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On force and energy

There are many ways to view the physical world. In science and engineering, it is often useful to view the world in terms of a concept called energy. Beginning with the concept of force, herein I set out to provide a tenacious understanding of energy and why it is a useful perspective for understanding physical systems.

What does it mean to “force” something?

Scientists and engineers generally use the concept of force to mean only a pushing or pulling, without implying that this push or pull did anything at all.

Something “exerts a force” when it pushes or pulls;
something “experiences a force” when it is pushed or pulled on.

The presence of forces does not mean that anything actually happens; it merely means that there was some factor exerting its influence. Just knowing the force does not tell you anything about the magnitude of its influence.

How do we talk about things actually happening?

Energy is the way that scientists and engineers talk about what actually happened. Roughly,

Energy is how much a force is able to make something move.

In other words, energy is a measure of the influence of a force on a system. When a force is exerted and its influence causes something to move, we say that energy is transferred (from the thing exerting a force to the thing experiencing the force—the thing that has moved). The transfer of energy is always associated with a movement, and movement is always associated with a distance over which a thing moves. The greater the distance over which something moves and the strength of the force causing it to move, the greater the energy that can be transferred. That is to say, two ways of increasing the transfer of energy are to:

make something travel further and
push or pull on it harder.

These words are easy to say and (hopefully) fairly straightforward to understand without too much contemplation; what is harder is understanding how to apply them to different systems. How do we use this concept of energy to learn something about the world? Why do we even need the concept of energy? Why can't we simply talk about forces and distances?

These questions are difficult to answer completely without at least some training in science or engineering. The basic idea is that since neither the exertion of forces nor the movement of objects alone imply that anything new has happened, in many situations we need to talk about the energy that can be transfered, which relates a specific force to the distance it can make something move. Saying the same thing differently, in order to glean useful information about the world, scientists and engineers often talk about the influence of a force or the energy it can transfer, before they talk about the specific forces and distances themselves.

OK, maybe I get it, maybe I don't. How do I use it?

One of the reasons scientists and engineers like to talk about the various energies associated with a system is because it makes understanding the influence of various parts of the system more manageable. For example, by considering the thermal energy, the electrostatic energy, and the hydrophobic energy, we can begin to understand how various factors affect a solution of proteins (e.g. milk). Let's look at each of these energies individually and consider if it is easier to think about the forces exherted and distances travelled or the associated energy.

The thermal energy is determined from the sum of the motion of all of the molecules in a substance—typically called the molecular vibrations. Consider a molecule that is moving around. Eventually it bounces into another molecule, and thus exerts a force on this molecule. This force causes the other molecule to move in a way that it would not have otherwise—in the language used above, something happens. In order to get the full story of what happens in terms of forces and distance, we need to consider all of the molecules along with their velocities and positions, as well as all of the instances when a molecule bounces into another molecule. Given that there are approximately 1025 molecules in a liter of water, that's an awful lot of data that we need to process! Considering instead the thermal energy, we simply need to know the number of molecules, the mass of a single molecule, and an average of the velocity at which the molecules travel. By considering the thermal energy rather than the thermal forces and movements, we have gone from an truly unmanageable set of data required to understand a system to only having to know three numbers! This is the immense power of the energy perspective. It's no wonder why we clapped for our equations of the week! (it's ok if you clap now... I won't tell anyone :])

Continuing on, the electrostatic energy is determined from the sum of the influence of the forces originating from electrically charged particles. Here, if we only wanted to consider forces and movements, we would have to consider all of the electrically charged particles present in the system along with their locations and movements, as well as all of the ways these charged particles cause the other charged particles in the system to move. Just like we did above with the thermal energy, we can use the electrostatic energy to reduce the amount of information we need to only a few parameters. For example, if we know the relationship between the pH of a solution and the electrostatic energy, we could determine the effects of adding an acid to our protein solution without having to know how every hydrogen ion (H+) interacted with every other molecule in the solution. In this case, as above, to say the energy perspective is more efficient is a gross understatement.

To conclude the examples, the hydrophobic energy is determined from the sum of the influence of the forces between hydrophobic molecules (or regions of molecules) and water. The hydrophobic energy is really a specific type of electrostatic energy and relates to the way that charged particles interact. Just as before, we can drastically reduce the number of parameters we need to understand the behavior of the system by using the energy perspective.

While I let that sink in, what can I take home to Mom and Pops?

Energy is nothing more than the influence of a force. This influence is manifest in the motion or potential for motion of an object. Some times it is easy to determine a force's influence by thinking about the forces and motion in the system; most times it is easier and significantly more efficient to think about the combined relationship between these forces and motion: the energy of the system.