Vector Mechanics for Engineers: Statics and Dynamics

Cover Page......Page 1
Title Page......Page 2
Copyright Page......Page 3
About the Authors......Page 4
Preface......Page 16
List of Symbols......Page 24
Contents......Page 6
1 Introduction......Page 27
1.2 Fundamental Concepts and Principles......Page 28
1.3 Systems of Units......Page 31
1.4 Conversion from One System of Units to Another......Page 36
1.5 Method of Problem Solution......Page 37
1.6 Numerical Accuracy......Page 39
2 Statics of Particles......Page 41
2.2 Force on a Particle. Resultant of Two Forces......Page 42
2.3 Vectors......Page 43
2.4 Addition of Vectors......Page 44
2.5 Resultant of Several Concurrent Forces......Page 46
2.6 Resolution of a Force into Components......Page 47
2.7 Rectangular Components of a Force. Unit Vectors......Page 53
2.8 Addition of Forces by Summing x and y Components......Page 56
2.9 Equilibrium of a Particle......Page 61
2.11 Problems Involving the Equilibrium of a Particle. Free-Body Diagrams......Page 62
2.12 Rectangular Components of a Force in Space......Page 71
2.13 Force Defined by Its Magnitude and Two Points on Its Line of Action......Page 74
2.14 Addition of Concurrent Forces in Space......Page 75
2.15 Equilibrium of a Particle in Space......Page 83
Review and Summary......Page 90
Review Problems......Page 93
Computer Problems......Page 96
3 Rigid Bodies: Equivalent Systems of Forces......Page 99
3.2 External and Internal Forces......Page 100
3.3 Principle of Transmissibility. Equivalent Forces......Page 101
3.4 Vector Product of Two Vectors......Page 103
3.5 Vector Products Expressed in Terms of Rectangular Components......Page 105
3.6 Moment of a Force about a Point......Page 107
3.8 Rectangular Components of the Moment of a Force......Page 109
3.9 Scalar Product of Two Vectors......Page 120
3.10 Mixed Triple Product of Three Vectors......Page 122
3.11 Moment of a Force about a Given Axis......Page 123
3.12 Moment of a Couple......Page 134
3.13 Equivalent Couples......Page 135
3.15 Couples Can Be Represented by Vectors......Page 137
3.16 Resolution of a Given Force into a Force at O and a Couple......Page 138
3.17 Reduction of a System of Forces to One Force and One Couple......Page 149
3.19 Equipollent Systems of Vectors......Page 151
3.20 Further Reduction of a System of Forces......Page 152
*3.21 Reduction of a System of Forces to a Wrench......Page 154
Review and Summary......Page 172
Review Problems......Page 177
Computer Problems......Page 180
4 Equilibrium of Rigid Bodies......Page 183
4.1 Introduction......Page 184
4.2 Free-Body Diagram......Page 185
4.3 Reactions at Supports and Connections for a Two-Dimensional Structure......Page 186
4.4 Equilibrium of a Rigid Body in Two Dimensions......Page 188
4.5 Statically Indeterminate Reactions. Partial Constraints......Page 190
4.6 Equilibrium of a Two-Force Body......Page 207
4.7 Equilibrium of a Three-Force Body......Page 208
4.9 Reactions at Supports and Connections for a Three-Dimensional Structure......Page 215
Review and Summary......Page 236
Review Problems......Page 239
Computer Problems......Page 242
5 Distributed Forces: Centroids and Centers of Gravity......Page 245
5.2 Center of Gravity of a Two-Dimensional Body......Page 246
5.3 Centroids of Areas and Lines......Page 248
5.4 First Moments of Areas and Lines......Page 249
5.5 Composite Plates and Wires......Page 252
5.6 Determination of Centroids by Integration......Page 262
5.7 Theorems of Pappus-Guldinus......Page 264
*5.8 Distributed Loads on Beams......Page 274
*5.9 Forces on Submerged Surfaces......Page 275
5.10 Center of Gravity of a Three-Dimensional Body. Centroid of a Volume......Page 284
