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ENGINEERING MECHANICS

DYNAMICS

TWELFTH EDITION

R. C. HIBBELER

P R E NTICE HALL

Upper Saddle River, NJ 07458

To the Student

With the hope that this work will stimulate

an interest in Engineering Mechanics

and provide an acceptable guide to its understanding.

PREFACE

The main purpose of this book is to provide the student with a clear and thorough presentation of the theory and application of engineering mechanics. To achieve this objective, this work has been shaped by the comments and suggestions of hundreds of reviewers in the teaching profession, as well as many of the author's students. The twelfth edition of this book has been significantly enhanced from the previous edition and it is hoped that both the instructor and student will benefit greatly from these improvements.

New Featu res Funda mental Pro b lems. These problem sets are located just after the example problems. They offer students simple applications of the concepts and, therefore, provide them with the chance to develop their problem-solving skills before attempting to solve any of the standard problems that follow. You may consider these problems as extended examples since they all have partial solutions and answers that are given in the back of the book. Additionally, the fundamental problems offer students an excellent means of studying for exams; and they can be used at a later time as a preparation for the Fundamentals in Engineering Exam. Rewriting. Each section of the text was carefully reviewed and, in many areas, the material has been redeveloped to better explain the concepts. This has included adding or changing several of the examples in order to provide more emphasis on the applications of the important concepts. Con ceptual Pro b lems. Throughout the text, usually at the end of each chapter, there is a set of problems that involve conceptual situations related to the application of the mechanics principles contained in the chapter. These analysis and design problems are intended to engage the students in thinking through a real-life situation as depicted in a photo. They can be assigned after the students have developed some expertise in the subject matter. Additional P h otos. The relevance of knowing the subject matter is reflected by realistic applications depicted in over 60 new and updated photos placed throughout the book. These photos are generally used to explain how the principles of mechanics apply to real-world situations. In some sections, photographs have been used to show how engineers must first make an idealized model for analysis and then proceed to draw a free-body diagram of this model in order to apply the theory. New Problems. There are approximately 50%, or about 850, new problems added to this edition including aerospace and petroleum engineering, and biomechanics applications. Also, this new edition now has approximately 17% more problems than in the previous edition.

VI P R E FA C E

• General Analysis and Design Problems. The majority o f problems in the book depict realistic situations encountered in engineering practice. Some of these problems come from actual products used in industry. It is hoped that this realism will both stimulate the student's interest in engineering mechanics and provide a means for developing the skill to reduce any such problem from its physical description to a model or symbolic representation to which the principles of mechanics may be applied. Throughout the book, there is an approximate balance of problems using either SI or FPS units. Furthermore, in any set, an attempt has been made to arrange the problems in order of increasing difficulty except for the end of chapter review problems, which are presented in random order.
• Computer Problems. An effort has been made to include some problems that may be solved using a numerical procedure executed on either a desktop computer or a programmable pocket calculator. The intent here is to broaden the student's capacity for using other forms of mathematical analysis without sacrificing the time needed to focus on the application of the principles of mechanics. Problems of this type, which either can or must be solved using numerical procedures, are identified by a "square" symbol (_) preceding the problem number. With so many homework problems in this new edition, they have now been placed in three different categories. Problems that are simply indicated by a problem number have an answer given in the back of the book. If a bullet (.) precedes the problem number, then a suggestion, key equation, or additional numerical result is given along with the answer. Finally, an asterisk (*) before every fourth problem number indicates a problem without an answer. Accu ra cy. As with the previous editions, apart from the author, the accuracy of the text and problem solutions has been thoroughly checked by four other parties: Scott Hendricks, Virginia Polytechnic Institute and State University; Karim Nohra, University of South Florida; Kurt Norlin, Laurel Tech Integrated Publishing Services; and finally Kai B eng Yap, a practicing engineer, who in addition to accuracy review provided content development suggestions.

