Tips and tricks
Technical mechanics - Maurer
TECHNICAL MECHANICS
BY EDWARD R. MAURER
Professor of Mechanics in the University of Wisconsin
NEW YORK, JOHN WILEY & SONS, 1913
DOWNLOAD FREE BOOK: Technical mechanics
INTRODUCTION
Mechanics had its origin in the experience of ancient peoples with devices for lifting and moving heavy things. The devices included the so-called simple machines or mechanical powers; namely, the lever, the pulley, the wheel and axle, the inclined plane, the wedge and the screw. That experience probably afforded fairly definite and full knowledge of the practical advantages of these various devices, but the simple and precise mechanical principles involved in them were long unrecognized. The first recognition of such a principle marked the real beginning of the science of Mechanics.
History records that the principle of the lever is the mechanical principle first discovered, and that Archimedes (287-212 B.C.), famous Greek mathematician, was the discoverer. He perceived the application of this principle to the wheel and axle (continuous lever), to the pulley (movable lever), and to certain combinations or systems of pulleys and cords, one of which still bears his name. The discovery of the principle of buoyant effort on a body floating on or immersed in a fluid is due to him. Apparently no additions to these achievements of Archimedes were made during the sixteen centuries following his time.
The principle of the lever as understood by Archimedes covered only the special case of two heavy weights suspended from a horizontal bar supported at a point (fulcrum) between them. For such case he stated that the weights are inversely as the distances from the fulcrum to the points of suspension. The principle was extended to include the case of forces applied obliquely, by Leonardo da Vinci (1452-1519), famous Italian artist and engineer. Heperceived that the efficacy of such a force depends on the distance from the fulcrum, not to the point of application of the force, but to its line of action.
The principle next discovered was that of the inclined plane, first definitely stated by Simon Stevin (1548-1620), Dutch mathematician and engineer. His statement of the principle was somewhat as follows: The force (acting along the plane) required to support a (frictionless) body resting upon it is to the weight of the body as the height of the plane is to its length (measured along the slope). This principle afforded the explanation of the wedge (double inclined plane) and the screw (continuous inclined plane). Stevin deduced the parallelogram law for two forces at right angles from the principle of the inclined plane; and from his study of pulleys he noted that what is gained in power is lost in speed. Thus he caught the first glimpse of two important principles, - that of the parallelogram of forces, and that of virtual velocity or work.
The first discoveries of laws of motion were made by Galileo (1564-1642), Italian astronomer and physicist. For 2000 years it had been believed that heavy bodies fall more rapidly than light ones. This Galileo disproved by actual trial at the leaning tower of Pisa. Next he was led to inquire about the manner in which a body falls, or how the speed changes. He made several guesses at this law, and finally verified one of them by indirect experiment and deduction. Up to Galileo's time, it was believed that rest was the natural condition for a body; and that motion was unnatural, requiring some outside cause (force) to maintain it, and ceasing only when the force ceases. Galileo perceived that motion is just as natural as rest; that motions cease not because they are unnatural, but because of some influence (force) from the outside operating to reduce the motion and eventually to destroy it. In short, he discovered the so-called first law of motion, usually credited to Newton. He invented the telescope.
Huygens (1629-1695), Dutch physicist, made some important contributions to this science. He developed the theory of the pendulum, determined the acceleration due to gravity from pendulum observations, and deduced certain theorems regarding centrifugal force. He invented the clock pendulum and escapement.
Newton (1642-1727), English mathematician and physicist, is generally regarded as the founder of Mechanics. At an early age he began an attempt to explain the motions of the planets, whose orbits and speeds were then well known, in terms of experience with more familiar motions. He succeeded in thus explaining many features of the planetary motions, and established that there are certain principles common to the motion of all bodies, celestial and terrestial. These principles are generally known as Newton's laws of motions (see index). His study of planetary motion led to other great achievements, among which may be mentioned the discovery of the law of universal gravitation, and the invention of the calculus (also invented independently by Leibnitz, German mathematician).
Since Newton, "no essentially new principle [of Mechanics] has been stated. All that has been accomplished since his day has been a deductive, formal, and mathematical development on the basis of Newton's laws." Such development constitutes the body of knowledge which we call Mechanics, or sometimes Rational and Theoretical Mechanics, to distinguish it from Applied Mechanics. It may be defined as the science of motion, but it includes the science of rest as a relatively minor part.
Adaptations of rational mechanics have played an important part in the development of the science of engineering, particularly in the departments of structures and machines. Such adaptations, together with our knowledge of friction, strength of materials, and certain properties of fluids, constitute Applied Mechanics. Among the pioneer workers in this field should be mentioned the following: Coulomb (1736-1806), Navier (1785-1836), Poncelet (1788-1867), Monn (1795-1880), Saint-Venant (1797-1886), Weisbach (1806-71), Rankine (1820-72), Grashof (1826-93) and Bauschinger (1834-93).
