energy of an isolated system

• I
If a closed system has kinetic and potential energy such as the total energy (the sum of the two) equals zero for all times, what does that mean? In other words, what does it physically mean that the total energy is always zero for a closed system?
I think I have a small misunderstanding of the interpretation because i ask myself: how can the system do anything at all if its total energy is zero? But at the same time i think, one can choose the zero potential energy such as the total energy is zero.

• Delta2

## Answers and Replies

troglodyte
Gold Member
If your energy is conserved which means there exist no perturbation from outside the energy environment then you have T+V=E=constant or equivalent dE\dt=0 .So,you have an fixed Energy value which will transform from the kinetic/-to potential energy and vice versa.Therefore both types of energy T and V are using the environment energy/total energy to transform into each other.They try to hold the Balance of the system

Maybe the total Energy could be E=2T-->2T=T+V then we get T=V,but this was one possibility of infinite many configurations.

Every conserved system follows the principle of least action!At this moment you gonna know how nature "thinks" Last edited:
• Delta2
Ibix
Science Advisor
2020 Award
But at the same time i think, one can choose the zero potential energy such as the total energy is zero.
This is the key point. The total energy can be anything you like, since you can add an arbitrary constant to the potential energy - so worrying that the total energy is zero is pointless. Add a constant if it bothers you. The internal configuration can change, possibly (but not necessarily) trading kinetic energy for potential energy, as long as the total energy remains the same.

• troglodyte and Delta2
kuruman
Science Advisor
Homework Helper
Gold Member
The idea is the same as having two bank accounts, one in checking (kinetic energy) and one in savings (potential energy). If you don't deposit or withdraw any money, you can move money from one account to the other and the total (zero of energy) that you have in the accounts together will be the same regardless of what that total is.

Of course in real life the bank may charge you a fee every time you transfer money between accounts so that if you do it enough times, you will be left with nothing. The physical equivalent of that is dissipative forces, such as friction, that reduce the mechanical energy and are always there.

Note that, in both the bank account and physical system examples, if you want to increase what's already there, you got to do some work.

• Hajarmq, troglodyte and Delta2