MECHANICS FOR ENGINEERS - > MECHANICS FOR ENGINEERS A TEXT-BOOK OF INTERMEDIATE STANDARD BY ARTHUR MORLEY M.Sc., UNIVERSITY SCHOLAR (VICT.) SENIOR LECTURER IN ENGINEERING IN UNIVERSITY COLLEGE NOTTINGHAM WITH 200 DIAGRAMS AND NUMEROUS EXAMPLES LONGMANS, GREEN, AND CO. PATERNOSTER ROW, LONDON 39 NEW YORK AND BOMBAY Allrightsreserved PREFACE ENGINEERING students constitute a fairly large proportion of those attending the Mechanics classes in technical colleges and schools, but their needs are not identical with those of the students of general science. It has recently become a common practice to provide separate classes in Mathematics, adapted to the special needs of engineering students, who are in most institutions sufficiently numerous to justify similar provision in Mechanics. The aim of this book is to provide a suitable course in the principles of Mechanics forengineering students. With this object in view, the gravitational system of units has been adopted in the English measures. A serious injustice is often done to this system in books on Mechanics by wrongly denning the pound unit of force as a variable quantity, thereby reducing the system to an irrational one. With proper premisesthe gravitationalsystem is just asrational as that in which the "poundal" is adopted as the unit of force, whilst it may be pointed out that the use of the latter system is practically confined to certain text-books and exami- nation papers, and does not enter into any engineering work. Teachers of Engineering often find that students who are learning Mechanics by use of the "poundal" system, fail to apply the principles to engineering problems stated in the only units which are used in such cases the gravitational vi Preface units. The use of the dual system is certainly confusing to the student, and in addition necessitates much time being spent on the re-explanation of principles, which might other- wise be devoted to more technical work. Graphical methods of solving problems have in some cases been used, by drawing vectors to scale, and by esti- mating slopesand areas under curves. It is believed that such exercises, although often taking more time to work than the easy arithmetic ones which are specially framed to give exact numerical answers, compel the student to think of the relations between the quantities involved, instead of merely performing operations by fixed rules, and that the principles so illustrated are more deeply impressed. The aim has not been to treat a wide range of academic problems, but rather to select a course through which the student may work in a reasonable time say a year and the principles have been illustrated, so far as the exclusion of technical knowledge and terms would allow, by examples likely to be most useful to the engineer. In view of the applications of Mechanics to Engineering, more prominence than usual has been given to such parts of the subject as energy, work of forces and torques, power, and graphical statics, while some other parts have received less attention or have been omitted. It is usual, in books on Mechanics, to devote a chapter to the equilibrium of simple machines, the frictional forces in them being considered negligible: this assumption is so far from the truth in actual machines as to create a false impres- sion, and as the subject is very simple when treated experi- mentally, it is left for consideration in lectures on Applied Mechanics and in mechanical laboratories. The calculus has not been used in this book, but the