Contents The book is divided into 11 chapters, in which the principles are applied first to simple, then to more complicated situations. The kinematics of a particle is discussed in Chapter 12, followed by a discussion of particle kinetics in Chapter 13 (Equation of Motion), Chapter 14 (Work and Energy), and Chapter 15 (Impulse and Momentum). The concepts of particle dynamics contained in these four chapters are then summarized in a "review" section, and the student is given the chance to identify and solve a variety of problems. A similar sequence of presentation is given for the planar motion of a rigid body: Chapter 16 (Planar Kinematics), Chapter 17 (Equations of Motion) , Chapter 18 (Work and Energy), and Chapter 19 (Impulse and Momentum), followed by a summary and review set of problems for these chapters.

If time permits, some of the material involving three-dimensional rigid-body motion may be included in the course. The kinematics and kinetics of this motion are discussed in Chapters 20 and 21, respectively. Chapter 22 (Vibrations) may be included if the student has the necessary mathematical background. Sections of the book that are considered to be beyond the scope of the basic dynamics course are indicated by a star (*) and may be omitted. Note that this material also provides a suitable reference for basic principles when it is discussed in more advanced courses. Finally, Appendix A provides a list of mathematical formulas needed to solve the problems in the book, Appendix B provides a brief review of vector analysis, and Appendix C reviews application of the chain rule. Alternative Coverage. At the discretion of the instructor, it is possible to cover Chapters 12 through 19 in the following order with no loss in continuity: Chapters 12 and 16 (Kinematics), Chapters 13 and 17 (Equations of Motion), Chapter 14 and 18 (Work and Energy), and Chapters 15 and 19 (Impulse and Momentum).

Ackn owl edgments The author has endeavored to write this book so that it will appeal to both the student and instructor. Through the years, many people have helped in its development, and I will always be grateful for their valued suggestions and comments. Specifically, I wish to thank the following individuals who have contributed their comments relative to preparing the Twelfth Edition of this work: Per Reinhall, University ofWashington Faissal A. Moslehy, University of Central Florida Richard R. Neptune, University of Texas at Austin Robert Rennaker, University of Oklahoma A particular note of thanks is also given to Professor Will Liddell, Jr., and Henry Kahlman. In addition, there are a few people that I feel deserve particular recognition. Vince O'Brien, Director of Team-Based Project Management at Pearson Education, and Rose Kernan, my production editor for many years, have both provided me with their encouragement and support. Frankly, without their help, this totally revised and enhanced edition would not be possible. Furthermore a long-time friend and associate, Kai Beng Yap, was of great help to me in checking the entire manuscript and helping to prepare the problem solutions. A special note of thanks also goes to Kurt NorIan of Laurel Tech Integrated Publishing Services in this regard. During the production process I am thankful for the assistance of my wife Conny and daughter Mary Ann with the proofreading and typing needed to prepare the manuscript for publication. Lastly, many thanks are extended to all my students and to members of the teaching profession who have freely taken the time to send me their suggestions and comments. Since this list is too long to mention, it is hoped that those who have given help in this manner will accept this anonymous recognition. I would greatly appreciate hearing from you if at any time you have any comments, suggestions, or problems related to any matters regarding this edition.

Russell Charles Hibbeler [email protected]

PREFACE VII

M asteri n g E n g i n eering for I nstructors Incorporate dynamic homework into your course with automatic grading and adaptive tutoring. Choose from a wide variety of stimulating problems, including free-body diagram drawing capabilities, algorithmically-generated problem sets, and more. MasteringEngineering emulates the instructor's office-hour environment, coaching students on problem-solving techniques by asking students simpler sub-questions.

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x R E S O U RC E S F O R I N ST R U CT O R S

