Statics and dynamics with background mathematics

Contents......Page 3
Part I Statics......Page 10
1.1 Force......Page 11
1.2 Forces of contact......Page 12
1.3 Mysterious forces......Page 13
1.4 Quantitative definition of force......Page 14
1.6 Line of action......Page 15
1.7 Equilibrium of two forces......Page 16
1.8 Parallelogram of forces (vector addition)......Page 17
1.9 Resultant of three coplanar forces acting at a point......Page 20
1.10 Generalizations for forces acting at a point......Page 21
1.11 More exercises......Page 23
1.12 Answers to exercises......Page 24
2.1 Moment of force......Page 33
2.2 Three or more non-parallel non-concurrent coplanar forces......Page 35
2.3 Parallel forces......Page 36
2.4 Couples......Page 39
2.5 Equations of equilibrium of coplanar forces......Page 41
2.6 Applications......Page 43
2.7 Answers to exercises......Page 45
3.1 Coplanar parallel forces......Page 53
3.2 Non-coplanar parallel forces......Page 55
3.3 Finding c.g. positions of uniform plane laminas without using calculus......Page 57
3.4 Using calculus to find c.g. positions of uniform plane laminas......Page 59
3.5 Centre of gravity positions of uniform solid bodies of revolution......Page 61
3.6 Answers to exercises......Page 63
4.1 Distributed loads......Page 67
4.2 Hydrostatics......Page 69
4.3 Buoyancy......Page 71
4.4 Centre of pressure on a plane surface......Page 72
4.5 Answers to exercises......Page 73
5.1 Method of sections......Page 78
5.2 Method of joints......Page 80
5.3 Bow’s notation......Page 84
5.4 Answers to exercises......Page 89
6.1 Shearing force and bending moment......Page 93
6.2 Uniformly distributed beam loading......Page 95
6.3 Using calculus......Page 98
6.4 Answers to exercises......Page 100
7.1 Force of friction......Page 106
7.2 Sliding or toppling?......Page 107
7.3 Direction of minimum pull......Page 109
7.4 Ladder leaning against a wall......Page 110
7.5 Motor vehicle clutch......Page 111
7.6 Capstan......Page 112
7.7 Answers to exercises......Page 113
8.1 Coplanar force and couple......Page 117
8.2 Effect of two non-coplanar couples......Page 119
8.3 The wrench......Page 122
8.4 Resultant of a system of forces and couples......Page 124
8.5 Equations of equilibrium......Page 125
8.6 Answers to exercises......Page 127
9.2 Work done by a couple......Page 131
9.3 Virtual work for a single body......Page 132
9.4 Virtual work for a system of bodies......Page 133
9.5 Stability of equilibrium......Page 138
9.6 Answers to exercises......Page 142
Part II Dynamics......Page 146
10.1 Rectilinear motion......Page 147
10.2 Simple harmonic motion......Page 148
10.3 Circular motion......Page 150
10.4 Velocity vectors......Page 151
10.5 Relative velocity......Page 152
10.6 Motion along a curved path......Page 153
10.7 Answers to exercises......Page 156
11.1 Newton’s laws of motion......Page 160
11.2 Sliding down a plane......Page 161
11.3 Traction and braking......Page 163
11.4 Simple harmonic motion......Page 164
11.5 Uniform circular motion......Page 166
11.6 Non-uniform circular motion......Page 167
11.7 Projectiles......Page 168
11.8 Motion of connected weights......Page 171
11.9 Answers to exercises......Page 173
12.2 Moment......Page 179
12.3 Instantaneous centre of rotation......Page 180
12.4 Angular velocity......Page 182
12.5 Centre of gravity......Page 184
12.6 Acceleration of the centre of gravity......Page 185
12.7 General dynamic equations......Page 186
12.8 Moments of inertia......Page 188
12.9 Perpendicular axis theorem......Page 190
12.10 Rotation about a fixed axis......Page 191
12.11 General plane motion......Page 194
12.12 More exercises......Page 197
12.13 Answers to exercises......Page 200
13.1 Definition of impulse and simple applications......Page 213
13.2 Pressure of a water jet......Page 215
13.3 Elastic collisions......Page 216
13.4 Moments of impulse and momentum......Page 217
13.5 Centre of percussion......Page 220
13.6 Conservation of moment of momentum......Page 221
13.7 Impacts......Page 222
13.8 Answers to exercises......Page 223
14.1 Work done by force on a particle......Page 227
14.2 Conservation of energy......Page 229
14.3 Spring energy......Page 230
14.5 Kinetic energy of translation and rotation......Page 231
14.6 Energy conservation with both translation and rotation......Page 232
14.7 Energy and moment of momentum......Page 233
14.8 Answers to exercises......Page 235
Part III Problems......Page 239
15 Statics......Page 240
16 Dynamics......Page 268
Part IV Background mathematics......Page 285
17.2 Logarithm......Page 286
Remainder theorem......Page 287
17.4 Partial fractions......Page 288
Sequence......Page 290
Geometricalprogression (G.P.)......Page 291
Convergence of a geometric series......Page 292
17.6 Binomial theorem......Page 293
18.1 Introduction......Page 295
18.2 Trigonometrical ratios to remember......Page 297
18.3 Radian measure......Page 298
18.4 Compound angles......Page 299
18.5 Solution of trigonometrical equations: inverse trigonometrical functions......Page 301
18.6 Sine and cosine rules......Page 303
19.1 Differential calculus......Page 304
19.2 Differentiation from first principles......Page 305
19.3 More derivative formulae......Page 307
19.4 Complex numbers......Page 311
19.5 Integral calculus......Page 313
19.6 The definite integral......Page 314
19.7 Methods of integration......Page 318
Simpson’s rule......Page 323
19.9 Exponentialfunction e and natural logarithm ln x......Page 326
19.10 Some more integrals using partial fractions and integration by parts......Page 329
19.11 Taylor, Maclaurin and exponential series......Page 330
20.1 Introduction......Page 332
20.2 Straight line......Page 334
20.3 Circle......Page 335
20.5 Parabola......Page 338
20.6 Ellipse......Page 341
20.7 Hyperbola......Page 342
20.8 Three-dimensional coordinate geometry......Page 344
20.9 Equations for a straight line......Page 346
20.10 The plane......Page 347
20.11 Cylindrical and spherical coordinates......Page 349
21.1 Vectors......Page 352
21.2 Straight line and plane......Page 354
21.3 Scalar product......Page 357
21.4 Vector product......Page 359
22.1 A simple differential equation......Page 362
22.2 Hyperbolic sines and cosines......Page 363
Appendix: answers to problems in Part III......Page 364
Index......Page 368