Mechanics is the study of force, deformation, and motion, and the relations between
them

Mechanics is the study of force, deformation, and motion, and the relations between
them. We care about forces because we want to know how hard to push something
to move it or whether it will break when we push on it for other reasons. We care
about deformation and motion because we want things to move or not move in certain
ways. Towards these ends we are confronted with this general mechanics problem.

Given some (possibly idealized) information about the properties, forces, deformations, and motions of a mechanical system, make useful predictions about other aspects of its properties, forces, deformations, and motions.

A note on computation :: Mechanics is a physical subject. The concepts in mechanics do not depend on computers. But mechanics is also a quantitative and applied subject described with numbers.
Computers are very good with numbers. Thus the modern practice of engineering
mechanics depends on computers. The most-needed computer skills for mechanics
are:

• solution of simultaneous algebraic equations,
• plotting, and
• numerical solution of ODEs.
  More basically, an engineer also needs the ability to routinely evaluate standard
  functions (x3, cos−1 θ, etc.), to enter and manipulate lists and arrays of numbers, and
  to write short programs.
  Classical languages, applied packages, and simulators
  Programming in standard languages such as Fortran, Basic, C, Pascal, or Java probably take too much time to use in solving simple mechanics problems. Thus an
  engineer needs to learn to use one or another widely available computational package
  (e.g., MATLAB, OCTAVE, MAPLE, MATHEMATICA, MATHCAD, TKSOLVER,
  LABVIEW, etc). We assume that students have learned, or are learning such a package. We also encourage the use of packaged mechanics simulators (e.g., WORKING
  MODEL, ADAMS, DADS, etc) for building intuition, but none of the homework here
  depends on access to such a packaged simulator.
  How we explain computation in this book.
  Solving a mechanics problem involves these major steps
  (a) Reducing a physical problem to a well posed mathematical problem;
  (b) Solving the math problem using some combination of pencil and paper and
  numerical computation; and
  (c) Giving physical interpretation of the mathematical solution.with Newtonian mechanics, or “Newton’s Laws”. Newtonian mechanics has held up, with minor refinement, for over three hundred years. Those who want to know how machines, structures, plants, animals and planets hold together and move about need to know mechanics. In another two or three hundred years people who want to design robots, buildings, airplanes, boats, prosthetic devices, and large or microscopic machines will probably still use the equations and principles we now call Newtonian
• mechanics. Any mechanics problem can be divided into 3 parts which we think of as the 3the mechanical behavior of objects and materials (constitutive laws);

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The first pillar of mechanics is mechanical behavior. The Mechanical behavior of something is the description of how loads cause deformation (or visa versa). When something carries a force it stretches, shortens, shears, bends, or breaks. Your finger tip squishes when you poke something. Too large a force on a gear in an engine causes it to break. The force of air on an insect wing makes it bend. Various geologic forces bend, compress and break rock. This relation between force and deformation can be viewed in a few ways. First, it gives us a definition of force. In fact, force can be defined by the amount of
spring stretch it causes. Thus most modern force measurement devices measure force indirectly by measuring the deformation it causes in a calibrated spring. This is one justification for calling ‘mechanical behavior’ the first pillar. It gives us a notion of force even before we introduce the laws of mechanics.
Second, a piece of steel distorts under a given load differently than a same-sized piece of chewing gum. This observation that different objects deform differently with the same loads implies that the properties of the object affect the solution of mechanics problems. The relations of an object’s deformations to the forces that are applied are called the mechanical properties of the object. Mechanical properties.

are sometimes called constitutive laws because the mechanical properties describe how an object is constituted (at least from a mechanics point of view). The classic example of a constitutive law is that of a linear spring which you remember from your elementary physics classes: ‘ F= kx’. When solving mechanics problems one has to make assumptions and idealizations about the constitutive laws applicable to the
parts of a system. How stretchy (elastic) or gooey (viscous) or otherwise deformable is an object? The set of assumptions about the mechanical behavior of the system is sometimes called the constitutive model
.
Distortion in the presence of forces is easy to see on squeezed fingertips, or when thin pieces of wood bend. But with pieces of rock or metal the deformation is essentially invisible and sometimes hard to imagine. With the exceptions of things like rubber, flesh, or compliant springs, solid objects that are not in the process of breaking typically change their dimensions much less than 1% when loaded. Most
structural materials deform less than one part per thousand with working loads. But even these small deformations can be important because they are enough to break bones and collapse bridges. When deformations are not of consequence engineers often idealize them away.

Mechanics, where deformation is neglected, is called rigid body mechanics because a rigid (infinitely stiff) solid would not deform. Rigidity is an extreme constitutive assumption. The assumption of rigidity greatly simplifies many calculations while generating adequate predictions for many practical problems. The assumption of rigidity also simplifies the introduction of more general mechanics concepts. Thus
for understanding the steering dynamics of a car we might model it as a rigid body, whereas for crash analysis where rigidity is clearly a poor approximation, we might model a car as a large collection of point masses connected by linear springs. Most constitutive models describe the material inside an object. But to solve a mechanics problem involving friction or collisions one also has to have a constitutive
model for the contact interactions. The standard friction model (or idealization) ‘F ≤ µN’ is an example of a contact constitutive model.

In all of mechanics, one needs constitutive models of a system and its components before one can make useful predictions.

The second pillar of mechanics concerns the geometry of deformation and motion. Classical Greek (Euclidean) geometry concepts are used. Deformation is defined by changes of lengths and angles between sets of points. Motion is defined by the changes of the position of points in time. Concepts of length, angle, similar triangles, the curves that particles follow and so on can be studied and understood without Newton’s laws and thus make up an independent pillar of the subject. We mentioned that understanding small deformations is often important to predict  when things break. But large motions are also of interest. In fact many machines and machine parts are designed to move something. Bicycles,   planes, elevators, and hearses are designed to move people; a clockwork, to move clock hands; insect wings, to move insect bodies; and forks, to move potatoes. A connecting rod is designed to move a crankshaft; a crankshaft, to move a transmission; and a transmission, to move a wheel. And wheels are designed to move bicycles, cars, and skateboards. The description of the motion of these things, of how the positions of the pieces change with time, of how the connections between pieces restrict the motion, of the curves traversed by the parts of a machine, and of the relations of these curves to
each other is called kinematics. Kinematics is the study of the geometry of motion(or geometry in motion).For the most part we think of deformations as involving small changes of distance
between points on one body, and of net motion as involving large changes of distance

Relation of force to motion, the laws of mechanics :::The third pillar of mechanics is loosely called Newton’s laws. One of Newton’s brilliant insights was that the same intuitive ‘force’ that causes deformation also causes motion, or more precisely, acceleration of mass. Force is related to deformation by material properties (elasticity, viscosity, etc.) and to motion by the laws of mechanics
summarized in the front cover. In words and informally.

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