How to Solve Physics Problems will prepare you for physics exams by focusing on problem-solving. You will learn to solve physics problems naturally and systematically–and in a way that will stick with you. Not only will it help you with your homework, but it will also give you a clear idea of what you can expect to encounter on exams.


How to Use This Book:
How to Solve Physics Problems book will teach you how to do physics problems. The explanation of not only how to do a problem but why we do it a certain way teaches you not just a collection of solved problems, but a collection of methods that can be used, modified and built upon to do other physics problems. As researchers and teachers, we know that the key to solving new and challenging problems is contained within the collection of techniques already learned for solving simpler problems. Seeing a problem solved and knowing why it was done in a certain manner is the best way to learn how to solve related, more difficult problems.

This book is not a presentation of every problem you are going to encounter on a test. It is a presentation of the methods that we have found to work for large groups of problems. If you develop the techniques we describe for solving problems then you will know how to successfully attack the problems you will encounter on the tests. This is the book you should have as a reference when you are doing your homework problems. It will show you how to work the problems and explain why they are being done the way they are.

The topics in this book are in the order of most physics texts. Each chapter begins with a theoretical discussion. Problems are mixed in with the discussion as soon as possible. These problems follow the development of the theory. In this way, you do not have to assimilate a large amount of conceptual material before beginning to work problems.
A “standard” route is followed for problems wherever possible. In this way, you will learn that broad categories of problems worked in a standard “logical” way always produce correct solutions. Our emphasis is on logic and order in solving problems. We avoid methods that may be quick and have limited application to problem-solving in favour of possibly longer solutions that have broad applications and always work. We believe that a lot of good physics can be taught in problems so we use problems to illustrate and expand a topic and sometimes introduce new concepts. For this reason, problems and text are integrated with a minimum of artificial barriers between them.
The book is intended as a complement to either the calculus-based or the non-calculus-based elementary physics course. It has been our experience that calculus concepts can be introduced into the traditional noncalculus course and used in the development of concepts. Conceptually, calculus is not difficult and when it is introduced in the context of a physics problem it is even easier. We use calculus concepts to explain a theory, but calculus is rarely used in problems. Even those students who are taking calculus concurrently with their physics course usually learn calculus concepts in physics before they see them in their calculus course.
In those instances where calculus is needed, the problems and paragraphs are marked with a calculus icon. Even the student without formal calculus training should read these sections. They are often explained in a simple manner so that the calculus does not present a problem.
The chapters on electricity and magnetism is also excellent background chapters for someone taking an undergraduate course in Electricity and Magnetism.
We have used two significant figures for the physical constants and most of the numbers in the problems. Results are given to two, and occasionally three, significant figures. Using two significant figures cuts down on the clutter in the problems, allowing the technique to receive greater exposure. Do not be concerned with working through the problems if your answers do not agree exactly with ours. This is no doubt due to when, or if, intermediate calculations were rounded off. SI units are used nearly universally throughout the book.

How to Excel in Your Physics Course:
Most students realize that putting off studying until the day before the exam and then cramming at the last minute is not efficient. Some students do this anyway because so far they have gotten away with it. Perhaps most of the other students you previously competed with had poor study skills. This may have allowed you to adopt poor or non-existent study habits and still keep up or even get good grades if you are naturally a better student. Now that you are in college, the courses will be more difficult and it is to your advantage to develop a more organized approach to handling your course work.

Successful people generally have three things in common. They make effective use of their time, they set goals for themselves, and they have a positive attitude. Physics is a challenging course for most students. It will take a well-organized consistent effort to do well in this course, but success in a challenging area is a worthwhile goal.

