Introduction to and Andy Ruina and Rudra Pratap

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Chapter 0. Preface 0.1. To the student (please read) 17
d D 1 2 at 2 when you want to find t from a and d, and
ax 2 C bx C c D 0 when you want to find x from a; b; and c.
Once you have got this far the only problem is math 4 . Here are two tricks
of the mind
1) You know a math and computer genius. She is helpful but doesn’t
know any mechanics. Make your first task writing things down so she
could finish up for you. She doesn’t want to help Then realize that
finishing up without her is a separate job for you. You will do this later
when you wear your math-genius cap.
2) Be an egotist. Pretend you are omniscient and know everything. Then
write down true statements about those things; equations that contain
terms that omniscient-you already know: “If I knew x; y and z the
following equation would be true.” Then relax your ego a bit. Count
equations and unknowns to see if you, or at least your math genius
friend, could solve for the things you previously pretended to know.
4 For this and other courses, you
should be good at solving math problems
with your pencil and with a computer.
But you should distinguish between
the task of setting up a math problem
and the solving of the problem.
The solving often takes the bulk of the
time and paper, but it’s not where your
thoughts should start. The material that
is new for you in this book is largely
about setting up, rather than solving, the
math problems that arrise in mechanics.
Vectors and free-body diagrams
In the toolbox of someone who can solve lots of mechanics problems are two
well-worn tools:
A vector calculator that always keeps vectors and scalars distinct, and
A reliable and clear free-body diagram drawing tool.
Because many of the terms in mechanics equations are vectors, the ability to
do vector calculations is essential. Because the concept of an isolated system
is at the core of mechanics, every mechanics practitioner needs the ability to
draw a good free-body diagram. The second and third chapters will help you
build your own set of these two most-important tools.
Outside the books
Guarantee: If you learn to do clear correct vector algebra and to draw
good free-body diagrams you will do well at mechanics. (Assuming, of
course, that you don’t totally stop studying then and there.)
Statics
Engineering
254
Math
The books
Thinking outside the books
We do mechanics because we like mechanics. We hope you will too. It’s fun
to puzzle out how things work. Its satisfying to do calculations that make
realistic predictions. Mechanics is interesting in its own right and it feels
good to take pride in new skills. We wrote this book because we want to help
you learn the subject if you are interested, and get through it if you must.
But we don’t know a straightforward path through your resources (say a path
with 4 straight segments) that really gets you to deeper understanding.
Filename:tfigure-outsidethebooks
Dynamics
Figure 0.1: Thinking outside of the
books. A famous puzzle asks: using
4 contiguous straightline segments connect
all 9 dots that are in a square 3 ¢ 3
array. The only solution has segments
extending outside the “box” of 9 points.
Hence the expression “thinking outside
of the box”.