J. W. McNabb

Dynamics for Engineers

Contents: Dynamics for Engineers.- 13 Kinematics of Particles.- 14 Particle Kinetics: Force and Accelerationno.- 15 Particle Kinetics: Energy.- 16 Particle Kinetics: Impulse-Momentum.- 17 Two-Dimensional Kinematics of Rigid Bodies.- 18 Two-Dimensional Kinetics of Rigid Bodies: Force and Acceleration.- 19 Two-Dimensional Kinetics of Rigid Bodies-Energy.- 20 Two-Dimensional Kinetics of Rigid Bodies: Impulse-Momentum.- 21 Three-Dimensional Kinematics of Rigid Bodies.- 22 Three-Dimensional Kinetics of Rigid Bodies.- 23 Vibrations.- Appendices.- Answers.

Statics for engineers

1 Introductory Principles.- 1.1 Review of Mechanics.- 1.2 Idealizations and Mathematical Models.- 1.3 Newtons Laws.- 1.4 Newtons Law of Universal Gravitation.- 1.5 Systems of Units and Conversion Factors.- 1.6 Dimensional Analysis.- 1.7 Problem Solving Techniques.- 1.8 Accuracy of Data and Solutions.- 2 Equilibrium of a Particle in Two Dimensions.- 2.1 Scalar and Vector Quantities.- 2.2 Elementary Vector Operations.- 2.3 Force Expressed in Vector Form.- 2.4 Addition of Forces Using Rectangular Components.- 2.5 Supports and Connections.- 2.6 The Free-Body Diagram.- 2.7 Equilibrium Conditions and Applications.- 3 Equilibrium of Particles in Three Dimensions.- 3.1 Force in Terms of Rectangular Components.- 3.2 Force in Terms of Magnitude and Unit Vector.- 3.3 Dot (Scalar) Product.- 3.4 Addition of Forces Using Rectangular Components.- 3.5 Equilibrium Conditions and Applications.- 4 Equilibrium of Rigid Bodies in Two Dimensions.- 4.1 Concept of the Moment-Scalar Approach.- 4.2 Internal and External Forces-Force Transmissibility Principle.- 4.3 Replacement of a Single Force by a Force and a Couple.- 4.4 Replacement of a Force System by a Force and a Couple.- 4.5 Replacement of a Force System by a Single Force.- 4.6 Replacement of a Distributed Force System by a Single Force.- 4.7 Supports and Connections.- 4.8 The Free-Body Diagram.- 4.9 Equilibrium Conditions and Applications.- 5 Equilibrium of Rigid Bodies in Three Dimensions.- 5.1 Definition of the Cross (Vector) Product.- 5.2 The Cross-Product in Terms of Rectangular Components.- 5.3 Vector Representation of the Moment of a Force.- 5.4 Varignons Theorem.- 5.5 Moment of a Force About a Specific Axis.- 5.6 Vector Representation of a Couple.- 5.7 Replacement of a Single Force by a Force and a Couple.- 5.8 Replacement of a General Force System by a Force and a Couple.- 5.9 Equilibrium Conditions and Applications.- 5.10 Determinacy and Constraints.- 6 Truss Analysis.- 6.1 Analysis of Simple Trusses.- 6.2 Member Forces Using the Method of Joints.- 6.3 Members Carrying No Forces.- 6.4 Member Forces Using the Method of Sections.- 6.5* Determinacy and Constraints.- 6.6 Compound Trusses.- 6.7* Three-Dimensional Trusses: Member Forces Using the Method of Joints.- 7 Frames and Machines.- 7.1 Multiforce Members.- 7.2 Frame Analysis.- 7.3 Machine Analysis.- 8 Internal Forces in Members.- 8.1 Internal Forces.- 8.2 Sign Conventions.- 8.3 Axial Force and Torque Diagrams.- 8.4 Shear and Moment at Specified Cross-Sections.- 8.5 Shear and Moment Equations.- 8.6 Load, Shear, and Moment Relationships.- 8.7 Shear and Moment Diagrams.- 8.8* Cables Under Concentrated Loads.- 8.9* General Cable Theorem.- 8.10* Cables Under Uniform Loads.- 8.11 Frames-Internal Forces at Specified Sections.- 8.12 Internal Force Diagrams for Two-Dimensional Frames.- 9 Friction.- 9.1 Nature and Characteristics of Dry Friction.- 9.2 Angles of Static and Kinetic Friction.- 9.3 Applications of the Fundamental Equations.- 9.4 The Six Fundamental Machines.- 9.5* Friction on V-Belts and Flat Belts.- 9.6* Friction on Pivot and Collar Bearings and Disks.- 9.7* Friction on Journal Bearings.- 9.8 Problems in Which Motion Is Not Predetermined.- 10 Centers of Gravity, Centers of Mass, and Centroids.- 10.1 Centers of Gravity and of Mass.- 10.2 Centroid of Volume, Area, or Line.- 10.3 Composite Objects.- 10.4 Centroids by Integration.- 10.5* Theorems of Pappus and Guldinus.- 10.6* Fluid Statics.- 11 Moments and Products of Inertia.- 11.1 Concepts and Definitions.- 11.2 Parallel-Axis Theorems.- 11.3 Moments of Inertia by Integration.- 11.4 Moments of Inertia of Composite Areas and Masses.- 11.5* Area Product of Inertia.- 11.6* Area Principal Axes and Principal Moments of Inertia.- 11.7* Mohrs Circle for Area Moments and Products of Inertia.- 11.8* Mass Principal Axes and Principal Moments of Inertia.- 12 Virtual Work and Stationary Potential Energy.- 12.1 Differential Work of a Force.- 12.2 Differential Work of a Couple.- 12.3 The Concept of Finite Work.- 12.4 The Concept of Virtual Work.- 12.5* Work of Conservative Forces.- 12.6* The Concept of Potential Energy.- 12.7* The Principle of Stationary Potential Energy.- 12.8* States of Equilibrium.- Appendix A. Properties of Selected Lines and Areas.- Appendix B. Properties of Selected Masses.- Appendix C. Useful Mathematical Relations.- Appendix D. Selected Derivatives.- Appendix E. Selected Integrals.- Appendix F. Supports and Connections.- Appendices.- Answers.