Resou rces for I n structo rs

• Instructor's Solutions Manual. This supplement provides complete solutions supported by problem statements and problem figures. The twelfth edition manual was revised to improve readability and was triple accuracy checked.
• Instructor's Resource CD-ROM. Visual resources to accompany the text are located on this CD as well as on the Pearson Higher Education website: www.pearsonhighered.com. If you are in need of a login and password for this site, please contact your local Pearson representative. Visual resources include all art from the text, available in PowerPoint slide and JPEG format.
• Video Solutions. Developed by Professor Edward Berger, University of Virginia, video solutions are located on the Companion Website for the text and offer step-by-step solution walkthroughs of representative homework problems from each section of the text. Make efficient use of class time and office hours by showing students the complete and concise problem-solving approaches that they can access any time and view at their own pace. The videos are designed to be a flexible resource to be used however each instructor and student prefers. A valuable tutorial resource, the videos are also helpful for student self-evaluation as students can pause the videos to check their understanding and work alongside the video. Access the videos at www.prenhall.com/hibbeler and follow the links for the Engineering Mechanics: Dynamics, Twelfth Edition text. Resou rces for Students
• Dynamics Study Pack. This supplement contains chapter-by-chapter study materials, a Free-Body Diagram Workbook and access to the Companion Website where additional tutorial resources are located.
• Companion Website. The Companion Website, located at www.prenhall.com/hibbeler. includes opportunities for practice and review including:
• Video Solutions- Complete, step-by-step solution walkthroughs of representative homework problems from each section. Videos offer:
• Fully worked Solutions- Showing every step of representative homework problems, to help students make vital connections between concepts.
• Self-paced Instruction- Students can navigate each problem and select, play, rewind, fast-forward, stop, and jump-to-sections within each problem's solution.
• 2417 Access-Help whenever students need it with over 20 hours of helpful review. An access code for the Engineering Mechanics: Dynamics, Twelfth Edition website is included inside the Dynamics Study Pack. To redeem the code and gain access to the site, go to www.prenhall.com/hibbeler and follow the directions on the access code card. Access can also be purchased directly from the site.
• Dynamics Practice Problems Workbook. This workbook contains additional worked problems. The problems are partially solved and are designed to help guide students through difficult topics.

Orderin g Options The Dynamics Study Pack and MasteringEngineering resources are available as stand-alone items for student purchase and are also available packaged with the texts. The ISBN for each valuepack is as follows:

• Engineering Mechanics: Dynamics with Study Pack: 0-13-700239-
• Engineering Mechanics: Dynamics with Study Pack and MasteringEngineering Student Access Card: 0-13-701630-

Custom Solutions New options for textbook customization are now available for Engineering Mechanics, Twelfth Edition. Please contact your local Pearson/Prentice Hall representative for details.

XII C O N T E N T S

15.3 Conservation of Linear Momentu m for a System of Pa rticles 236 15.4 I mpact 248 15.5 Ang u l a r Momentu m 262 15.6 Relation Between Mom ent of a Force and Ang u l a r Momentu m 263 15.7 Principle of Ang u l a r I mpu lse and Momentu m 266 15.8 Steady Flow of a F l u id Stream 277 *15.9 Propulsion with Va riable M ass 282

Review

1. Kinematics and Kinetics of a Particle 298

1 6

Planar Kinematics of a

Rigid Body 311

Chapter Objectives 311 16.1 P lanar Rigid-Body Motion 311 16.2 Translation 313 16.3 Rotation about a Fixed Axis 31 4 16.4 Absol ute Motion Analysis 329

1 7

Planar Kinetics of a Rigid

Body: Force and

Acceleration 395

Chapter Objectives 395 17.1 Mom ent of Inertia 395 17.2 Planar Kinetic Equations of Motion 409 17.3 Equations of Motion: Translation 41 2 17.4 Equations of Motion: Rotation about a Fixed Axis 425 17.5 Equations of Motion: General P lane Motion 440

1 8

Planar Kinetics of a

Rigid Body: Work and

Energy 455

Chapter Objectives 455 18.1 Kinetic Energy 455 18.2 The Work of a Force 458 18.3 The Work of a Couple 460 18.4 Principle of Work and Energy 18.5 Conservation of Energy 477

16.5 Relative-Motion Analysis: Velocity (^337) 1 9 16.6 Instantaneous Center of Zero Velocity 351 16.7 Relative- Motion Ana lysis: Acce leration 363 16.8 Relative-Motion Analysis u sing Rotating Axes 377

