A closed system is an environment where it is impossible for matter or energy to enter or leave. Sometimes, it’s thought of as a universe-in-a-box. In practice, there is no such thing as a closed system other than the entire universe itself. However, this is a great conceptual tool that allows us to eliminate distractions and focus on just the ideas that we are interested in thinking about.

At a certain level, the conservation of energy is just a definition. The reason that energy is conserved is because we’ve declared that energy can’t leave the system. In fact, there are models of physics where energy is not conserved. This gets really complicated because you have to get very technical with the definition of energy (which we’ve already seen is somewhat elusive) and you need to have a technical understanding of what it means to be conserved. Ultimately, we need to remember that we’re just creating models and not declaring truths about the universe.

The work-energy theorem is a particular representation of the principle of conservation of energy. Here is how it is stated:

The assumption of the work-energy theorem is that all of the energy went into changing the kinetic energy of the object. This theorem is particularly useful for solving problems where the net work is challenging to calculate directly, which is actually a very broad range of interactions.

A basic example of this is determining the work done by a golf club striking a golf ball. Let’s say that, after being struck by the club, the ball has a speed of 40 meters per second. If we wanted to calculate the work done by the club directly, we would have to come up with some sort of model of how the club and ball interact. It would need to involve details such as how fast the club head was moving, how long the club and ball were in contact with each other. Instead, we can just look at the the initial and final states, and skip over all of the details of the interaction.