Tài liệu Engineering mechanics - dynamics (si edn) 3rd ed - a. pytel, j. kiusalaas (cengage, 2010)

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CONVERSIONS BETWEEN U.S. CUSTOMARY UNITS AND SI UNITS (Continued) Times conversion factor U.S. Customary unit Equals SI unit Moment of inertia (area) inch to fourth power in.4 inch to fourth power in.4 Accurate Practical 416,231 416,000 0.416231 3 1026 millimeter to fourth power meter to fourth power mm4 m4 kilogram meter squared kg·m2 watt (J/s or N·m/s) watt watt W W W 47.9 6890 47.9 6.89 pascal (N/m2) pascal kilopascal megapascal Pa Pa kPa MPa 16,400 16.4 3 1026 millimeter to third power meter to third power mm3 m3 meter per second meter per second meter per second kilometer per hour m/s m/s m/s km/h cubic meter cubic meter cubic centimeter (cc) liter cubic meter m3 m3 cm3 L m3 0.416 3 1026 Moment of inertia (mass) slug foot squared slug-ft2 1.35582 1.36 Power foot-pound per second foot-pound per minute horsepower (550 ft-lb/s) ft-lb/s ft-lb/min hp 1.35582 0.0225970 745.701 1.36 0.0226 746 Pressure; stress pound per square foot pound per square inch kip per square foot kip per square inch psf psi ksf ksi Section modulus inch to third power inch to third power in.3 in.3 Velocity (linear) foot per second inch per second mile per hour mile per hour ft/s in./s mph mph Volume cubic foot cubic inch cubic inch gallon (231 in.3) gallon (231 in.3) ft3 in.3 in.3 gal. gal. 47.8803 6894.76 47.8803 6.89476 16,387.1 16.3871 3 1026 0.3048* 0.0254* 0.44704* 1.609344* 0.0283168 16.3871 3 1026 16.3871 3.78541 0.00378541 0.305 0.0254 0.447 1.61 0.0283 16.4 3 1026 16.4 3.79 0.00379 *An asterisk denotes an exact conversion factor Note: To convert from SI units to USCS units, divide by the conversion factor Temperature Conversion Formulas 5 T(°C) 5 } }[T(°F) 2 32] 5 T(K) 2 273.15 9 5 T(K) 5 } }[T(°F) 2 32] 1 273.15 5 T(°C) 1 273.15 9 9 9 T(°F) 5 } }T(°C) 1 32 5 } }T(K) 2 459.67 5 5 This page intentionally left blank Engineering Mechanics Dynamics Third Edition SI Edition Andrew Pytel The Pennsylvania State University Jaan Kiusalaas The Pennsylvania State University SI Edition prepared by Ishan Sharma Indian Institute of Technology, Kanpur Australia · Brazil · Japan · Korea · Mexico · Singapore · Spain · United Kingdom · United States Engineering Mechanics: Dynamics, Third Edition Andrew Pytel and Jaan Kiusalaas SI Edition prepared by Ishan Sharma Publisher, Global Engineering Program: Christopher M. 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To Jean, Leslie, Lori, John, Nicholas and To Judy, Nicholas, Jennifer, Timothy This page intentionally left blank Contents Preface to the SI Edition xi Preface xiii Chapter 11 11.1 11.2 11.3 11.4 Introduction to Dynamics Introduction 1 Derivatives of Vector Functions 3 Position, Velocity, and Acceleration of a Particle Newtonian Mechanics 5 1 4 Chapter 12 Dynamics of a Particle: Rectangular Coordinates 12.1 12.2 12.3 12.4 12.5 *12.6 Chapter 13 Dynamics of a Particle: Curvilinear Coordinates 13.1 13.2 13.3 13.4 69 Introduction 69 Kinematics—Path (Normal-Tangential) Coordinates 70 Kinematics—Polar and Cylindrical Coordinates 82 Kinetics: Force-Mass-Acceleration Method 95 Chapter 14 Work-Energy and Impulse-Momentum Principles for a Particle 14.1 14.2 14.3 14.4 15 Introduction 15 Kinematics 16 Kinetics: Force-Mass-Acceleration Method 27 Dynamics of Rectilinear Motion 29 Curvilinear Motion 44 Analysis of Motion by the Area Method 56 117 Introduction 117 Work of a Force 118 Principle of Work and Kinetic Energy 122 Conservative Forces and the Conservation of Mechanical Energy 133 * Indicates optional articles vii viii Contents 14.5 14.6 14.7 *14.8 Power and Efficiency 144 Principle of Impulse and Momentum 150 Principle of Angular Impulse and Momentum 158 Space Motion under a Gravitational Force 168 Chapter 15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 15.10 *15.11 Chapter 16 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 *16.10 Dynamics of Particle Systems Planar Kinematics of Rigid Bodies 273 Introduction 273 Plane Angular Motion 275 Rotation about a Fixed Axis 278 Relative Motion of Two Points in a Rigid Body 287 Method of Relative Velocity 288 Instant Center for Velocities 301 Method of Relative Acceleration 312 Absolute and Relative Derivatives of Vectors 326 Motion Relative to a Rotating Reference Frame 329 Method of Constraints 344 Chapter 17 Planar Kinetics of Rigid Bodies: Force-Mass-Acceleration Method 17.1 17.2 17.3 17.4 17.5 *17.6 185 Introduction 185 Kinematics of Relative Motion 186 Kinematics of Constrained Motion 192 Kinetics: Force-Mass-Acceleration Method 198 Work-Energy Principles 214 Principle of Impulse and Momentum 217 Principle of Angular Impulse and Momentum 