SOLUTION MANUAL
SOLUTION MANUAL
, Preface v
Suggestions for Study
We have seen a lot of successful physics students. The question, “How should I study
this subject?” has no single answer, but we offer some suggestions that may be useful to you.
1. Work to understand the basic concepts and principles before attempting to solve
assigned problems. Carefully read the textbook before attending your lecture on that
material. Jot down points that are not clear to you, take careful notes in class, and ask
questions. Reduce memorization of material to a minimum. Memorizing sections of a
text or derivations would not necessarily mean you understand the material.
2. After reading a chapter, you should be able to define any new quantities that were
introduced and discuss the first principles that were used to derive fundamental equa-
tions. A review is provided in each chapter of the Study Guide for this purpose, and
the marginal notes in the textbook (or the index) will help you locate these topics.
You should be able to correctly associate with each physical quantity the symbol used
to represent that quantity (including vector notation if appropriate) and the SI unit
in which the quantity is specified. Furthermore, you should be able to express each
important formula or equation in a concise and accurate prose statement.
3. Try to solve plenty of the problems at the end of the chapter. The worked examples
in the text will serve as a basis for your study. This Study Guide contains detailed
solutions to about fifteen of the problems at the end of each chapter. You will be able
to check the accuracy of your calculations for any odd-numbered problems, since the
answers to these are given at the back of the text.
4. Besides what you might expect to learn about physics concepts, a very valuable skill
you can take away from your physics course is the ability to solve complicated prob-
lems. The way physicists approach complex situations and break them down into
manageable pieces is widely useful. At the end of Chapter 2, the textbook develops
a general problem-solving strategy that guides you through the steps. To help you
remember the steps of the strategy, they are called Conceptualize, Categorize, Ana-
lyze, and Finalize.
General Problem-Solving Strategy
Conceptualize
• The first thing to do when approaching a problem is to think about and understand
the situation. Read the problem several times until you are confident you understand
what is being asked. Study carefully any diagrams, graphs, tables, or photographs that
accompany the problem. Imagine a movie, running in your mind, of what happens in
the problem.
• If a diagram is not provided, you should almost always make a quick drawing of the
situation. Indicate any known values, perhaps in a table or directly on your sketch.
Copyright 2010 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
48541_00_frontmatter.indd v 9/25/09 2:37:27
, vi Preface
• Now focus on what algebraic or numerical information is given in the problem. In
the problem statement, look for key phrases such as “starts from rest” (vi = 0), “stops”
(vf = 0), or “falls freely” (ay = –g = –9.80 m/s2). Key words can help simplify the
problem.
• Next, focus on the expected result of solving the problem. Precisely what is the ques-
tion asking? Will the final result be numerical or algebraic? If it is numerical, what
units will it have? If it is algebraic, what symbols will appear in the expression?
• Incorporate information from your own experiences and common sense. What should
a reasonable answer look like? What should its order of magnitude be? You wouldn’t
expect to calculate the speed of an automobile to be 5 × 106 m/s.
Categorize
• After you have a really good idea of what the problem is about, you need to simplify the
problem. Remove the details that are not important to the solution. For example, you
can often model a moving object as a particle. Key words should tell you whether
you can ignore air resistance or friction between a sliding object and a surface.
• Once the problem is simplified, it is important to categorize the problem. How does it
fit into a framework of ideas that you construct to understand the world? Is it a simple
plug-in problem, such that numbers can be simply substituted into a definition? If so,
the problem is likely to be finished when this substitution is done. If not, you face
what we can call an analysis problem—the situation must be analyzed more deeply to
reach a solution.
• If it is an analysis problem, it needs to be categorized further. Have you seen this type
of problem before? Does it fall into the growing list of types of problems that you
have solved previously? Being able to classify a problem can make it much easier to
lay out a plan to solve it. For example, if your simplification shows that the problem
can be treated as a particle moving under constant acceleration and you have already
solved such a problem (such as the examples in Section 2.6), the solution to the new
problem follows a similar pattern. From the textbook you can make an explicit list of
the analysis models.
Analyze
• Now, you need to analyze the problem and strive for a mathematical solution. Because
you have categorized the problem and identified an analysis model, you can select
relevant equations that apply to the situation in the problem. For example, if your cat-
egorization shows that the problem involves a particle moving under constant accel-
eration, Equations 2.13 to 2.17 are relevant.