Planar Kinetics of a Rigid

Body: Impulse and

Momentum 495

Chapter Objectives 495 19.1 Linea r and Ang u l a r Momentu m 495

19.2 Principle of Impulse and Mo mentum 501 19.3 Conservation of M omentum 517 *19.4 Eccentric Impact 521

Review

2. P lanar Kinematics and Kinetics of a Rig id Body 534

20

Three-Dimensional

Kinematics of a Rigid

Body 549

Chapter Objectives 549 20.1 Rotation About a Fixed Point 549 *20.2 The Time Derivative of a Vector Measured from Either a Fixed or Translating-Rotating System 552 20.3 General M otion 557 *20.4 Relative-Motion Ana lysis Using Translating and Rotating Axes 566

2 1

Three-Dimensional

Kinetics of a Rigid

Body 579

Chapter Objectives 579 *21.1 Moments and Products of Inertia 21.2 Ang u l a r M omentum 589 21.3 Kinetic Energy 592 *21.4 Equations of M otion 600

CONTENTS X III

*21.5 Gyroscopic M otion 614 21.6 To rq ue- Free Motion 620

2 2

Vibrations 631

Chapter Objectives 631 *22.1 Und amped Free Vibration 631 *22.2 Energy M ethods 645 *22.3 Und amped Forced Vibration 651 *22.4 Viscous Damped Free Vibration 655 *22.5 Viscous Damped Forced Vibration 658 *22.6 Electrical Circuit Analogs 661

Appendix

A. M athe matica l Expressions 670 B. C.

Vector Analysis 672 The Chain R u l e 677

Fundamental Problems

Partial Solutions and

Answers 680

Answers to Selected

Problems 699

Index 725

Credits

Chapter 12, The United States Navy Blue Angels perform in an air show as part of San Francisco's Fleet Week celebration. ©Roger Ressmeyer/CORBIS. All Rights Reserved. Chapter 13, Orange juice factory, elevated view. Getty Images. Chapter 14, White roller coaster of the Mukogaokayuen ground, Kanagawa. ©Yoshio Kosaka/CORBIS. All Rights Reserved. Chapter 15, Close-up of golf club hitting a golf ball off the tee. Alamy Images Royalty Free. Chapter 16, Windmills in Livermore, part of an extensive wind farm, an alternative source of electrical power, California, United States. Brent Winebrenner/Lonely Planet Images/Photo 20-20. Chapter 17, Burnout drag racing car at Santa Pod Raceway, England. Alamy Images. Chapter 18, Drilling rig. Getty Images. Chapter 19, NASA shuttle docking with the International Space Station. Dennis Hallinan/Alamy Images. Chapter 20, Man watching robotic welding. ©Ted Horowitz/CORBIS. All Rights Reserved. Chapter 21, A spinning Calypso ride provides a blur of bright colors at Waldameer Park and Water World in Erie, Pennsylvania. Jim Cole/ Alamy Images. Chapter 22, A train track and train wheel give great perspective to the size and power of railway transportation. Joe Belanger/Alamy Images. Cover 1, Lightflight Helecopter in flight. Lightflight Helecopter is used by Stanford University Hospital Santa Clara Valley Medical Center. ©CORBIS/ All rights reserved. Cover 2, Helecopter tail rotor blades detail. Steve Mann/Shutterstock. Other images provided by the author.

xv

Although each of these planes is rather large, from a distance their motion can be analysed as if each plane were a particle.

Ki n e m ati cs of a P a rti c l e

CHAPTER OBJECTIVES

• To introduce the concepts of position, displacem ent, velocity, and acceleration.
• To study particle motion a long a straig ht line and represent this motion g raphica l l y.
• To investig ate particl e motion a long a curved path using different coordinate systems.
• To present an analysis of dependent motion of two particles.
• To exa mine the principles of relative motion of two particles using translating axes.

1 2. 1 I ntroduction

Mechanics is a branch of the physical sciences that is concerned with the state of rest or motion of bodies subjected to the action of forces. Engineering mechanics is divided into two areas of study, namely, statics and dynamics. Statics is concerned with the equilibrium of a body that is either at rest or moves with constant velocity. Here we will consider dynamics, which deals with the accelerated motion of a body. The subject of dynamics will be presented in two parts: kinematics, which treats only the geometric aspects of the motion, and kinetics, which is the analysis of the forces causing the motion. To develop these principles, the dynamics of a particle will be discussed first, followed by topics in rigid-body dynamics in two and then three dimensions.