,THE
MECHANICS
PROBLEM SOLVER ®
A Co111plete Solution Guide to Any Textbook
Statt of Research and Education Association
Dr. M. Fogiel, Chief Editor
Research and Education Association
61 Ethel Road West
Piscataway, New Jersey 08854
, CONTENTS
Chapter No. Page No.
UNITS CONVERSION FACTORS ..................................... xili
1 STATISTICS .......................................................................... 1
Representing Force by Vectors ................................................. 1
Equilibrium of a Particle ......................................................... 10
Equivalent Force Systems ....................................................... 19
Equilibrium of a Rigid Body ................................................... 34
2 ANALYSIS OF STRUCTURES ........................................... 54
3 FORCES IN BEAMS AND CABLES .................................. 72
Sheer and Bending Moment Diagrams of Beams ................... 72
Distributed Loads Acting on Beams ....................................... 80
Cables ...................................................................................... 92
4 FRICTION .......................................................................... 105
Stati.c Friction ........................................................................ 105
Kinerle Friction ..................................................................... 120
0 5 RIGID BODIES .. .. ... .. ......... ........ ...... ........... .... .. ............ ... . 128
Center of Mass and Center of Gravity .................................. 128
Areas and Volumes ............................................................... 133
Centroids of Areas and Volumes .......................................... 136
Inertia and the Moments and Products of Inertia .................. 139
Genera.l Theorems ................................................................. 167
6 RECTILINEAR KINEMATICS ........................................... 171
ix
, 7 CURVILINEAR KINEMATICS ........................................... 184
.Projectile Motion •........•.........•............................................... 184
Equations of Motion in Two Dimensions ............................. 197
8 RIGID BODY KINEMATICS .............................................. 211
Angular Motion ..................................................................... 211
Instantaneous Center Methoo ...•...........................•,., ............... 225
Relative Spatial Motion ......................................................... 250
9 PARTICLE KINETICS: FORCE, ACCELERATION ......... 271
Newton 's Second Law of Motion ..•...................................... 271
Motion of the Center of Mass ................ - ............................. 290
Frictional Foi'Ces .............. _........................................................ 292
Uniform. Circular Motion ...................................................... 300
Central Forces and the Conservation
of Angular Momentum .......................................................... 309
Falling BOOies and Damping
.Problems Depending on the Velocity .................................... 318
10 PARTICLE KINETICS: WORK-ENERGY ........................ 322
Work ....................................................................................... 322
Conservation of Energy and Momentum .............................. 338
Conservation Forces .............................•................................ 351
Power and Efficiency ............................................................ 353
Forces and Eq_uilibriums ........................................................ 357
11 IMPULSE AND MOMENTUM ........................................... 374
Impulsive Forces in Elastic Impacts ...................................... 374
Impulsive Forces in lnelastic Impacts ................................... 388
Impulsive Torque and Angular Momentum .......................... 397
Green' s Function Technique ....................................................400
12 SYSTEMS OF PARTICLES .............................................. 405
Center of .Mals ••••.•"................................: •.........••..•...............•.. 405
Conservation ofLinear Momentum ..................................... 415
Newton' s Second Law of Motion ........................................ .420
Angular Momentum and ToiQ.ue .....................•..•.................. 439
X
MECHANICS
PROBLEM SOLVER ®
A Co111plete Solution Guide to Any Textbook
Statt of Research and Education Association
Dr. M. Fogiel, Chief Editor
Research and Education Association
61 Ethel Road West
Piscataway, New Jersey 08854
, CONTENTS
Chapter No. Page No.
UNITS CONVERSION FACTORS ..................................... xili
1 STATISTICS .......................................................................... 1
Representing Force by Vectors ................................................. 1
Equilibrium of a Particle ......................................................... 10
Equivalent Force Systems ....................................................... 19
Equilibrium of a Rigid Body ................................................... 34
2 ANALYSIS OF STRUCTURES ........................................... 54
3 FORCES IN BEAMS AND CABLES .................................. 72
Sheer and Bending Moment Diagrams of Beams ................... 72
Distributed Loads Acting on Beams ....................................... 80
Cables ...................................................................................... 92
4 FRICTION .......................................................................... 105
Stati.c Friction ........................................................................ 105
Kinerle Friction ..................................................................... 120
0 5 RIGID BODIES .. .. ... .. ......... ........ ...... ........... .... .. ............ ... . 128
Center of Mass and Center of Gravity .................................. 128
Areas and Volumes ............................................................... 133
Centroids of Areas and Volumes .......................................... 136
Inertia and the Moments and Products of Inertia .................. 139
Genera.l Theorems ................................................................. 167
6 RECTILINEAR KINEMATICS ........................................... 171
ix
, 7 CURVILINEAR KINEMATICS ........................................... 184
.Projectile Motion •........•.........•............................................... 184
Equations of Motion in Two Dimensions ............................. 197
8 RIGID BODY KINEMATICS .............................................. 211
Angular Motion ..................................................................... 211
Instantaneous Center Methoo ...•...........................•,., ............... 225
Relative Spatial Motion ......................................................... 250
9 PARTICLE KINETICS: FORCE, ACCELERATION ......... 271
Newton 's Second Law of Motion ..•...................................... 271
Motion of the Center of Mass ................ - ............................. 290
Frictional Foi'Ces .............. _........................................................ 292
Uniform. Circular Motion ...................................................... 300
Central Forces and the Conservation
of Angular Momentum .......................................................... 309
Falling BOOies and Damping
.Problems Depending on the Velocity .................................... 318
10 PARTICLE KINETICS: WORK-ENERGY ........................ 322
Work ....................................................................................... 322
Conservation of Energy and Momentum .............................. 338
Conservation Forces .............................•................................ 351
Power and Efficiency ............................................................ 353
Forces and Eq_uilibriums ........................................................ 357
11 IMPULSE AND MOMENTUM ........................................... 374
Impulsive Forces in Elastic Impacts ...................................... 374
Impulsive Forces in lnelastic Impacts ................................... 388
Impulsive Torque and Angular Momentum .......................... 397
Green' s Function Technique ....................................................400
12 SYSTEMS OF PARTICLES .............................................. 405
Center of .Mals ••••.•"................................: •.........••..•...............•.. 405
Conservation ofLinear Momentum ..................................... 415
Newton' s Second Law of Motion ........................................ .420
Angular Momentum and ToiQ.ue .....................•..•.................. 439
X
