Solving Physics Problems
At some point in their studies, almost all physics students find themselves thinking, “I understand the concepts, but I just can’t solve the problems.” But in physics, truly understanding a concept means being able to apply it to a variety of problems. Learning how to solve problems is absolutely essential; you don’t know physics unless you can do physics.
How do you learn to solve physics problems? In every chapter of this book you will find Problem-Solving Strategies that offer techniques for setting up and solving problems efficiently and accurately. Following each Problem-Solving Strategy are one or more worked Examples that show these techniques in action. (The Problem-Solving Strategies will also steer you away from some incorrect techniques that you may be tempted to use.) You’ll also find additional examples that aren’t associated with a particular Problem-Solving Strategy. In addition, at the end of each chapter you’ll find a Bridging Problem that uses more than one of the key ideas from the chapter. Study these strategies and problems carefully, and work through each example for yourself on a piece of paper.
Different techniques are useful for solving different kinds of physics problems, which is why this book offers dozens of Problem-Solving Strategies. No matter what kind of problem you’re dealing with, however, there are certain key steps that you’ll always follow. (These same steps are equally useful for problems in math, engineering, chemistry, and many other fields.) In this book we’ve organized these steps into four stages of solving a problem.
All of the Problem-Solving Strategies and Examples in this book will follow these four steps. (In some cases we will combine the first two or three steps.) We encourage you to follow these same steps when you solve problems yourself. You may find it useful to remember the acronym I SEE—short for Identify, Set up, Execute, and Evaluate.
In everyday conversation we use the word “model” to mean either a small-scale replica, such as a model railroad, or a person who displays articles of clothing (or the absence thereof). In physics a model is a simplified version of a physical system that would be too complicated to analyze in full detail.
For example, suppose we want to analyze the motion of a thrown baseball (Fig. 1.2a). How complicated is this problem? The ball is not a perfect sphere (it has raised seams), and it spins as it moves through the air. Air resistance and wind influence its motion, the ball’s weight varies a little as its altitude changes, and so on. If we try to include all these things, the analysis gets hopelessly complicated. Instead, we invent a simplified version of the problem. We ignore the size and shape of the ball by representing it as a point object, or particle. We ignore air resistance by making the ball move in a vacuum, and we make the weight constant. Now we have a problem that is simple enough to deal with (Fig. 1.2b). We will analyze this model in detail in Chapter 3.
We have to overlook quite a few minor effects to make an idealized model, but we must be careful not to neglect too much. If we ignore the effects of gravity completely, then our model predicts that when we throw the ball up, it will go in a straight line and disappear into space. A useful model simplifies a problem enough to make it manageable, yet keeps its essential features.
The validity of the predictions we make using a model is limited by the validity of the model. For example, Galileo’s prediction about falling objects (see Section 1.1) corresponds to an idealized model that does not include the effects of air resistance. This model works fairly well for a dropped cannonball, but not so well for a feather.
Idealized models play a crucial role throughout this book. Watch for them in discussions of physical theories and their applications to specific problems.