5.12 Determination of Centroids of Volumes by Integration......Page 287
Review and Summary......Page 300
Review Problems......Page 304
Computer Problems......Page 307
6 Analysis of Structures......Page 311
6.1 Introduction......Page 312
6.2 Definition of a Truss......Page 313
6.3 Simple Trusses......Page 315
6.4 Analysis of Trusses by the Method of Joints......Page 316
*6.5 Joints under Special Loading Conditions......Page 318
*6.6 Space Trusses......Page 320
6.7 Analysis of Trusses by the Method of Sections......Page 330
*6.8 Trusses Made of Several Simple Trusses......Page 331
6.10 Analysis of a Frame......Page 342
6.11 Frames Which Cease to Be Rigid When Detached from Their Supports......Page 343
6.12 Machines......Page 357
Review and Summary......Page 371
Review Problems......Page 374
Computer Problems......Page 376
7 Forces in Beams and Cables......Page 379
*7.2 Internal Forces in Members......Page 380
*7.3 Various Types of Loading and Support......Page 388
*7.4 Shear and Bending Moment in a Beam......Page 389
*7.5 Shear and Bending-Moment Diagrams......Page 391
*7.6 Relations among Load, Shear, and Bending Moment......Page 399
*7.7 Cables with Concentrated Loads......Page 409
*7.8 Cables with Distributed Loads......Page 410
*7.9 Parabolic Cable......Page 411
*7.10 Catenary......Page 421
Review and Summary......Page 429
Review Problems......Page 432
Computer Problems......Page 434
8 Friction......Page 437
8.2 The Laws of Dry Friction. Coefficients of Friction......Page 438
8.3 Angles of Friction......Page 441
8.4 Problems Involving Dry Friction......Page 442
8.5 Wedges......Page 455
8.6 Square-Threaded Screws......Page 456
*8.7 Journal Bearings. Axle Friction......Page 465
*8.8 Thrust Bearings. Disk Friction......Page 467
*8.9 Wheel Friction. Rolling Resistance......Page 468
*8.10 Belt Friction......Page 475
Review and Summary......Page 486
Review Problems......Page 489
Computer Problems......Page 493
9 Distributed Forces: ixMoments of Inertia......Page 497
9.1 Introduction......Page 498
9.2 Second Moment, or Moment of Inertia, of an Area......Page 499
9.3 Determination of the Moment of Inertia of an Area by Integration......Page 500
9.4 Polar Moment of Inertia......Page 501
9.5 Radius of Gyration of an Area......Page 502
9.6 Parallel-Axis Theorem......Page 509
9.7 Moments of Inertia of Composite Areas......Page 510
*9.8 Product of Inertia......Page 523
*9.9 Principal Axes and Principal Moments of Inertia......Page 524
*9.10 Mohr’s Circle for Moments and Products of Inertia......Page 532
9.11 Moment of Inertia of a Mass......Page 538
9.12 Parallel-Axis Theorem......Page 540
9.13 Moments of Inertia of Thin Plates......Page 541
9.15 Moments of Inertia of Composite Bodies......Page 542
*9.16 Moment of Inertia of a Body with Respect to an Arbitrary Axis through O . Mass Products of Inertia......Page 558
*9.17 Ellipsoid of Inertia. Principal Axes of Inertia......Page 559
*9.18 Determination of the Principal Axes and Principal Moments of Inertia of a Body of Arbitrary Shape......Page 561
Review and Summary......Page 573
Review Problems......Page 579
Computer Problems......Page 581
10 Method of Virtual Work......Page 583
*10.2 Work of a Force......Page 584
*10.3 Principle of Virtual Work......Page 587
*10.4 Applications of the Principle of Virtual Work......Page 588
*10.5 Real Machines. Mechanical Efficiency......Page 590
*10.6 Work of a Force during a Finite Displacement......Page 604
*10.7 Potential Energy......Page 606
*10.8 Potential Energy and Equilibrium......Page 607
*10.9 Stability of Equilibrium......Page 608
Review and Summary......Page 618
Review Problems......Page 621
Computer Problems......Page 624
