Definition of Mechanics Basic Concepts Newton s Laws Units

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1 INTRODUCTION

2 *Definition of Mechanics *Basic Concepts *Newton s Laws *Units

4 Mechanics may be defined as the physical science which describes and predicts the conditions of rest or motion of bodies under the action of force systems. Although the principles of mechanics are few, they have wide applications in engineering.

5 Modern research and development in the fields of vibrations, stability and strength of machines and structures, rocket and spacecraft design, robots, automatic control, engine performance, fluid flow, electrical machines and all sorts of apparatus, and molecular, atomic and subatomic behavior are highly dependent upon the basic principles of mechanics.

6 A thorough understanding of STATICS is an essential prerequisite for work in these and many other fields.

7 Mechanics is the oldest of the physical sciences. The early history of this subject is synonymous with the very beginnings of engineering. In engineering, mechanics is generally based on Newton s Laws and is often called Newtonian Mechanics (or Classical Mechanics) after the English scientist Sir Isaac Newton ( ).

8 The course of Statics will be concerned with both the development of the principles of mechanics and their application. The principles of mechanics as a science are rigorously expressed by mathematics and thus mathematics plays an important role in the application of these principles to the solution of practical problems.

9 Mechanics is divided into three parts as shown below: As seen, mechanics of rigid bodies are divided into two parts as Statics and Dynamics.

10 Statics is the branch of mechanics that deals with the bodies that are acted on by balanced forces. A force system acting on a body is said to be balanced if it has no tendency to change the state of rest or motion of the body in any way. If a body is in equilibrium, the force system acting on it must be balanced.

11 Furthermore, a body in a state of equilibrium must be either at rest or moving along a straight path with a constant velocity. Most problems in Statics concern bodies at rest.

12 Dynamics is that branch of mechanics which deals with the motion of bodies under the action of forces. Dynamics has two distinct parts: kinematics and kinetics. Kinematics is the study of motion without reference to the forces which cause motion. Kinetics relates the action of forces on bodies to their resulting motions.

13 BASIC CONCEPTS

14 The basic concepts in mechanics are space, time, mass and force. In Newtonian mechanics, space, time and mass are absolute quantities, which mean that they are independent of each other (this is not true in Relativistic Mechanics, where the time of an event depends upon its position and the mass of a body varies with its velocity) and cannot be defined in terms of other quantities or in simpler terms. Force is a derived quantity.

Space is the geometric region occupied by bodies whose positions are described by linear or angular measurements relative to a specific reference system.

15 Space is the geometric region occupied by bodies whose positions are described by linear or angular measurements relative to a specific reference system. In Newtonian Mechanics the basic reference system is named as the primary inertial system and it is a virtual system assumed as neither rotating or translating in space.

16 For two dimensional problems only two coordinates will be required. For three dimensional problems, three independent coordinates are needed.

17 Time is a concept for measuring the succession and the duration of events. Time is not directly involved in the analysis of problems in Statics.

18 Mass is a measure of the translational inertia of the body, which is its resistance to a change in velocity.

19 Mass can also be thought of as the quantity of matter in a body. The mass of a body affects the gravitational attraction force between it and other bodies. Although the mass of a body is an absolute quantity, its weight (W) can change depending on the gravitational force.

20 Force is the action of one body on another. A force tends to move a body in the direction of its action. Forces always occur in pairs. This pair of forces is always equal in magnitude and opposite in direction.

21 Force is a vector quantity. The action of a force is characterized by its magnitude, by the direction of its action and by its point of application. O F O F Magnitude : F Direction : OO Sense : From O to O Point of application : O

22 Particle is a body of negligible dimensions. In the mathematical sense, a particle is a body whose dimensions are considered to be near zero so that it may be analyzed as a mass concentrated at a point. We often choose a particle as a differential element of a body.

23 But we may treat a large body as a particle when its dimensions are irrelevant to the description of its position or the action of forces applied to it. F 3 F 1 F 2 F 4

24 A particle has mass but no shape and dimensions. In so doing, the principles of mechanics are reduced to a rather simplified form, since the geometry of the body will not be involved in the analysis of the problem.

25 Since a particle has mass but no shape and dimensions the body is considered to be concentrated at a single point, which usually will be the particle s mass center. All the forces acting on the body will have to pass from this point, i.e. the forces will be concurrent.

26 Some examples to particles are shown here; a ball, a block, even an airplane can be considered as particles.

28 Rigid Body is an idealized body composed of a large number of particles all of which always remain at fixed distances from each other. In addition to the tendency to move a body in the direction of its application, a force may also tend to rotate a body about an axis.

29 A rigid body is assumed to undergo no deformation under the action of applied forces. Its shape and dimensions remain fixed under all loading conditions and at all times.

30 Some examples of rigid bodies are shown here.

32 NEWTON S LAWS

33 F 0

34 F ma F ma kg m s 2 Newton (N)

F 1 F 2 G m m 1 2 2 r G = a universal constant called the constant of gravitation

36 F 1 F 2 G m m r G = a universal constant called the constant of gravitation G m 3 kg s 2 G F r m m N m kg kg 2 kg m m 2 s kg kg 3 m kg s 2

37 UNITS

38 The International System of metric units (SI) is defined and used in this lecture. Units Quantity Symbol Unit Mass m kg (kilogram) Time t s (second) Length L m (meter) Force F N (Newton)

CHAPTER 1 INTRODUCTION

CHAPTER 1 INTRODUCTION DEFINITION OF MECHANICS Mechanics may be defined as the physical science which describes and predicts the conditions of rest or motion of bodies under the action of force systems.