218 Plastic Impact 234 Impulsive Motion 236 Elastic Impact 248 Mass Flow 257 357 Introduction 357 Mass Moment of Inertia; Composite Bodies 358 Angular Momentum of a Rigid Body 368 Equations of Motion 371 Force-Mass-Acceleration Method: Plane Motion 373 Differential Equations of Motion 398 Chapter 18 Planar Kinetics of Rigid Bodies: Work-Energy and Impulse-Momentum Methods 18.1 Introduction 415 Part A: Work-Energy Method 416 18.2 Work and Power of a Couple 416 18.3 Kinetic Energy of a Rigid Body 418 18.4 Work-Energy Principle and Conservation of Mechanical Energy 429 415 Contents Part B: Impulse-Momentum Method 18.5 Momentum Diagrams 442 18.6 Impulse-Momentum Principles 18.7 Rigid-Body Impact 459 442 444 Chapter 19 Rigid-Body Dynamics in Three Dimensions *19.1 *19.2 *19.3 *19.4 *19.5 *19.6 Introduction 475 Kinematics 476 Impulse-Momentum Method 491 Work-Energy Method 497 Force-Mass-Acceleration Method 511 Motion of an Axisymmetric Body 527 Chapter 20 20.1 20.2 20.3 20.4 *20.5 475 Vibrations Introduction 547 Free Vibrations of Particles 548 Forced Vibrations of Particles 565 Rigid-Body Vibrations 578 Methods Based on Conservation of Energy 547 587 Appendix D Proof of the Relative Velocity Equation for Rigid-Body Motion 599 Appendix E Equations 601 E.1 E.2 E.3 E.4 Introduction 601 Numerical Methods 601 Application of MATLAB 602 Linear Interpolation 605 Appendix F F.1 F.2 F.3 F.4 F.5 F.6 F.7 F.8 Numerical Solution of Differential Mass Moments and Products of Inertia 607 Introduction 607 Review of Mass Moment of Inertia 607 Moments of Inertia of Thin Plates 608 Mass Moment of Inertia by Integration 609 Mass Products of Inertia; Parallel-Axis Theorems 616 Products of Inertia by Integration; Thin Plates 617 Inertia Tensor; Moment of Inertia about an Arbitrary Axis 618 Principal Moments and Principal Axes of Inertia 619 Answers to Even-Numbered Problems 633 Index 641 ix This page intentionally left blank Preface to the SI Edition This edition of Engineering Mechanics: Dynamics has been adapted to incorporate the International System of Units (Le Système International d’Unités or SI) throughout the book. Le Système International d’Unités The United States Customary System (USCS) of units uses FPS (footpound−second) units (also called English or Imperial units). SI units are primarily the units of the MKS (meter-kilogram-second) system. However, CGS (centimeter-gram-second) units are often accepted as SI units, especially in textbooks. Using SI Units in this Book In this book, we have used both MKS and CGS units. USCS units or FPS units used in the US Edition of the book have been converted to SI units throughout the text and problems. However, in case of data sourced from handbooks, government standards, and product manuals, it is not only extremely difficult to convert all values to SI, it also encroaches upon the intellectual property of the source. Also, some quantities such as the ASTM grain size number and Jominy distances are generally computed in FPS units and would lose their relevance if converted to SI. Some data in figures, tables, examples, and references, therefore, remains in FPS units. For readers unfamiliar with the relationship between the FPS and the SI systems, conversion tables have been provided inside the front and back covers of the book. To solve problems that require the use of sourced data, the sourced values can be converted from FPS units to SI units just before they are to be used in a calculation. To obtain standardized quantities and manufacturers’ data in SI units, the readers may contact the appropriate government agencies or authorities in their countries/regions. xi xii Preface to the SI Edition Instructor Resources A Printed Instructor’s Solution Manual in SI units is available on request. An electronic version of the Instructor’s Solutions Manual, and PowerPoint slides of the figures from the SI text are available through www.cengage.com/ engineering. The readers’ feedback on this SI Edition will be highly appreciated and will help us improve subsequent editions. The Publishers Preface Statics and dynamics are the foundation subjects in the branch of engineering known as engineering mechanics. Engineering mechanics is, in turn, the basis of many of the traditional fields of engineering, such as aerospace engineering, civil engineering, and mechanical engineering. In addition, engineering mechanics often plays a fundamental role in such diverse fields as medicine and biology. Applying the principles of statics and dynamics to such a wide range of applications requires reasoning and practice rather than memorization. Although the principles of statics and dynamics are relatively few, they can only be truly mastered by studying and analyzing