Introduction to and Andy Ruina and Rudra Pratap

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Chapter 0. Preface Preface 13 or Serway) would encompass some of this book’s contents. However, after freshman physics students often have only a vague notion of what mechanics is, and how it can be used. For example many students leave freshman physics with the sense that a free-body diagram (or ‘force diagram’) is a vague conceptual picture with arrows for various forces and motions drawn on it this way and that. Even the freshman-text illustrations sometimes do not make clear which force is acting on which object. Also, because freshman physics tends to avoid use of college math, many students leave freshman physics with little sense of how to use vectors or calculus to solve mechanics problems. This book aims to lead students who may start with these fuzzy freshman-physics notions into a world of precise, yet still intuitive, mechanics. Various statics and dynamics textbooks cover much of the same material as this one. These textbooks have modern applications, ample samples, lots of pictures, and lots of homework problems. Many are excellent in some ways. Most of today’s engineering professors learned from one of these books. Nonetheless we wrote this book hoping to do still better. Some of our goals include showing the unity of the subject, presenting a complete description of the subject, clear notation in figures and equations, integration of the applicability of computers, consistent use of units throughout, introduction of various insights into how things work, a friendly writing style. Between about 1689 and 1960 hundreds of books were written with titles like Statics, Engineering mechanics, Dynamics, Machines, Mechanisms, Kinematics, or Elementary physics. Many thoughtfully cover most of the material here and sometimes much more. But none are good modern textbooks; they lack an appropriate pace, style and organization; they are too reliant on geometry skills and not enough on vectors and numerics; and they don’t have enough modern applications, samples calculations, illustrations, or homework problems. But much good mechanics can be found only in these older books 2 . If you love mechanics you will enjoy pondering ideas in some of these books. What do you think We have tried to make it as easy as possible for you to learn basic mechanics from this book. We present truth as we know it and as we think it is effectively communicated. Nonetheless we have surely made some technical and strategic errors. Please let us know your thoughts so that we can improve future editions. Rudra Pratap, pratap@mecheng.iisc.ernet.in Andy Ruina, ruina@cornell.edu 2 Here are three good and universally respected classics: J.P. Den Hartog’s Mechanics originally published in 1948 but still available as an inexpensive reprint (well written and insightful); J.L. Synge and B.A. Griffith, Principles of Mechanics through page 408. Originally published in 1942, reprinted in 1959 (good pedagogy but dry); and E.J. Routh’s, Dynamics of a System of rigid bodies, Vol 1 (the “elementary” part through chapter 7. Originally published in 1905, but reprinted in 1960). Routh also has 5 other idea- packed statics and dynamics books. Routh shared college graduation honors with the now-more-famous physicist James Clerk Maxwell.
14 Chapter 0. Preface 0.1. To the student (please read) 0.1 To the student (please read) Nature’s rules are so strict that, to the extent that you know the rules, you can make reliable predictions about how Nature, the set of all things, behave. In particular, most objects of concern to engineers obediently follow a subset of Nature’s rules called the laws of Newtonian mechanics. So, if you learn the laws of mechanics, as this book should help you to do, you will be able to make quantitative predictions about how things stand, move, and fall. And you will gain intuition about the mechanics part of Nature’s rules. How to use this book Here is some general guidance. 1 “Exams are harder than homework.” Some struggling students say “I can do the homework problems. I just can’t do the exams. Exams are harder and trickier.” These students may be fooling themselves. Most exams are not trickier than the homework. And when we have checked, many students who got through homework with help, can’t do simplified versions of those same problems when they have no help. Check your own understanding Most likely you want a decent grade by successfully getting through the homework assignements and exams. You will naturally get help by looking at examples and samples in the text or lecture notes, by looking up formulas in the front and back covers of this book, and by asking questions of friends, teaching assistants and professors. What good are books, notes, classmates or teachers if they don’t help you do the homework All the examples and sample problems in this book, for example, are just for this purpose. But watch out. Too-much use of help from books, notes and people can lead to self deception 1 . After you have got through a problem using such help you should, at least sometimes, check that you have actually learned to solve the problem. To see if you have learned to do a problem, do it again, justifying each step, without looking up even one small (‘oh, I almost knew that’) thing. If you can’t do this, you gain two learning opportunities. First, you can learn the missing skill or idea. But more deeply, by getting stuck after you have been able to get through with help, you can learn things about your learning process. Often the real source of difficulty isn’t a key formula or fact, but something more subtle. Some useful more subtle ideas might be explained in the general text discussions. Read the parts that are at your level You might be science and math school-smart, mechanically inclined, or are especially motivated to learn mechanics. Or you might be reluctantly taking this class to fulfil a requirement. In either case this book is meant for you. The sections start with generally accessible introductory material and include simple examples. The early sample problems in each section are also easy. But we also have discussions of the theory and other more advanced applications and asides to challenge more motivated students. If you are a nerd,
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