General Approach for Studying Physics:
Many people believe the following: more work and more study results in higher grades. This is not necessarily so. You certainly must be willing to make a certain commitment of time and energy to this course, but the key to academic success is concentrating your efforts on the right things at the right times. You may have noticed that those students who receive the highest grades are not necessarily the ones who work the greatest number of hours. Some students may boast that they have studied all night for an exam, but don’t be impressed by this habit. “Allnighters” and the like are almost always the result of procrastination and bad study habits. Getting no sleep before an exam is foolish and it usually takes several days to recover from this kind of activity. By taking advantage of the study techniques that follow you can achieve higher grades with less effort.
The most efficient way of learning Physics by attending lectures, problem-solving sessions, and performing supplementary readings is to:
1. Do a quick reading on the topics to be covered in the lecture before attending class. Ten or fifteen minutes may be sufficient for a one hour lecture. The purpose here is to generally familiarize yourself with the topics to be discussed. Perhaps you can identify one or two questions or key points to listen for during the lecture.
2. Attend class and take notes. Attend all of the classes. Someone is paying for these classes so BE THERE! Be on the alert for any indication by the instructor of possible test questions. If the professor says something like “This is very important, you may be seeing this again,” make a special note of this in your notebook.
3. Review your lecture notes. Don’t save this step until a few days before the exam. It is far more efficient to review your notes a little bit at a time during the semester than to try and do it all at once. At this point, you should also do a more detailed reading of the text to fill in any gaps in your class notes.

4. This may be the most important step. Do the homework problems regularly. In other courses, it may be sufficient to read the text and review your notes, but in Physics you must be able to work the problems. You don’t learn problem-solving skills by just reading examples of solved problems, you must do the problems yourself. By doing the homework problems on a regular basis you will be able to identify areas that you need more work on well in advance of the test. Physics problems can be difficult. Therefore, when you set out to work problems do not set yourself the task of working a certain number of problems, but rather set out a certain amount of time to work on problems.
5. Compile a formal set of notes and prepare a detailed outline. The general strategy here is that a number of short exposures to manageable pieces of the course are more efficient than one long exposure to a large amount of material. As you progress through the course, you first get your information in an initial reading of the material, then again in the lecture, then again in a second reading, and yet again in an organizing session where you prepare a detailed outline. The detailed outline is essential to success on the exams. It contains the examination questions. Your main preparation for the exam will be to extract the questions and prepare to answer them. Notice we did not say “study for the exam;” the studying for the exam has been going on all along. That is what you have been doing as you make up your formal notes, outline, etc. What you have done with this systematic approach is to reproduce the notes and outline that the instructor is using. If you are reasonably good at it, you will have as good a source of exam questions as the instructor.

How to Prepare for a Physics Test:
Examine the shelves of any bookstore catering to career-oriented students and you will find books with titles such as: How to Pass the Real Estate Licensing Exam, or How to Succeed on the S.A.T. Examining these books will help you to develop your personal exam-taking program. One common thread in all books on how to pass particular exams is to know the questions in advance. Most writers of these types of books are in the business of training people in their particular areas, so they are close to the people who are making up the exams. This gives them a ready source of test questions and knowing the questions (or at least the type of questions) is halfway to knowing the answers. Therefore we make the following suggestions:
1. Almost all instructors in physics will place some problems on the test that are very similar to examples that they have done in class. Many times you may encounter the same problem with different numbers. This makes it very important to attend every class so as not to miss the opportunity to see possible test questions. If you do miss class, always get the notes from a friend.

2. Another frequent occurrence is for slight modifications of homework problems to appear on the test. Join a study group that does homework problems together. This can be more efficient than grinding away on your own. Don’t waste too much time with a study group unless it is productive. Your final preparations for a test should be done privately so that you can concentrate on developing a plan for taking the test.
3. Find sample physics tests given by your instructor for the past few years. It is a good bet that most of the questions for the exams in the near future will be very much like those of the immediate past.
4. Some physics problems involve mathematics that can be deceptively easy. For example, if you expect problems involving the manipulation of logarithms or exponents be sure you practice the mathematical operations and entering the numbers into your calculator so you don’t have to stop and figure out how to take exponents during the test. Practice any unfamiliar mathematical operations before the test.

Timing and the Use of the Subconscious:
Have you ever experienced the frustration of having a conversation with someone and forgetting momentarily a name or fact that is very familiar to you? Usually, shortly after such an experience, the name or fact will come to you when you are not consciously trying to recall it. Another variation of this same phenomenon is when a person doesn’t feel right about making a decision immediately upon receiving or defining a problem. They like to “sleep on it.” Both of these situations have a common characteristic – the use of the subconscious. The fact that solutions are often presented to us in the absence of active work on the problem at the moment we receive the solution indicates that another part of the brain was analyzing the pertinent information and providing a solution. We call this part of the brain the subconscious, and this part of the brain is very effective at solving problems.



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