《 SECTION 7.1 introduced interaction diagrams and the very important distinction between the system, those objects whose motion and interactions we wish to analyze, and the environment, objects external to the system but exerting forces on the system. The most important step in an energy analysis is to clearly define the system. Why? Because energy is not some disembodied, ethereal substance; it’s the energy of something. Specifically, it’s the energy of a system.

FIGURE 9.1 illustrates the idea pictorially. The system has energy, the system energy, which we’ll designate $E_{\text{sys}}$. There are many kinds or forms of energy: kinetic energy K, potential energy U, thermal energy $E_{\text{th}}$, chemical energy $E_{\text{chem}}$, and so on. We’ll introduce these one by one as we go along. The system energy is simply the sum of these: $E_{\text{sys}}=K+U+E_{\text{th}}+E_{\text{chem}}+.\; .\; .$ .

FIGURE 9.1 A system-environment perspective on energy.

Within the system, energy can be transformed without loss. For example, chemical energy can be transformed into kinetic energy, which is then transformed into thermal energy. We can indicate this process symbolically as $E_{\text{chem}}\to K\to E_{\text{th}}$. As long as the system is not interacting with the environment, the total energy of the system is unchanged. You’ll recognize this idea as an initial statement of the law of conservation of energy.

But systems often do interact with their environment. Those interactions change the energy of the system, either increasing it (energy added) or decreasing it (energy removed). We say that interactions with the environment transfer energy into or out of the system. Interestingly, there are only two ways to transfer energy. One is by mechanical means, using forces to push and pull on the system. A process that transfers energy to or from a system by mechanical means is called work, with the symbol W. We’ll have a lot to say about work in this chapter. The second is by thermal means when the environment is hotter or colder than the system. A process that transfers energy to or from a system by thermal means is called heat. We’ll defer a discussion of heat until Chapter 19, but we wanted to mention it now in order to gain an overview of what the energy story is all about.

The key ideas are energy transfer between the environment and the system and energy transformation within the system. This is much like what happens with money. You may have several accounts at the bank—perhaps a checking account and a couple of savings accounts. You can move money back and forth between the accounts, thus transforming it without changing the total amount of money. Of course, you can also transfer money into or out of your accounts by making deposits or withdrawals. If we treat a withdrawal as a negative deposit—which is exactly what accountants do—simple accounting tells you that

That is, the change in your bank balance is simply the sum of all your deposits.

Energy accounting works the same way. Transformations of energy within the system move the energy around but don’t change the total energy of the system. Change occurs only when there’s a transfer of energy between the system and the environment. If we treat incoming energy as a positive transfer and outgoing energy as a negative transfer, and with work being the only energy-transfer process that we consider for now, we can write

where W represents work that is done on the system by the environment. This very simple looking statement, which is just a statement of energy accounting, is called the energy principle. But don’t let the simplicity fool you; this will turn out to be an incredibly powerful tool for analyzing physical situations and solving problems.