problems. Therefore, all modern textbooks, including ours, contain a large number of problems to be solved by the student. Learning the engineering approach to problem solving is one of the more valuable lessons to be learned from the study of statics and dynamics. In this, our third edition of Statics and Dynamics, we have made every effort to improve our presentation without compromising the following principles that formed the basis of the previous editions. • Each sample problem is carefully chosen to help students master the intricacies of engineering problem analysis. • The selection of homework problems is balanced between “textbook” problems that illustrate the principles of engineering mechanics in a straightforward manner, and practical engineering problems that are applicable to engineering design. • The number of problems using U.S. Customary Units and SI Units are approximately equal. • The importance of correctly drawn free-body diagrams is emphasized throughout. • Whenever applicable, the number of independent equations is compared to the number of unknowns before the governing equations are written. • Numerical methods for solving problems are seamlessly integrated into the text, the emphasis being on computer applications, not on computer programming. • Review Problems appear at the end of each chapter to encourage students to synthesize the topics covered in the chapter. Both Statics and Dynamics contain several optional topics, which are marked with an asterisk (*). Topics so indicated can be omitted without jeopardizing the presentation of other subjects. An asterisk is also used to xiii xiv Preface indicate problems that require advanced reasoning. Articles, sample problems, and problems associated with numerical methods are preceded by an icon representing a compact disk. In this third edition of Dynamics, we have made what we consider to be a number of significant improvements based upon the feedback received from students and faculty who have used the previous editions. In addition, we have incorporated many of the suggestions provided by the reviewers of the second edition. A number of articles have been reorganized, or rewritten, to make the topics easier for the student to understand. For example, the discussion of the work-energy method in Chapter 18 has been streamlined. Also, Chapter 20 (Vibrations) has been reorganized to provide a more concise presentation of the material. In addition, sections entitled Review of Equations have been added at the end of each chapter as an aid to problem solving. The total numbers of sample problems and problems remain about the same as in the previous edition; however, the introduction of two colors improves the overall readability of the text and artwork. Compared with the previous edition, approximately one-third of the problems are new, or have been modified. New to this edition, the Sample Problems that require numerical solutions have been solved using MATLAB© , the software program that is familiar to many engineering students. Study Guide to Accompany Pytel and Kiusalaas Engineering Mechanics, Dynamics, Third Edition, J.L. Pytel and A. Pytel, 2009. The goals of this study guide are two-fold. First, self-tests are included to help the student focus on the salient features of the assigned reading. Second, the study guide uses “guided” problems which give the student an opportunity to work through representative problems, before attempting to solve the problems in the text. Ancillary We are grateful to the following reviewers for their valuable suggestions: Acknowledgments Hamid R. Hamidzadeh, Tennessee State University Aiman S. Kuzmar, The Pennsylvania State University—Fayette, The Eberly Campus Gary K. Matthew, University of Florida Noel Perkins, University of Michigan Corrado Poli, University of Massachusetts, Amherst ANDREW PYTEL JAAN KIUSALAAS 11 Introduction to Dynamics 11.1 Introduction Sir Isaac Newton (1643–1727) in his treatise Philosophiae Naturalis Principia Mathematica established the groundwork for dynamics with his three laws of motion and the universal theory of gravitation, which are discussed in this chapter. (Time & Life Pictures/Getty Images) Classical dynamics studies the motion of bodies using the principles established by Newton and Euler.* The organization of this text is based on the subdivisions of classical dynamics shown in Fig. 11.1. * Sir Isaac Newton is credited with laying the foundation of classical mechanics with the publication of Principia in 1687. However, the laws of motion as we use them today were developed by Leonhard Euler and his contemporaries more than sixty years later. In particular, the laws for the motion of finite bodies are attributable to Euler. 