ENGINEERING MECHANICS STATICS AND DYNAMICS Chapter 1. General Principles part - 1
ENGINEERING MECHANICS
STATICS AND DYNAMICS
Chapter 1. General Principles
Part - 1 Mechanics , Fundamental Concepts
Author:- Jakkir Hussain.
CHAPTER OBJECTIVES
◆ To provide an introduction to the basic quantities and idealizations of mechanics.
◆ To give a statement of Newton's Laws of Motion and Gravitation.
◆ To review the principles for applying the Sl system of units.
◆ To examine the standard procedures for performing numerical calculations.
◆ To present a general guide for solving problems.
1.1 Mechanics
Mechanics is a branch of the physical sciences that is concerned with the state of rest or motion of bodies that are subjected to the action of forces. In general, this subject can be subdivided into three branches: rigid-body mechanics, deformable-body mechanics, and fluid mechanics. In this book we will study rigid-body mechanics since it is a basic requirement for the study of the mechanics of deformable bodies and the mechanics of fluids. Furthermore, rigid-body mechanics is essential for the design and analysis of many types of structural members, mechanical components, or electrical devices encountered in engineering.
Rigid-body mechanics is divided into two areas: statics and dynamics. Staties deals with the equilibrium of bodies, that is, those that are either at rest or move with a constant velocity; whereas dynamics is concerned with the accelerated motion of bodies. We can consider statics as a special case of dynamics, in which the acceleration is zero; however, statics deserves separate treatment in engineering education since many objects are designed with the intention that they remain in equilibrium.
Historical Development : The subject of statics developed very early in history because its principles can be formulated simply from measurements of geometry and force. For example, the writings of Archimedes (287-212 B.C.) deal with the principle of the lever. Studies of the pulley, inclined plane, and wrench are also recorded in ancient writings-at times when the requirements for engineering were limited primarily to building construction.
Since the principles of dynamics depend on an accurate measurement of time, this subject developed much later. Galileo Galilei (1564-1642) was one of the first major contributors to this field. His work consisted of experiments using pendulums and falling bodies. The most significant contributions in dynamics, however, were made by Isaac Newton (1642-1727), who is noted for his formulation of the three fundamental laws of motion and the law of universal gravitational attraction. Shortly after these laws were postulated, important techniques for their application were developed by other scientists and engineers, some of whom will be mentioned throughout the text.
1.2 Fundamental Concepts
Before we begin our study of engineering mechanics, it is important to understand the meaning of certain fundamental concepts and principles.
Basic Quantities : The following four quantities are used throughout mechanics.
Length : Length is used to locate the position of a point in space and thereby describe the size of a physical system. Once a standard unit of length is defined, one can then use it to define distances and geometric properties of a body as multiples of this unit.
Time : Time is conceived as a succession of events. Although the principles of statics are time independent, this quantity plays an important role in the study of dynamics.
Mass : Mass is a measure of a quantity of matter that is used to compare the action of one body with that of another. This property manifests itself as a gravitational attraction between two bodies and provides a measure of the resistance of matter to a change in velocity.
Force : In general, force is considered as a "push" or "pull" exerted by one body on another. This interaction can occur when there is direct contact between the bodies, such as a person pushing on a wall, or it can occur through a distance when the bodies are physically separated. Examples of the latter type include gravitational, electrical, and magnetic forces. In any case, a force is completely characterized by its magnitude, direction, and point of application.
Idealizations : Models or idealizations are used in mechanics in order to simplify application of the theory. Here we will consider three important idealizations.
Particle : A particle has a mass, but a size that can be neglected. For example, the size of the earth is insignificant compared to the size of its orbit, and therefore the earth can be modeled as a particle when studying its orbital motion. When a body is idealized as a particle, the principles of mechanics reduce to a rather simplified form since the geometry of the body will not be involved in the analysis of the problem.
Rigid Body : A rigid body can be considered as a combination of a large number of particles in which all the particles remain at a fixed distance from one another, both before and after applying a load. This model is important because the body's shape does not change when a load is applied, and so we do not have to consider the type of material from which the body is made. In most cases the actual deformations occurring in structures, machines, mechanisms, and the like are relatively small, and the rigid-body assumption is suitable for analysis.
Concentrated Force : A concentrated force represents the effect of a loading which is assumed to act at a point on a body. We can represent a load by a concentrated force, provided the area over which the load is applied is very small compared to the overall size of the body. An example would be the contact force between a wheel and the ground.
Steel is a common engineering material that does not deform very much under load. Therefore, we can consider this railroad wheel to be a rigid body acted upon by the concentrated force of the rail. (Russell C. Hibbeler)
Newton's Three Laws of Motion : Engineering mechanics is formulated on the basis of Newton's three laws of motion, the validity of which is based on experimental observation. These laws apply to the motion of a particle as measured from a nonaccelerating reference frame. They may be briefly stated as follows.
First Law : A particle originally at rest, or moving in a straight line with constant velocity, tends to remain in this state provided the particle is not subjected to an unbalanced force, Fig. 1 - 1 a
 |
Second Law : A particle acted upon by an unbalanced force F experiences an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force, Fig. 1 - b .^ + If F is applied to a particle of mass m, this law may be expressed mathematically as
Third Law : The mutual forces of action and reaction between two particles are equal, opposite, and collinear. Fig. 1-1c.
"Stated another way, the unbalanced force acting on the particle is proportional to the time rate of change of the particle's linear momentum.
Newton's Law of Gravitational Attraction :
Shortly after formulating his three laws of motion, Newton postulated a law governing the gravitational attraction between any two particles. Stated mathematically.
Weight : According to Eq. 1-2, any two particles or bodies have a mutual attractive (gravitational) force acting between them. In the case of a particle located at or near the surface of the earth, however, the only gravitational force having any sizable magnitude is that between the earth and the particle. Consequently, this force, termed the weight, will be the only gravitational force considered in our study of mechanics.
From Eq. 1-2, we can develop an approximate expression for finding the weight W of a particle having a mass m_{1} = m If we assume the earth to be a nonrotating sphere of constant density and having a mass m_{2} = M_{2} then if is the distance between the earth's center and the particle, we have
By comparison with F = ma we can see that g is the acceleration due to gravity. Since it depends on r, then the weight of a body is not an absolute quantity. Instead, its magnitude is determined from where the measurement was made. For most engineering calculations, however, g is determined at sea level and at a latitude of 45 deg which is considered the "standard location."
Comments
Post a Comment