11 Kinematics of Particles......Page 627
11.1 Introduction to Dynamics......Page 628
11.2 Position, Velocity, and Acceleration......Page 629
11.3 Determination of the Motion of a Particle......Page 633
11.4 Uniform Rectilinear Motion......Page 642
11.5 Uniformly Accelerated Rectilinear Motion......Page 643
11.6 Motion of Several Particles......Page 644
*11.7 Graphical Solution of Rectilinear-Motion Problems......Page 656
*11.8 Other Graphical Methods......Page 657
11.9 Position Vector, Velocity, and Acceleration......Page 667
11.10 Derivatives of Vector Functions......Page 669
11.11 Rectangular Components of Velocity and Acceleration......Page 671
11.12 Motion Relative to a Frame in Translation......Page 672
11.13 Tangential and Normal Components......Page 691
11.14 Radial and Transverse Components......Page 694
Review and Summary......Page 708
Review Problems......Page 712
Computer Problems......Page 714
12 Kinetics of Particles: Newton’s Second Law......Page 717
12.1 Introduction......Page 718
12.2 Newton’s Second Law of Motion......Page 719
12.3 Linear Momentum of a Particle. Rate of Change of Linear Momentum......Page 720
12.4 Systems of Units......Page 721
12.5 Equations of Motion......Page 723
12.6 Dynamic Equilibrium......Page 725
12.7 Angular Momentum of a Particle. Rate of Change of Angular Momentum......Page 747
12.8 Equations of Motion in Terms of Radial and Transverse Components......Page 748
12.9 Motion under a Central Force. Conservation of Angular Momentum......Page 749
12.10 Newton’s Law of Gravitation......Page 750
*12.11 Trajectory of a Particle under a Central Force......Page 760
*12.12 Application to Space Mechanics......Page 761
*12.13 Kepler’s Laws of Planetary Motion......Page 764
Review and Summary......Page 772
Review Problems......Page 776
Computer Problems......Page 779
13 Kinetics of Particles: Energy and Momentum Methods......Page 781
13.2 Work of a Force......Page 782
13.3 Kinetic Energy of a Particle. Principle of Work and Energy......Page 786
13.4 Applications of the Principle of Work and Energy......Page 788
13.5 Power and Efficiency......Page 789
13.6 Potential Energy......Page 808
*13.7 Conservative Forces......Page 810
13.8 Conservation of Energy......Page 811
13.9 Motion under a Conservative Central Force. Application to Space Mechanics......Page 813
13.10 Principle of Impulse and Momentum......Page 832
13.11 Impulsive Motion......Page 835
13.13 Direct Central Impact......Page 847
13.14 Oblique Central Impact......Page 850
13.15 Problems Involving Energy and Momentum......Page 853
Review and Summary......Page 869
Review Problems......Page 875
Computer Problems......Page 878
14 Systems of Particles......Page 881
14.2 Application of Newton’s Laws to the Motion of a System of Particles. Effective Forces......Page 882
14.3 Linear and Angular Momentum of a System of Particles......Page 885
14.4 Motion of the Mass Center of a System of Particles......Page 886
14.5 Angular Momentum of a System of Particles about Its Mass Center......Page 888
14.6 Conservation of Momentum for a System of Particles......Page 890
14.7 Kinetic Energy of a System of Particles......Page 898
14.9 Principle of Impulse and Momentum for a System of Particles......Page 900
*14.11 Steady Stream of Particles......Page 911
*14.12 Systems Gaining or Losing Mass......Page 914
Review and Summary......Page 931
Review Problems......Page 935
Computer Problems......Page 938
15.1 Introduction......Page 941
15.2 Translation......Page 944
15.3 Rotation About a Fixed Axis......Page 945
15.4 Equations Defining the Rotation of a Rigid Body About a Fixed Axis......Page 948
15.5 General Plane Motion......Page 958
15.6 Absolute and Relative Velocity in Plane Motion......Page 960