1 2 CHAPTER 11 Introduction to Dynamics Absolute motion Kinematics Relative motion Particles Classical dynamics Force-mass-acceleration method Rigid bodies Kinetics Work-energy method Impulse-momentum method Fig. 11.1 The first part of this text deals with dynamics of particles. A particle is a mass point; it possesses a mass but has no size. The particle is an approximate model of a body whose dimensions are negligible in comparison with all other dimensions that appear in the formulation of the problem. For example, in studying the motion of the earth around the sun, it is permissible to consider the earth as a particle, because its diameter is much smaller than the dimensions of its orbit. The second part of this text is devoted mainly to dynamics of rigid bodies. A body is said to be rigid if the distance between any two material points of the body remains constant, that is, if the body does not deform. Because any body undergoes some deformation when loads are applied to it, a truly rigid body does not exist. However, in many applications the deformation is so small (relative to the dimensions of the body) that the rigid-body idealization is a good approximation. As seen in Fig. 11.1, the main branches of dynamics are kinematics and kinetics. Kinematics is the study of the geometry of motion. It is not concerned with the causes of motion. Kinetics, on the other hand, deals with the relationships between the forces acting on the body and the resulting motion. Kinematics is not only an important topic in its own right but is also a prerequisite to kinetics. Therefore, the study of dynamics always begins with the fundamentals of kinematics. Kinematics can be divided into two parts as shown in Fig. 11.1: absolute motion and relative motion. The term absolute motion is used when the motion is described with respect to a fixed reference frame (coordinate system). Relative motion, on the other hand, describes the motion with respect to a moving coordinate system. Figure 11.1 also lists the three main methods of kinetic analysis. The force-mass-acceleration (FMA) method is a straightforward application of the Newton-Euler laws of motion, which relate the forces acting on the body to its mass and acceleration. These relationships, called the equations of motion, must be integrated twice in order to obtain the velocity and the position as functions of time. The work-energy and impulse-momentum methods are integral forms of Newton-Euler laws of motion (the equations of motion are integrated with respect to position or time). In both methods the acceleration is eliminated by 11.2 Derivatives of Vector Functions the integration. These methods can be very efficient in the solution of problems concerned with velocity-position or velocity-time relationships. The purpose of this chapter is to review the basic concepts of Newtonian mechanics: displacement, velocity, acceleration, Newton’s laws, and units of measurement. 11.2 Derivatives of Vector Functions A knowledge of vector calculus is a prerequisite for the study of dynamics. Here we discuss the derivatives of vectors; integration is introduced throughout the text as needed. The vector A is said to be a vector function of a scalar parameter u if the magnitude and direction of A depend on u. (In dynamics, time is frequently chosen to be the scalar parameter.) This functional relationship is denoted by A(u). If the scalar variable changes from the value u to (u + u), the vector A will change from A(u) to A(u + u). Therefore, the change in the vector A can be written as A = A(u + u) − A(u) (11.1) As seen in Fig. 11.2, A is due to a change in both the magnitude and the direction of the vector A. The derivative of A with respect to the scalar u is defined as A A(u + u) − A(u) dA = lim = lim u→0 u u→0 du u ΔA (11.2) A(u + Δu) assuming that the limit exists. This definition resembles the derivative of the scalar function y(u), which is defined as y y(u + u) − y(u) dy = lim = lim u→0 u u→0 du u A(u) (11.3) Caution In dealing with a vector function, the magnitude of the derivative |dA/du| must not be confused with the derivative of the magnitude d|A|/du. In general, these two derivatives will not be equal. For example, if the magnitude of a vector A is constant, then d|A|/du = 0. However, |dA/du| will not equal zero unless the direction of A is also constant. The following useful identities can be derived from the definitions of derivatives (A and B are assumed to be vector functions of the scalar u, and m is also a scalar): d(mA) du d(A + B) du d(A · B) du d(A × B) du dA dm + A du du dA dB = + du du dB dA = A· + ·B du du dB dA =A× + ×B du du =m (11.4) (11.5) (11.6) (11.7) O Fig. 11.2 3
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