What's Mechanics

Mechanics can be defined as that science which describes and predicts the conditions of rest or motion of bodies under the action of forces. It is divided into three parts: mechanics of rigid bodies,mechanics of deformable bodies,and mechanics of fluids.

 The mechanics of rigid bodies is subdivided into staticsand dynamics,the former dealing with bodies at rest, the latter with bodies in motion. In this part of the study of mechanics, bodies are assumed to be perfectly rigid. Actual structures and machines, however, are never absolutely rigid and deform under the loads to which they are subjected. But these deformations are usually small and do not appreciably affect the conditions of equilibrium or motion of the structure under consideration. They are important, though, as far as the resistance of the structure to failure is concerned and are studied in mechanics of materials, which is a part of the mechanics of deformable bodies. The third division of mechanics, the mechanics of fluids, is subdivided into the study of incompressible fluidsand of compressible fluids.An important subdivision of the study of incompressible fluids is hydraulics,which deals with problems involving water.

Mechanics is a physical science, since it deals with the study of physical phenomena. However, some associate mechanics with mathematics, while many consider it as an engineering subject. Both these views are justified in part. Mechanics is the foundation of most engineering sciences and is an indispensable prerequisite to their study. 

However, it does not have the empiricismfound in some engineering sciences, i.e., it does not rely on experience or observation alone; by its rigor and the emphasis it places on deductive reasoning, it resembles mathematics. But, again, it is not an abstractor even a pure science; mechanics is an appliedscience. The purpose of mechanics is to explain and predict physical phenomena and thus to lay the foundations for engineering applications.

FUNDAMENTAL CONCEPTS AND PRINCIPLES MECHANICS OF RIGID BODIES

Although the study of mechanics of rigid bodies goes back to the time of Aristotle (384–322 b.c.) and Archimedes (287–212 b.c.), one has to wait until Newton (1642–1727) to find a satisfactory formulation of its fundamental principles. These principles were later expressed in a modified form by d’Alembert, Lagrange, and Hamilton. Their validity remained unchallenged, however, until Einstein formulated his theory of relativity(1905). While its limitations have now been recognized, newtonian mechanics still remains the basis of today’s engineering sciences.

The basic concepts used in mechanics are space, time, mass, and force.These concepts cannot be truly defined; they should be accepted on the basis of our intuition and experience and used as a mental frame of reference for our study of mechanics.

The concept of spaceis associated with the notion of the position of a point P.The position of Pcan be defined by three lengths measured from a certain reference point, or origin,in three given directions. These lengths are known as the coordinatesof P. 

To define an event, it is not sufficient to indicate its position in space. The timeof the event should also be given.  The  concept  of  massis used to characterize and compare bodies on the basis of certain fundamental mechanical experiments. Two bodies of the same mass, for example, will be attracted by the earth in the same manner; they will also offer the same resistance to a change in translational motion. 

A  forcerepresents the action of one body on another. It can be exerted by actual contact or at a distance, as in the case of gravitational forces and magnetic forces. A force is characterized by its point of application ,its magnitude ,and its direction ;a force is represented by a vector.

In newtonian mechanics, space, time, and mass are absolute concepts, independent of each other. (This is not true in relativistic mechanics ,where the time of an event depends upon its position, and where the mass of a body varies with its velocity.) On the other hand, the concept of force is not independent of the other three. Indeed, one of the fundamental principles of newtonian mechanics listed below indicates that the resultant force acting on a body is related to the mass of the body and to the manner in which its velocity varies with time. 

In the first part of the book, the four basic concepts that we have introduced are used to study the conditions of rest or motion of particles and rigid bodies. By particlewe mean a very small amount of matter which may be assumed to occupy a single point in space. A rigid bodyis a combination of a large number of particles occupying fixed positions with respect to each other. 

The study of the mechanics of particles is obviously a prerequisite to that of rigid bodies. Besides, the results obtained for a particle can be used directly in a large number of problems dealing with the conditions of rest or motion of actual bodies.The study of elementary mechanics rests on six fundamental principles based on experimental evidence.

The Parallelogram Law for the Addition of Forces.   

This states that two forces acting on a particle may be replaced by a single force, called their resultant ,obtained by drawing the diagonal of the parallelogram which has sides equal to the given forces

The Principle of Transmissibility.   

This states that the conditions of equilibrium or of motion of a rigid body will remain unchanged if a force acting at a given point of the rigid body is replaced by a force of the same magnitude and same direction, but acting at a different point, provided that the two forces have the same line of action

Newton’s Three Fundamental Laws.   

Formulated by Sir Isaac Newton in the latter part of the seventeenth century, these laws can be stated as follows:  

FIRST LAW.   If the resultant force acting on a particle is zero, the particle will remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally in motion).

SECOND LAW.   If the resultant force acting on a particle is not zero, the particle will have an acceleration proportional to the magnitude of the resultant and in the direction of this resultant force. 

This law can be stated as :  F = m a

where  F,  m, and arepresent, respectively, the resultant force acting on the particle, the mass of the particle, and the acceleration of the particle, expressed in a consistent system of units. 

THIRD LAW.   

The forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense.