1.2 Models and Modeling
We can model an airplane’s takeoff as a particle (a descriptive model) undergoing constant acceleration (a descriptive model) in response to constant forces (an explanatory model).
The real world is messy and complicated. Our goal in physics is to brush aside many of the real-world details in order to discern patterns that occur over and over. For example, a swinging pendulum, a vibrating guitar string, a sound wave, and jiggling atoms in a crystal are all very different—yet perhaps not so different. Each is an example of a system moving back and forth around an equilibrium position. If we focus on understanding a very simple oscillating system, such as a mass on a spring, we’ll automatically understand quite a bit about the many real-world manifestations of oscillations.
Stripping away the details to focus on essential features is a process called modeling. A model is a highly simplified picture of reality, but one that still captures the essence of what we want to study. Thus “mass on a spring” is a simple but realistic model of almost all oscillating systems.
Models allow us to make sense of complex situations by providing a framework for thinking about them. One could go so far as to say that developing and testing models is at the heart of the scientific process. Albert Einstein once said, “Physics should be as simple as possible—but not simpler.” We want to find the simplest model that allows us to understand the phenomenon we’re studying, but we can’t make the model so simple that key aspects of the phenomenon get lost.
We’ll develop and use many models throughout this textbook; they’ll be one of our most important thinking tools. These models will be of two types:
Descriptive models: What are the essential characteristics and properties of a phenomenon? How do we describe it in the simplest possible terms? For example, the mass-on-a-spring model of an oscillating system is a descriptive model.
Explanatory models: Why do things happen as they do? Explanatory models, based on the laws of physics, have predictive power, allowing us to test—against experimental data—whether a model provides an adequate explanation of our observations.