Under Technical Mechanics, the present author includes those principles of rational mechanics which are especially applicable in various fields of engineering, and some of our knowledge of friction. The book is divided into two parts called Statics and Dynamics. The first deals with certain of the circumstances of bodies at rest, and the second with those of bodies in motion. The certain circumstances dealt with will become apparent to the student as he progresses in the subject.
DOWNLOAD FREE BOOK: Technical mechanics
History records that the principle of the lever is the mechanical principle first discovered, and that Archimedes (287-212 B.C.), famous Greek mathematician, was the discoverer. He perceived the application of this principle to the wheel and axle (continuous lever), to the pulley (movable lever), and to certain combinations or systems of pulleys and cords, one of which still bears his name. The discovery of the principle of buoyant effort on a body floating on or immersed in a fluid is due to him. Apparently no additions to these achievements of Archimedes were made during the sixteen centuries following his time.
The principle of the lever as understood by Archimedes covered only the special case of two heavy weights suspended from a horizontal bar supported at a point (fulcrum) between them. For such case he stated that the weights are inversely as the distances from the fulcrum to the points of suspension. The principle was extended to include the case of forces applied obliquely, by Leonardo da Vinci (1452-1519), famous Italian artist and engineer. Heperceived that the efficacy of such a force depends on the distance from the fulcrum, not to the point of application of the force, but to its line of action.
The principle next discovered was that of the inclined plane, first definitely stated by Simon Stevin (1548-1620), Dutch mathematician and engineer. His statement of the principle was somewhat as follows: The force (acting along the plane) required to support a (frictionless) body resting upon it is to the weight of the body as the height of the plane is to its length (measured along the slope). This principle afforded the explanation of the wedge (double inclined plane) and the screw (continuous inclined plane). Stevin deduced the parallelogram law for two forces at right angles from the principle of the inclined plane; and from his study of pulleys he noted that what is gained in power is lost in speed. Thus he caught the first glimpse of two important principles, - that of the parallelogram of forces, and that of virtual velocity or work.
The first discoveries of laws of motion were made by Galileo (1564-1642), Italian astronomer and physicist. For 2000 years it had been believed that heavy bodies fall more rapidly than light ones. This Galileo disproved by actual trial at the leaning tower of Pisa. Next he was led to inquire about the manner in which a body falls, or how the speed changes. He made several guesses at this law, and finally verified one of them by indirect experiment and deduction. Up to Galileo's time, it was believed that rest was the natural condition for a body; and that motion was unnatural, requiring some outside cause (force) to maintain it, and ceasing only when the force ceases. Galileo perceived that motion is just as natural as rest; that motions cease not because they are unnatural, but because of some influence (force) from the outside operating to reduce the motion and eventually to destroy it. In short, he discovered the so-called first law of motion, usually credited to Newton. He invented the telescope.
Huygens (1629-1695), Dutch physicist, made some important contributions to this science. He developed the theory of the pendulum, determined the acceleration due to gravity from pendulum observations, and deduced certain theorems regarding centrifugal force. He invented the clock pendulum and escapement.
Newton (1642-1727), English mathematician and physicist, is generally regarded as the founder of Mechanics. At an early age he began an attempt to explain the motions of the planets, whose orbits and speeds were then well known, in terms of experience with more familiar motions. He succeeded in thus explaining many features of the planetary motions, and established that there are certain principles common to the motion of all bodies, celestial and terrestial. These principles are generally known as Newton's laws of motions (see index). His study of planetary motion led to other great achievements, among which may be mentioned the discovery of the law of universal gravitation, and the invention of the calculus (also invented independently by Leibnitz, German mathematician).
Since Newton, "no essentially new principle [of Mechanics] has been stated. All that has been accomplished since his day has been a deductive, formal, and mathematical development on the basis of Newton's laws." Such development constitutes the body of knowledge which we call Mechanics, or sometimes Rational and Theoretical Mechanics, to distinguish it from Applied Mechanics. It may be defined as the science of motion, but it includes the science of rest as a relatively minor part.
Adaptations of rational mechanics have played an important part in the development of the science of engineering, particularly in the departments of structures and machines. Such adaptations, together with our knowledge of friction, strength of materials, and certain properties of fluids, constitute Applied Mechanics. Among the pioneer workers in this field should be mentioned the following: Coulomb (1736-1806), Navier (1785-1836), Poncelet (1788-1867), Monn (1795-1880), Saint-Venant (1797-1886), Weisbach (1806-71), Rankine (1820-72), Grashof (1826-93) and Bauschinger (1834-93).
Under Technical Mechanics, the present author includes those principles of rational mechanics which are especially applicable in various fields of engineering, and some of our knowledge of friction. The book is divided into two parts called Statics and Dynamics. The first deals with certain of the circumstances of bodies at rest, and the second with those of bodies in motion. The certain circumstances dealt with will become apparent to the student as he progresses in the subject.
DOWNLOAD FREE BOOK: Technical mechanics
Free books category: