Basic mechanics with engineering applications

419 Pages·2011·29.18 MB·English

Basic Mechanics
with Engineering
Applications

Basic Mechanics
with Engineering
Applications
J. N. FawceH and J. S. Burdess

I
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LONDON AND NEW YORK
First published by Butterworth-Heinemann
First published 1988
This edition published 2011 by Routledge
2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN
711 Third Avenue, New York, NY 10017, USA
Routledge is an imprint of the Taylor & Francis Group, an informa business
Copyright© 1988, J. N. Fawcett and J. S. Burdess.
All rights reserved
No part of this publication maybe reproduced in any material form (including
photocopying or storing in any medium by electronic meahSand whether. or not
transiently or inc~9.entally to Some other use of this pUblication) without the writterl
permission of the copyright holder except in accordance with the provisions of th~
Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by
the Copyright Licensing Agen~y Ltd, 90 Tottenham Court Road, London, Englanq
W1T 4LP. Applications for the copyright holder's written permission to reproduce
any part of this publication shoqld be addressed to the publisher
BritishUbrary Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 978-0-415-50317-4
Preface
Modern societies depend upon machines to provide standards of living far
beyond the level that man alone can provide. The human body is very limited
in its ability to generate large, or very small forces and cannot work at high
speeds or with high accuracy for long periods. To overcome these limitations
man has striven to develop machines which augment his own strength and
reduce the drudgery of repetitive tasks. We all now depend upon machines to
provide us with our food, clothing, energy, transport and defence. Most
households, in addition to possessing some form of transport, have machines
to reduce the effort involved in washing, cleaning and preparing food. Agricul-
ture and medicine depend upon machines to increase their efficiency. Less
familiar are the machines used on an industrial scale for knitting and weaving,
for food processing and packaging and for the manufacture of metal goods
of all sorts.
All engineers will at some time have a professional interest in machines,
perhaps as a designer, but more often as a user of machines. A sound
understanding of the physical principles which govern the behaviour of
machines is therefore an essential part of an engineer's education.
A machine is an assembly of fixed and moving bodies connected together
in some manner. Dynamics is the study of bodies in motion and provides the
basic tools for the analysis and synthesis of machines. The subject is usually
split into two parts. The first, kinematics, is the study of the geometric properties
of motion, and the second, kinetics, is concerned with the forces which cause,

or maintain, motion.
The book is intended as a first year undergraduate course for Mechanical
Engineering students, and as a course in basic mechanics suitable for students
in other engineering subjects.
The authors have taught Machine Dynamics courses at undergraduate and
postgraduate level for a number of years. They have found that the good text
books available generally cover a full undergraduate course and use a formal
vector approach. For first year students, or for those engineering students who
follow only a limited course in Mechanics, they feel that a course restricted
to consider only plane motion is adequate. The use of formal vector algebra
is not required for a basic course of this type and an informal vector approach
can give a greater understanding of the basic principles. It is essential however
that derivations of formulae should be rigorous and that any assumptions
made in their derivation are fully explained.
VI Preface
In each section of this book the basic theory is presented in a rigorous
manner and then applied to typical engineering problems. The relevance of
the mathematical model used to represent each real system is considered and
the meaning of the results is discussed. The importance of understanding the
underlying theory, and the use of free body diagrams or system boundaries is
emphasised throughout the text.
It is expected that students following this text will develop a thorough
understanding of basic mechanics which will enable them to tackle many
engineering problems. It will also provide a valuable foundation for more
advanced courses in Mechanics.
The authors have carefully checked the text and the examples for student
solution. They would welcome notification of any errors which remain, and
suggestions for improving the layout and content of the book would also be
appreciated.
Finally the authors would like to thank Sheila Stone and Joyce McLean for
their efforts well beyond the call of duty in the preparation of the manuscript
and figures for the book.
J. N. Fawcett
J. S. Burdess
1988
Contents
Preface v
1. Kinematics 1
Basic Theory
1.1 Vector quantities 1
1.2 Motion of a point 3
1.3 Motion of a point along a straight line 4
1.4 Angular motion 12
1.5 Motion of a point in a plane 13
1.6 Plane motion of a rigid body 23
Engineering Applications
1.1 Rolling wheel 33
1.2 Belt and chain drives 36
1.3 Toothed gearing 37
1.4 Epicylic gear trains 39
1.5 Eccentric cam mechanism 41
1.6 Slider crank mechanism 43
1.7 Four bar linkage 48
Exercises 56
2. Newton's laws of motion 64
2.1 Laws of motion 64
2.2 Units 65
3. Statics 66
Basic Theory
3.1 Introduction 66
3.2 Equilibrium of a particle in a plane 66
3.3 Equilibrium of rigid bodies 70
3.4 Alternative formulations of equilibrium conditions 75
3.5 Special cases 80
3.6 Distributed forces 83
3.7 Centres of mass 86
3.8 Internal forces 94
3.9 Connected systems 99
viii Contents
Engineering Applications
3.1 Frameworks 105
3.2 Toggle linkage 110
3.3 Lifting tongs 112
3.4 Wall crane 118
3.5 Power transmission systems 121
3.6 Shear forces and bending moments in beams 134
Exercises 138
4. Dynamics 152
Basic Theory
4.1 Dynamics of particles and rigid bodies 152
4.2 Dynamics of a particle 152
4.3 Application of Newton's laws to rigid bodies 157
4.4 Moment of inertia 174
Engineering Applications
4.1 Turbo generator 185
4.2 Pendulum accelerometer 187
4.3 Eccentric cam mechanism 188
4.4 Belt drive 191
4.5 Winches and hoists 194
4.6 Balancing of rotating systems 200
4.7 The slider crank mechanism 204
4.8 Balancing of reciprocating machines 209
4.9 Robot arm 211
4.10 Vibration and vibration isolation 214
Exercises 224
5. Work and Energy 235
Basic Theory
5.1 Work done by a force 235
5.2 Conservative and non-conservative forces 241
5.3 Power 245
5.4 Internal energy 247
5.5 Potential energy 250
5.6 Kinetic energy 253
5.7 Strain energy 268
5.8 Thermal energy 276
Engineering Applications
5.1 Child's toy 277
5.2 Lift system 280
5.3 Flywheel press 283
Contents ix
5.4 Circuit breaker 289
5.5 Disc brake 295
Exercises 300
6. Impulse and Momentum 308
Basic Theory
6.1 Linear momentum 308
6.2 Angular momentum 321
6.3 Impacts involving rigid bodies 339
Engineering Applications
6.1 Surveillance satellite 355
6.2 Robot arm 357
6.3 Friction clutch 360
Exercises 366
7. Momentum and mass transfer 376
Basic Theory
7.1 Variable mass and fluid flow systems 376
7.2 Conditions for steady flow 381
Engineering Applications
7.1 Impulse turbine 385
Exercises 389

Solutions to Exercises 393
Index 403