• Use algebra (and calculus, if necessary) to solve symbolically for the unknown variable
in terms of what is given. Substitute in the appropriate numbers, calculate the result,
and round it to the proper number of significant figures.
Copyright 2010 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
48541_00_frontmatter.indd vi 9/25/09 2:37:27
, Preface vii
Finalize
• This final step is the most important part. Examine your numerical answer. Does it
have the correct units? Does it meet your expectations from your conceptualization
of the problem? What about the algebraic form of the result—before you substituted
numerical values? Does it make sense? Try looking at the variables in it to see whether
the answer would change in a physically meaningful way if they were drastically
increased or decreased or even became zero. Looking at limiting cases to see whether
they yield expected values is a very useful way to make sure that you are obtaining
reasonable results.
• Think about how this problem compares with others you have done. How was it
similar? In what critical ways did it differ? Why was this problem assigned? You
should have learned something by doing it. Can you figure out what? Can you use
your solution to expand, strengthen, or otherwise improve your framework of ideas?
If it is a new category of problem, be sure you understand it so that you can use it as
a model for solving future problems in the same category.
When solving complex problems, you may need to identify a series of subproblems
and apply the problem-solving strategy to each. For very simple problems, you probably
don’t need this whole strategy. But when you are looking at a problem and you don’t know
what to do next, remember the steps in the strategy and use them as a guide.
Work on problems in this Study Guide yourself and compare your solutions to ours.
Your solution does not have to look just like the one presented here. A problem can some-
times be solved in different ways, starting from different principles. If you wonder about
the validity of an alternative approach, ask your instructor.
5. We suggest that you use this Study Guide to review the material covered in the text
and as a guide in preparing for exams. You can use the sections Review Checklist,
Equations and Concepts, and Suggestions, Skills, and Strategies to focus in on points
that require further study. The main purpose of this Study Guide is to improve the effi-
ciency and effectiveness of your study hours and your overall understanding of physi-
cal concepts. However, it should not be regarded as a substitute for your textbook or
for individual study and practice in problem solving.
Copyright 2010 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
48541_00_frontmatter.indd vii 9/25/09 2:37:27
SOLUTION MANUAL
, Preface v
Suggestions for Study
We have seen a lot of successful physics students. The question, “How should I study
this subject?” has no single answer, but we offer some suggestions that may be useful to you.
1. Work to understand the basic concepts and principles before attempting to solve
assigned problems. Carefully read the textbook before attending your lecture on that
material. Jot down points that are not clear to you, take careful notes in class, and ask
questions. Reduce memorization of material to a minimum. Memorizing sections of a
text or derivations would not necessarily mean you understand the material.
2. After reading a chapter, you should be able to define any new quantities that were
introduced and discuss the first principles that were used to derive fundamental equa-
tions. A review is provided in each chapter of the Study Guide for this purpose, and
the marginal notes in the textbook (or the index) will help you locate these topics.
You should be able to correctly associate with each physical quantity the symbol used
to represent that quantity (including vector notation if appropriate) and the SI unit
in which the quantity is specified. Furthermore, you should be able to express each
important formula or equation in a concise and accurate prose statement.
3. Try to solve plenty of the problems at the end of the chapter. The worked examples
in the text will serve as a basis for your study. This Study Guide contains detailed
solutions to about fifteen of the problems at the end of each chapter. You will be able
to check the accuracy of your calculations for any odd-numbered problems, since the
answers to these are given at the back of the text.
4. Besides what you might expect to learn about physics concepts, a very valuable skill
you can take away from your physics course is the ability to solve complicated prob-
lems. The way physicists approach complex situations and break them down into
manageable pieces is widely useful. At the end of Chapter 2, the textbook develops
a general problem-solving strategy that guides you through the steps. To help you
remember the steps of the strategy, they are called Conceptualize, Categorize, Ana-
lyze, and Finalize.
General Problem-Solving Strategy
Conceptualize
• The first thing to do when approaching a problem is to think about and understand
the situation. Read the problem several times until you are confident you understand
what is being asked. Study carefully any diagrams, graphs, tables, or photographs that
accompany the problem. Imagine a movie, running in your mind, of what happens in
the problem.
• If a diagram is not provided, you should almost always make a quick drawing of the
situation. Indicate any known values, perhaps in a table or directly on your sketch.
