A Textbook of Applied Mechanics

409 Pages·2011·5.579 MB·English

by  R.K. Rajput

A TEXTBOOK
OF
APPLIED MECHANICS

A TEXTBOOK
OF
APPLIED MECHANICS
(Including Laboratory Practicals)
S.I. UNITS
By
R.K. RAJPUT
M.E. (Heat Power Engg.) Hons.–Gold Medallist ; Grad. (Mech. Engg. & Elect. Engg.) ;
M.I.E. (India) ; M.S.E.S.I. ; M.I.S.T.E. ; C.E. (India)
Principal (Formerly),
Punjab College of Information Technology
PATIALA (Punjab)
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Typeset at : Goswami Associates, Delhi Printed at : Mehra Offset Printer, Delhi
CONTENTS
Chapters Pages
INTRODUCTION TO S.I. UNITS AND CONVERSION FACTORS (i)–(v)
Part I—APPLIED MECHANICS—THEORY
1. BASIC CONCEPTS 3–8
1.1. Introduction to Mechanics ... 3
1.2. Basic Definitions ... 4
1.3. Rigid Body ... 5
1.4. Scalar and Vector Quantities ... 5
1.5. Fundamental Units and Derived Units ... 5
1.6. Systems of Units ... 6
Highlights ... 7
Objective Type Questions ... 8
Exercises ... 8
2. LAWS OF FORCES 9–50
2.1. Force ... 9
2.2. Units of Force ... 9
2.3. Characteristics of a Force ... 10
2.4. Representation of Forces ... 10
2.5. Classification of Forces ... 10
2.6. Force Systems ... 11
2.7. Free Body Diagrams ... 12
2.8. Transmissibility of a Force ... 13
2.9. Particle ... 14
2.10. Resultant Force ... 14
2.11. Component of a Force ... 14
2.12. Principle of Resolved Parts ... 15
2.13. Laws of Forces ... 15
2.14. Resultant of Several Coplanar Concurrent Forces ... 17
2.15. Equilibrium Conditions for Coplanar Concurrent Forces ... 27
2.16. Lami’s Theorem ... 27
Highlights ... 47
Objective Type Questions ... 48
Exercises ... 49
Theoretical Questions ... 49
Unsolved Examples ... 49
3. MOMENTS 51–86
3.1. Moments ... 51
3.2. Clockwise and Anti-clockwise Moments ... 52
(v)
(vi)
3.3. Principle of Moments ... 52
3.4. Equilibrium Conditions for Bodies Under Coplanar
Non-concurrent Forces ... 53
3.5. Varignon’s Theorem ... 54
3.6. Parallel Forces ... 55
3.7. Graphical Method for Finding the Resultant of any Number of Like
or Unlike Parallel Forces ... 55
3.8. Couple ... 56
3.9. Properties of a Couple ... 57
3.10. Engineering Applications of Moments ... 58
3.11. Resultant of a Coplanar, Non-concurrent Non-parallel Force System ... 63
Highlights ... 82
Objective Type Questions ... 82
Exercises ... 83
Theoretical Questions ... 83
Unsolved Examples ... 83
4. CENTRE OF GRAVITY AND CENTROID 87–123
4.1. Centre of Gravity of a Body ... 87
4.2. Determination of Centre of Gravity ... 88
4.3. Centroid ... 88
4.4. Positions of Centroids of Plane Geometrical Figures ... 89
4.5. Positions of Centre of Gravity of Regular Solids ... 90
4.6. (a) Centroids of Composite Areas ... 91
4.6. (b) Centre of Gravity of Simple Solids ... 91
4.7. Areas and Volumes—Centroid Method ... 92
4.8. Centre of Gravity in a Few Simple Cases ... 93
Highlights ... 117
Objective Type Questions ... 117
Exercises ... 118
Theoretical Questions ... 118
Unsolved Examples ... 118
5. MOMENT OF INERTIA 124–150
5.1. Moment of Inertia ... 124
5.2. Theorem of Parallel Axes ... 126
5.3. Theorem of Perpendicular Axes ... 126
5.4. Radius of Gyration of the Section ... 127
5.5. Moment of Inertia of Laminae of Different Shapes ... 128
Highlights ... 146
Objective Type Questions ... 147
Exercises ... 147
Theoretical Questions ... 147
Unsolved Examples ... 147
(vii)
6. FRICTION 151–187
6.1. Concept of Friction ... 151
6.2. Characteristics of Frictional Force ... 152
6.3. Types of Friction ... 152
6.4. Static and Dynamic Friction ... 152
6.5. Limiting Friction ... 153
6.6. Laws of Friction ... 153
6.7. Angle of Friction ... 154
6.8. Co-efficient of Friction ... 154
6.9. Angle of Repose ... 154
6.10. Cone of Friction ... 155
6.11. Motion of Body on Horizontal Plane ... 155
6.12. Motion up an Inclined Plane ... 156
6.13. Motion Down an Inclined Plane ... 157
6.14. Screw Friction ... 172
6.15. Screw Jack ... 172
Highlights ... 184
Objective Type Questions ... 185
Exercises ... 185
Theoretical Questions ... 185
Unsolved Examples ... 186
7. RECTILINEAR MOTION 188–214
