How To Solve Physics Problems.pdf

How to Use This Book

This 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 begining 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 favor 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 non-

calculus 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 theory, but

calculus is rarely used in problems. Even those students who are taking calculus concurrent 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 are 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 in 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 is 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 half way

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.

Here are some tips for effectively using the subconscious:

1. Your subconscious will not work without information. You must consciously sort out all of the facts or

information for a particular problem. If you are having difficulty with a problem, try to get straight in your mind

what you do know about the problem. Then also define in your mind what specifically you don't know or don't

understand about the problem.

2. Put conscious effort into the problem up to the point of confusion. Many people grind and grind on a problem

after this point and accomplish very little. It is more efficient for you to plan your study time so that you do not

put yourself in a situation where your only choice is to grind on a problem.

3. After you have done all you can consciously on the problem, “Put it in the back of your mind.” Don't keep

worrying about it. It is important that you clear your mind so that you can accept the solution when it comes.

4. Be sure you have a deadline for the solution.

5. When a solution comes, be sure to act on it quickly, so you can go on to something else. Sometimes instead

of a solution to the problem you will receive a request for more information. The problem may still be

unanswered, but will be clearer to you. What could be happening here is that your subconscious has analyzed

the problem and found an essential piece of information missing and is asking you for it.

The study program that we have outlined, consisting of regular review of lecture notes, frequent working of

homework problems, and periodic updates of your formal notes and outline, makes maximum use of your

subconscious. The periodic intake of new material and the required conscious review serves to keep you

subconsciously analyzing and fitting new information into the body of knowledge you are accumulating.

Here would be a good approach to practicing for a Physics test:

ED - 4:

(Exam day minus four) Prepare a sample exam from your outline.

This may consist of questions from previous exams given by the

instructor and variations of homework problems or examples

done in class. Keep in mind that this is probably the same way

that the professor is making up your exam.

ED - 3:

Study for your first sample exam. Go over your notes, text, and

homework problems.

ED - 2:

Take your first sample exam. As soon as possible after the exam,

do a detailed review concentrating on the weaker areas. Make up

your final sample exam.

ED - 1:

Take your final sample exam. Again review the difficult points of

this sample exam. Get a good night's sleep tonight.

ED:

Do as little as possible on the day of the exam. You may want to

quickly review your outline or a couple of difficult points.

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