Particle Kinetics: Force and Acceleration

The design of machines to achieve maximum performance is one of humanity’s oldest engineering challenges. The design of sailing vessels and some understanding of the wind’s propulsive force go far back in history. The first sailing ship may have been designed by the Egyptians some 5000 years ago. The Egyptians learned about sail forces, as they affected steering, and placed the single mast well forward for sailing down the Nile before a constant southerly breeze. For use on the Mediterranean, the mast was located nearly amidships. Such vessels were followed by Homeric Greek ships which became more specialized and larger.

Kinetics of Particles: Impulse-Momentum

Since the beginning of time, the principles of impact and momentum have influenced our daily lives here on Earth and in the depth of space. There is strong evidence that the universe exploded from an infinitely dense primal seed, possibly 8 to 18 billion years ago, and that it will continue to expand forever. In these respects, this event inaugurated an eternal potential for collisions between debris and planet Earth. In fact, it is now believed that the collision of a large comet with Earth is the reason for the extinction of the dinosaurs from the face of our planet.

Three-Dimensional Kinetics of Rigid Bodies

On the occasion of its 25th anniversary, the National Academy of Engineering selected the Moon landing as the single most impressive engineering achievement in the past 25 years. That event, which was witnessed on television in 1969 by six hundred million people marked the pinnacle of engineering vision and daring. When Neil Armstrong set the first earthling foot onto that celestial body, human consciousness leaped into space to a degree unequaled since the discovery of the New World. That small step by Armstrong was a triumph for humankind and a fulfillment of the hopes and aspirations of people everywhere without regard to race and national origin. The Moon landing illustrated the vitality and importance of teamwork while eloquently emphasizing the essence of a great nation.

Two-Dimensional Kinetics of Rigid Bodies: Impulse-Momentum

Mars has always been a cause of fascination to scientists and a source of inspiration to poets. The remarkable and vivid pictures sent back to Earth by Vikings 1 and 2 spacecraft revealed that Mars was once a living planet with water flowing freely and possibly a civilization that no longer exists. Despite the preliminary nature of these conclusions, Mars has become a case study of how to prevent this from happening to Earth.

Two-Dimensional Kinetics of Rigid Bodies: Energy

In 1893, George Washington Ferris was the champion of U.S. technology, the engineer whose vision and relentless pursuit of his deam proved that America could top the Eiffel Tower. That magnificent structure which could carry 2,160 passengers at a time to a height equivalent to 26 story building was a significant engineering triumph in an era when most people had never seen a skyscraper. His reputation quickly grew as the press recounted his struggle to build the machine that other engineers had said could not be built.

Three-Dimensional Kinematics of Rigid Bodies

Engineers are increasingly challenged to develop the technology necessary for faster, smaller, lighter, cheaper, and more efficient systems. Modern engineering systems, such as cars, airplanes, buildings, bridges, space stations, and others, require expertise offered by different disciplines and especially by mechanical, civil, and electrical engineering. With so many technical disciplines involved and shrinking resources, the solution is partnering for success. Consequently, future engineers are faced with the daunting but exciting task of having to work as teams rather than individual.

Two-Dimensional Kinetics of Rigid Bodies: Force and Acceleration

Automobile and aircraft manufacturers perform windtunnel tests to determine resisting forces applied by the air to their models. Recent developments may enable engineers to replace wind tunnels with computer simulation packages similar to the one shown on the cover page of this chapter. The substantial saving in time and money make simulation an attractive alternative to traditional wind tunnel testing. This fact reflects the incredible evolution of the engineering fields and manifests the relentless efforts and genius of engineers from years past. Future engineers need to be exposed to, and learn more about, emerging technologies.

Kinematics of Particles

As you begin the study of dynamics, you should be filled with excitement, interest, and a craving to discover new principles, conquer new frontiers, and develop new insights. This is a necessary step to establishing a solid foundation for your future development as an engineer. At times you may question the benefits of some topics and their real engineering value. This is not an unexpected reaction for a beginning engineering student whose sense of the profession is yet to be developed.