# The elements of statics and dynamics - by S. L. Loney - PDF book

## The elements of statics and dynamics - part 1 Statics

The book has been somewhat altered, and I hope improved, for this edition, and the type entirely re-set. Graphic solutions have been introduced much earlier, and more use has been made of graphic methods throughout the book. More experimental work has also been introduced.

The chapter on Work has been placed earlier, and much greater stress has been laid upon the Principle of Work. Sundry somewhat long analytical proofs have been relegated to the last chapter, and here I have not scrupled to introduce alternative proofs involving the use of the Differential Calculus. For ten of the new figures in this book, I am much indebted to the kindness and courtesy of Dr R. T. Glazebrook, who allowed me to use the blocks prepared for his Statics. Most of these figures have the additional merit of having been drawn from actual apparatus in use at the Cavendish Laboratory at Cambridge.

1. A Body is a portion of matter limited in every direction. 2. Force is anything that changes, or tends to change, the state of rest, or uniform motion, of a body. 3. Rest. A body is said to be at rest when it does not change its position with respect to surrounding objects. 4. Statics is the science that treats of the action of forces on bodies, the forces being so arranged that the bodies are at rest. The science which treats of the action of force on bodies in motion is called Dynamics. In the more modern system of nomenclature which is gradually gaining general acceptance, the science which treats of the action of force on bodies is called Dynamics, and it has two subdivisions. Statics and Kinetics, treating of the action of forces on bodies which are at rest and in motion respectively. 5. A Particle is a portion of matter which is in- definitely small in size, or which, for the purpose of our investigations, is so small that the distances between its different parts may be neglected.

### Contents:

I. Introduction 1
II. Composition and Resolution of Forces . . 8
III. Composition and Resolution of Forces (continued) 29
IV. Parallel Forces 47
V. Moments 58
VI. Couples 75
VII. Equilibrium of a rigid body acted upon by
three forces in a plane .... 84
VIII. General conditions of equilibrium of a rigid
BODY acted on BY A SYSTEM OF FORCES IN
ONE PLANE . 97
IX. Centre of Gravity 119
Centre of gravity of a Triangle, Tetrahedron,
etc 123
General formulae for the determination of the
centre of gravity 129
X. Centre of Gravity (continued).
Properties of the centre of gravity . . . 149
Stable and unstable equilibrium . . . 153
XI. Work .... 163
XII. Machines 171
I. The Lever 174
11. Pulleys and Systems of Pulleys . . 180
III. The Inclined Piano . . . .196
IV. The Wheel and Axle . . . .203
Weston's Differential Pulley . . 207
V. The Common Balance .... 209
VI. The Steelyards 218
VII. The Screw 224
XIII. Friction 232
Laws of Friction 233
Equilibrium on a Rough Inclined Plane . . 241
The efficiency of machines ..... 246
Machines with friction 248
XIV. Problems with Friction 260
XV. ]\IlSCELLANEOUS.
Smooth Hinges 274
Funicular Polygon 279
Tensions of Elastic Strings .... 282
Graphic Constructions. Link and Force Poly-
gons 286
XVI. Some Additional Propositions .... 297
Formal proof of the Parallelogram of Forces. 297
Centre of gravity of a Circular Arc, and of a
Sector and Segment of a Circle . . 301
Centre of gravity of a Zone of a Sphere. 305
Centres of gravity of a Hollow and a Solid
Hemisphere 308
Virtual Work 310
Roberval's Balance 314
Easy Miscellaneous Examples 318
Harder miscellaneous Examples 320