Roberts - Statics and Dynamics with Background Mathematics (Cambridge, 2003).pdf

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Statics and Dynamics
with Background Mathematics
A. P. Roberts
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Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge , United Kingdom
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521817660
© Cambridge University Press 2003
This book is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format
2003
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hardback
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Cambridge University Press has no responsibility for the persistence or accuracy of
s for external or third-party internet websites referred to in this book, and does not
guarantee that any content on such websites is, or will remain, accurate or appropriate.
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Contents
Preface
page xiii
Part I Statics
1
1 Forces
3
1.1 Force
3
1.2 Forces of contact
4
1.3 Mysterious forces
5
1.4 Quantitative definition of force
6
1.5 Point of application
7
1.6 Line of action
7
1.7 Equilibrium of two forces
8
1.8 Parallelogram of forces (vector addition)
9
1.9 Resultant of three coplanar forces acting at a point
12
1.10 Generalizations for forces acting at a point
13
1.11 More exercises
15
1.12 Answers to exercises
16
2 Moments
25
2.1 Moment of force
25
2.2 Three or more non-parallel non-concurrent coplanar forces
27
2.3 Parallel forces
28
2.4 Couples
31
2.5 Equations of equilibrium of coplanar forces
33
2.6 Applications
35
2.7 Answers to exercises
37
3 Centre of gravity 45
3.1 Coplanar parallel forces 45
3.2 Non-coplanar parallel forces 47
3.3 Finding c.g. positions of uniform plane laminas without using calculus 49
3.4 Using calculus to find c.g. positions of uniform plane laminas
51
vii
 
viii
Contents
3.5 Centre of gravity positions of uniform solid bodies of revolution
53
3.6 Answers to exercises
55
4 Distributed forces
59
4.1 Distributed loads
59
4.2 Hydrostatics
61
4.3 Buoyancy
63
4.4 Centre of pressure on a plane surface
64
4.5 Answers to exercises
65
5 Trusses
70
5.1 Method of sections
70
5.2 Method of joints
72
5.3 Bow’s notation
76
5.4 Answers to exercises
81
6 Beams
85
6.1 Shearing force and bending moment
85
6.2 Uniformly distributed beam loading
87
6.3 Using calculus
90
6.4 Answers to exercises
92
7 Friction
98
7.1 Force of friction
98
7.2 Sliding or toppling?
99
7.3 Direction of minimum pull
101
7.4 Ladder leaning against a wall
102
7.5 Motor vehicle clutch
103
7.6 Capstan
104
7.7 Answers to exercises
105
8 Non-coplanar forces and couples
109
8.1 Coplanar force and couple
109
8.2 Effect of two non-coplanar couples
111
8.3 The wrench
114
8.4 Resultant of a system of forces and couples
116
8.5 Equations of equilibrium
117
8.6 Answers to exercises
119
9 Virtual work
123
9.1 Work done by a force
123
9.2 Work done by a couple
123
9.3 Virtual work for a single body
124
9.4 Virtual work for a system of bodies
125
9.5 Stability of equilibrium
130
9.6 Answers to exercises
134
 
ix
Contents
Part II Dynamics
139
10 Kinematics of a point
141
10.1 Rectilinear motion
141
10.2 Simple harmonic motion
142
10.3 Circular motion
144
10.4 Velocity vectors
145
10.5 Relative velocity
146
10.6 Motion along a curved path
147
10.7 Answers to exercises
150
11 Kinetics of a particle
154
11.1 Newton’s laws of motion
154
11.2 Sliding down a plane
155
11.3 Traction and braking
157
11.4 Simple harmonic motion
158
11.5 Uniform circular motion
160
11.6 Non-uniform circular motion
161
11.7 Projectiles
162
11.8 Motion of connected weights
165
11.9 Answers to exercises
167
12 Plane motion of a rigid body
173
12.1 Introduction
173
12.2 Moment
173
12.3 Instantaneous centre of rotation
174
12.4 Angular velocity
176
12.5 Centre of gravity
178
12.6 Acceleration of the centre of gravity
179
12.7 General dynamic equations
180
12.8 Moments of inertia
182
12.9 Perpendicular axis theorem
184
12.10 Rotation about a fixed axis
185
12.11 General plane motion
188
12.12 More exercises
191
12.13 Answers to exercises
194
13 Impulse and momentum
207
13.1 Definition of impulse and simple applications
207
13.2 Pressure of a water jet
209
13.3 Elastic collisions
210
13.4 Moments of impulse and momentum
211
13.5 Centre of percussion
214
13.6 Conservation of moment of momentum
215
13.7 Impacts
216
13.8 Answers to exercises
217
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