15.7 Instantaneous Center of Rotation in Plane Motion......Page 972
15.8 Absolute and Relative Acceleration in Plane Motion......Page 983
*15.9 Analysis of Plane Motion in Terms of a Parameter......Page 985
15.10 Rate of Change of a Vector with Respect to a Rotating Frame......Page 997
15.11 Plane Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration......Page 999
*15.12 Motion about a Fixed Point......Page 1010
*15.13 General Motion......Page 1013
*15.14 Three-Dimensional Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration......Page 1024
*15.15 Frame of Reference in General Motion......Page 1025
16 Plane Motion of Rigid Bodies: Forces and Accelerations......Page 1051
16.1 Introduction......Page 1052
16.2 Equations of Motion for a Rigid Body......Page 1053
16.3 Angular Momentum of a Rigid Body in Plane Motion......Page 1054
16.4 Plane Motion of a Rigid Body. D’Alembert’s Principle......Page 1055
*16.5 A Remark on the Axioms of the Mechanics of Rigid Bodies......Page 1056
16.6 Solution of Problems Involving the Motion of a Rigid Body......Page 1057
16.7 Systems of Rigid Bodies......Page 1058
16.8 Constrained Plane Motion......Page 1078
Review and Summary......Page 1100
Review Problems......Page 1102
Computer Problems......Page 1105
17 Plane Motion of Rigid Bodies: Energy and Momentum Methods......Page 1107
17.2 Principle of Work and Energy for a Rigid Body......Page 1108
17.3 Work of Forces Acting on a Rigid Body......Page 1109
17.4 Kinetic Energy of a Rigid Body in Plane Motion......Page 1110
17.5 Systems of Rigid Bodies......Page 1111
17.6 Conservation of Energy......Page 1112
17.7 Power......Page 1113
17.8 Principle of Impulse and Momentum for the Plane Motion of a Rigid Body......Page 1129
17.10 Conservation of Angular Momentum......Page 1132
17.12 Eccentric Impact......Page 1145
Review and Summary......Page 1161
Review Problems......Page 1165
Computer Problems......Page 1168
18 Kinetics of Rigid Bodies in Three Dimensions......Page 1171
*18.1 Introduction......Page 1172
*18.2 Angular Momentum of a Rigid Body in Three Dimensions......Page 1173
*18.3 Application of the Principle of Impulse and Momentum to the Three-Dimensional Motion of a Rigid Body......Page 1177
*18.4 Kinetic Energy of a Rigid Body in Three Dimensions......Page 1178
*18.5 Motion of a Rigid Body in Three Dimensions......Page 1191
*18.6 Euler’s Equations of Motion. Extension of D’Alembert’s Principle to the Motion of a Rigid Body in Three Dimensions......Page 1192
*18.7 Motion of a Rigid Body about a Fixed Point......Page 1193
*18.8 Rotation of a Rigid Body about a Fixed Axis......Page 1194
*18.9 Motion of a Gyroscope. Eulerian Angles......Page 1210
*18.10 Steady Precession of a Gyroscope......Page 1212
*18.11 Motion of an Axisymmetrical Body under No Force......Page 1213
Review and Summary......Page 1227
Review Problems......Page 1232
Computer Problems......Page 1235
19 Mechanical Vibrations......Page 1239
19.2 Free Vibrations of Particles. Simple Harmonic Motion......Page 1240
19.3 Simple Pendulum (Approximate Solution)......Page 1244
*19.4 Simple Pendulum (Exact Solution......Page 1245
19.5 Free Vibrations of Rigid Bodies......Page 1254
19.6 Application of the Principle of Conservation of Energy......Page 1266
19.7 Forced Vibrations......Page 1276
*19.8 Damped Free Vibrations......Page 1286
*19.9 Damped Forced Vibrations......Page 1289
*19.10 Electrical Analogues......Page 1290
Review and Summary......Page 1303
Review Problems......Page 1308
Computer Problems......Page 1312
Appendix Fundamentals of Engineering Examination......Page 1315
Photo Credits......Page 1317
Index......Page 1319
Answers to Problems......Page 1331