Copyright 2010 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
48541_00_frontmatter.indd v 9/25/09 2:37:27
, vi Preface
• Now focus on what algebraic or numerical information is given in the problem. In
the problem statement, look for key phrases such as “starts from rest” (vi = 0), “stops”
(vf = 0), or “falls freely” (ay = –g = –9.80 m/s2). Key words can help simplify the
problem.
• Next, focus on the expected result of solving the problem. Precisely what is the ques-
tion asking? Will the final result be numerical or algebraic? If it is numerical, what
units will it have? If it is algebraic, what symbols will appear in the expression?
• Incorporate information from your own experiences and common sense. What should
a reasonable answer look like? What should its order of magnitude be? You wouldn’t
expect to calculate the speed of an automobile to be 5 × 106 m/s.
Categorize
• After you have a really good idea of what the problem is about, you need to simplify the
problem. Remove the details that are not important to the solution. For example, you
can often model a moving object as a particle. Key words should tell you whether
you can ignore air resistance or friction between a sliding object and a surface.
• Once the problem is simplified, it is important to categorize the problem. How does it
fit into a framework of ideas that you construct to understand the world? Is it a simple
plug-in problem, such that numbers can be simply substituted into a definition? If so,
the problem is likely to be finished when this substitution is done. If not, you face
what we can call an analysis problem—the situation must be analyzed more deeply to
reach a solution.
• If it is an analysis problem, it needs to be categorized further. Have you seen this type
of problem before? Does it fall into the growing list of types of problems that you
have solved previously? Being able to classify a problem can make it much easier to
lay out a plan to solve it. For example, if your simplification shows that the problem
can be treated as a particle moving under constant acceleration and you have already
solved such a problem (such as the examples in Section 2.6), the solution to the new
problem follows a similar pattern. From the textbook you can make an explicit list of
the analysis models.
Analyze
• Now, you need to analyze the problem and strive for a mathematical solution. Because
you have categorized the problem and identified an analysis model, you can select
relevant equations that apply to the situation in the problem. For example, if your cat-
egorization shows that the problem involves a particle moving under constant accel-
eration, Equations 2.13 to 2.17 are relevant.
• Use algebra (and calculus, if necessary) to solve symbolically for the unknown variable
in terms of what is given. Substitute in the appropriate numbers, calculate the result,
and round it to the proper number of significant figures.
Copyright 2010 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
48541_00_frontmatter.indd vi 9/25/09 2:37:27
, Preface vii
Finalize
• This final step is the most important part. Examine your numerical answer. Does it
have the correct units? Does it meet your expectations from your conceptualization
of the problem? What about the algebraic form of the result—before you substituted
numerical values? Does it make sense? Try looking at the variables in it to see whether
the answer would change in a physically meaningful way if they were drastically
increased or decreased or even became zero. Looking at limiting cases to see whether
they yield expected values is a very useful way to make sure that you are obtaining
reasonable results.
• Think about how this problem compares with others you have done. How was it
similar? In what critical ways did it differ? Why was this problem assigned? You
should have learned something by doing it. Can you figure out what? Can you use
your solution to expand, strengthen, or otherwise improve your framework of ideas?
If it is a new category of problem, be sure you understand it so that you can use it as
a model for solving future problems in the same category.
When solving complex problems, you may need to identify a series of subproblems
and apply the problem-solving strategy to each. For very simple problems, you probably
don’t need this whole strategy. But when you are looking at a problem and you don’t know
what to do next, remember the steps in the strategy and use them as a guide.
Work on problems in this Study Guide yourself and compare your solutions to ours.
Your solution does not have to look just like the one presented here. A problem can some-
times be solved in different ways, starting from different principles. If you wonder about
the validity of an alternative approach, ask your instructor.
5. We suggest that you use this Study Guide to review the material covered in the text
and as a guide in preparing for exams. You can use the sections Review Checklist,
Equations and Concepts, and Suggestions, Skills, and Strategies to focus in on points
that require further study. The main purpose of this Study Guide is to improve the effi-
ciency and effectiveness of your study hours and your overall understanding of physi-
cal concepts. However, it should not be regarded as a substitute for your textbook or
for individual study and practice in problem solving.
Copyright 2010 Cengage Learning, Inc. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
48541_00_frontmatter.indd vii 9/25/09 2:37:27
