Solving Problems in Physics

This page written by Dan Styer, Oberlin College Physics Department;
http://www.oberlin.edu/physics/dstyer/SolvingProblems.html;
last updated 9 January 2002.

Contents

Introduction
Strategy Design
Execution (Tactics)
Answer Checking
Further Reading
Introduction

The problems and examinations in this physics course exercise not only your knowledge of physics but also your skill in solving problems. Professional physicists earn their salaries not particularly for their knowledge of physics but for their ability to solve workplace problems. This document presents tips for honing your problem solving skills. These tips and techniques will prove useful to you in your physics courses, in your other college courses, in your career, and in your everyday life.
To set the stage, I want to discuss an example of problem solving from everyday life, namely building a jigsaw puzzle. There are a number of different approaches to building a jigsaw puzzle: My approach is to first turn all the pieces face up, then put together the edge pieces to make a frame, then sort the remaining pieces into piles corresponding to small "sub-puzzles" (blue pieces over here, red pieces over there). I build the sub-puzzles, then piece the sub-puzzles together to build the whole thing. Other people have different approaches to building jigsaw puzzles, but nobody, nobody, builds a puzzle by picking up the first piece and putting it in exactly the correct position, then picking up the second piece and putting it in exactly the correct position, and so forth. Solving a jigsaw puzzle involves an approach--a strategy--and a lot of "creative fumbling" as well.

Your physics textbook contains many solved "sample problems". The solutions presented there are analogous to the completed jigsaw puzzle, with every piece in its proper position. No one solves a physics problem by simply writing down the correct equations and the correct reasoning with the correct connections the first time through, just as no one builds a jigsaw puzzle by putting every piece in its correct position the first time through. The "solved problems" in your book are extraordinarily valuable and they deserve your careful study, but they represent the end product of a problem solving session and they rarely show the process involved in reaching that end product. This document aims to expose you to the process.

Solving a physics problem usually breaks down into three stages:

Design a strategy.
Execute that strategy.
Check the resulting answer.
This document treats each of these three elements in turn, and concludes with a summary.
Strategy Design

Look before you leap. Whenever you face a problem, there is an immediate temptation to rush in, roll up your sleeves, and begin tinkering with it. Resist that temptation. If you start your detailed work--the execution stage--immediately, you will likely write down a lot of correct statements that do not lead to an answer. Instead, think about the problem on an overview level. What sort of conceptual tools will you need to solve the problem? What path will you take to the solution, and in what direction should you start off? Concretely, it often helps to classify your problem by its method of solution.
If you are looking for a child lost in the woods, your first step is to sit down, think about what the child probably did and where he probably is, and devise a strategy that will allow you to effectively rescue him. If, instead, you just rush about the woods in random directions, you're likely to become lost yourself.

Where are you now, and where do you want to go? Before you can design a path that takes you from the statement of the problem to its answer, you must be clear about what the situation is and what the goals are. It often helps to check off each given datum of the problem, and to underline the objective. But for getting an overall sense of the problem, nothing beats summarizing the whole situation with a diagram. The diagram will organize your work and suggest ways to proceed. One of my course graders told me that "When students draw a diagram and label it carefully, they are forced to think about what's going on, and they usually do well. If they just try a globule of math, they mess up."

Keep the goal in sight. Don't get caught in blind alleys that lead nowhere, or even in broad boulevards that lead somewhere but not to where you want to go. It sometimes helps to map a strategy backwards, by saying: "I want to find the answer Z. If I knew Y I could find Z. If I knew X I could find Y . . . " and so forth until you get back to something you are given in the problem statement.