7.1. Concept of Motion ... 188
7.2. Definitions ... 188
7.3. Displacement-Time Graphs ... 190
7.4. Velocity-Time Graphs ... 190
7.5. Equations of Motion Under Uniform Acceleration ... 191
7.6. Distance Covered in nth Second by a Body Moving with Uniform
Acceleration ... 192
7.7. Motion Under Gravity ... 201
7.8. Some Hints on the use of Equations of Motion ... 201
Highlights ... 211
Objective Type Questions ... 212
Exercises ... 213
Theoretical Questions ... 213
Unsolved Examples ... 213
8. LAWS OF MOTION 215–246
8.1. Introduction ... 215
8.2. Momentum ... 215
8.3. Newton’s First Law of Motion ... 215
8.4. Newton’s Second Law of Motion ... 215
8.5. Newton’s Third Law of Motion ... 216
8.6. Gravitational and Absolute Units of Force ... 217
8.7. Law of Conservation of Momentum ... 218
8.8. Impulse and Impulsive Force ... 219
(viii)
8.9. D’alembert’s Principle ... 227
8.10. Motion of a Lift ... 228
8.11. Motion of two Bodies Connected by a String Passing over a Smooth Pulley ... 230
8.12. Motion of two Bodies Connected at the Edge of a Horizontal Surface ... 233
8.13. Motion of two Bodies Connected by a String One End of which is Hanging
Free and the other Lying on a Rough Inclined Plane ... 237
8.14. Motion of Two Bodies Connected Over Rough Inclined Planes ... 240
Highlights ... 243
Objective Type Questions ... 243
Unsolved Examples ... 244
9. WORK, POWER AND ENERGY 247–268
9.1. Concept of Work ... 247
9.2. Units of Work ... 248
9.3. Graphical Representations of Work ... 248
9.4. Power ... 249
9.5. Law of Conservation of Energy ... 251
Highlights ... 265
Objective Type Questions ... 266
Unsolved Examples ... 267
10. SIMPLE MACHINES 269–308
10.1. General Concept of a Machine ... 269
10.2. Important Definitions ... 269
10.3. Relation between M.A., V.R. and η ... 270
10.4. Concept of Friction in a Machine ... 270
10.5. Condition for Reversibility of a Machine ... 271
10.6. Non-reversible/Irreversible or Self-locking Machine ... 272
10.7. Law of a Machine ... 272
10.8. Maximum Mechanical Advantage and Efficiency ... 273
10.9. Some Lifting Machines ... 280
10.10. Simple Wheel and Axle ... 281
10.11. Wheel and Differential Axle ... 283
10.12. Pulleys ... 285
10.13. Weston’s Differential Pulley Block ... 292
10.14. Worm and Worm Wheel ... 295
10.15. Single Purchase Crab Winch ... 297
10.16. Double Purchase Crab Winch ... 300
10.17. Simple Screw Jack ... 303
10.18. Differential Screw Jack ... 303
Highlights ... 304
Objective Type Questions ... 306
Exercises ... 306
Theoretical Questions ... 306
Unsolved Examples ... 307
(ix)
11. CIRCULAR AND CURVILINEAR MOTION 309–330
11.1. Introduction and Definitions ... 309
11.2. Equations of Angular Motion ... 310
11.3. Equations of Linear Motion and Angular Motion ... 311
11.4. Relation between Linear and Angular Motion ... 311
11.5. Centrifugal and Centripetal Force ... 312
11.6. Motion of a Cyclist Round a Curve ... 317
11.7. Motion of a Vehicle on a Level Curved Path ... 319
11.8. Motion of a Vehicle on a Banked Circular Track ... 321
11.9. Super Elevation for Railways ... 324
Highlights ... 327
Objective Type Questions ... 328
Exercises ... 329
Theoretical Questions ... 329
Unsolved Examples ... 329
12. SIMPLE STRESSES AND STRAINS 331–366
12.1. Classification of Loads ... 331
12.2. Stress ... 331
12.3. Simple Stress ... 332
12.4. Strain ... 333
12.5. Hooke’s Law ... 334
12.6. Mechanical Properties of Metals ... 335
12.7. Tensile Test ... 336
12.8. Strain Hardening (or Work Hardening) ... 340
12.9. Poisson’s Ratio ... 340
12.10. Relations between the Elastic Modulii ... 341
12.11. Stresses Induced in Compound Ties or Struts ... 344
12.12. Thermal Stresses and Strains ... 344
Highlights ... 360
Objective Type Questions ... 361
Theoretical Questions ... 363
Unsolved Examples ... 363
Part II—EXPERIMENTS
Experiment No. 1 ... 369
Experiment No. 2 ... 371
Experiment No. 3 ... 373
Experiment No. 4 ... 375
Experiment No. 5 ... 379
Experiment No. 6 ... 381
Experiment No. 7 ... 383
Experiment No. 8 ... 385
Experiment No. 9 ... 387
Experiment No. 10 ... 389