# Elements of mechanics - Merriman

ELEMENTS OF MECHANICS

Forty Lessons for Beginners in Engineering.

BY MANSFIELD MERRIMAN

NEW YORK, JOHN WILEY AND SONS, 1905

Elements of mechanics

PREFACE

During the past forty years great advances have been made in the methods of instruction in all branches of applied mechanics, but little or no change has taken place in the manner of presenting the subject of rational mechanics. This elementary volume is an attempt to apply the best methods of applied mechanics to the development of the fundamental principles and methods of rational mechanics. To this end, constant appeals are made to experience, by which alone the laws of mechanics can be established, numerous numerical illustrations are given, many queries and problems are stated as exercises for the student, and a system of units is employed with which every boy is acquainted.

The field of rational mechanics is so vast that no book can present more than a part of the same. Even the limited course usually given in engineering colleges is so difficult and appeals so little to the students' experience that few acquire a complete mastery of it. In the opinion of the author there should be given in every engineering college two courses in rational mechanics, an elementary one during the freshman year in which only as much mathematics is employed as is indispensably necessary, and an advanced one after the completion of the course in calculus. It is the principles and fundamental methods which are of the greatest value and importance, and if no course in mechanics is given until calculus has been completed, as is now generally the case, the student is introduced to a wilderness of algebraic matter in which these principles are largely obscured. Fortunately the fundamental elements can be presented without such advanced mathematics, and this book is an attempt in that direction.

To read this volume with interest and profit, only a knowledge of plane geometry, elementary algebra, and plane trigonometry is required. It is intended for manual training schools, freshman classes in engineering colleges, and for young men in general who have the preparation just indicated. To all who may use the book, it is strongly recommended that many numerical problems should be solved, and that in so doing the actual forces and bodies should be always kept in mind with the principles that govern their relations. Forty lessons thoroughly mastered will form a solid substructure on which applied mechanics may safely stand. If this be accomplished and an advanced course be later pursued, as above advocated, it is believed that the interests of sound engineering education will be materially promoted.

CONTENTS

Chapter I. CONCURRENT FORCES
1. Definitions
2. Axioms or Laws
3. Components of Forces
4. The Resultant of Forces
5. Conditions of Equilibrium
6. The Parallelogram of Forces

Chapter II. PARALLEL FORCES
7. Definitions and Axioms
8. The Principle of Moments
9. The Resultant
10. Couples
11. Non-concurrent Forces
12. Parallel Forces in Space

Chapter III. CENTER OF GRAVITY
13. Definitions and Principles
14. Centers of Gravity for Lines
15. Centers of Gravity for Surfaces
16. Stable and Unstable Equilibrium
17. Stability against Rotation

Chapter IV. RESISTANCE AND WORK
18. Resisting Forces
19. Friction
20. Stability against Sliding
21. Gravity and Work
22. Work against Friction

Chapter V. SIMPLE MACHINES
23. The Simple Lever
24. Systems of Levers
25. The Inclined Plane
26. The Screw
27. The Pulley
28. Effect and Efficiency

Chapter VI. GRAVITY AND MOTION
29. Velocity and Acceleration
30. Vertical Fall of Bodies
31. Oblique Fall
32. Potential and Kinetic Energy
33. Motion of Projectiles
34. Composition op Velocities

Chapter VII. INERTIA AND ROTATION
35. Force and Inertia
36. Work against Inertia
37. Centrifugal Force
38. Revolving Bodies
39. Rolling Bodies
40. Pendulums

APPENDIX

Trigonometric Functions

Index

CHAPTER I - CONCURRENT FORCES

Article 1. Definitions

Mechanics is the science that treats of forces and of their effects. Archimedes, a celebrated mathematician and engineer, announced some of its fundamental principles about 250 B.C., and these were greatly extended by Galileo and Newton in the seventeenth century. Mechanics is the foundation of modern engineering, and works on applied mechanics treat mainly of engineering problems. The principles and methods set forth in this elementary volume are the foundation of all branches of applied mechanics.

Force is manifested to our sense of feeling by pressure and by tension; when the hand pushes a body pressure is felt, when it pulls a body tension is felt. These applied forces of pressure and tension will cause the body to move if they are sufficient to overcome the resisting forces. Force may arise from muscular effort, from gravitation, from magnetic or electric action, from molecular attraction or repulsion, but elementary mechanics treats only of the pressure and tension which it causes and of the motions of bodies which it produces. This volume deals with solid bodies only.

A force has both magnitude and direction. Its magnitude may be measured in pounds, the unit of magnitude being the force exerted by gravity in London upon the standard block of platinum called the pound weight; or it may be measured in kilograms, the unit being the force exerted by gravity in Paris upon the standard block called the kilogram weight. Its direction is indicated by the statement as to whether it acts toward or away from a given body, and by the angle which its line of action makes with a fixed line of reference.