Elementary statics - Rawlinson
ELEMENTARY STATICS
BY GEORGE RAWLINSON,
MACMILLAN AND CO.; LONDON; 1860
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PREFACE
A Treatise on Elementary Statics for the use of Students in Elphinstone College was in course of preparation by my lamented friend, Mr Bawlinson, when death brought all this labours in the cause of education to a sudden end. What he had written on this subject was sent to me with a request that I would prepare it for the press. In doing so I found a considerable portion of the plan of the work only sketched out in the manuscript, this I had to fill in as best I could. I am also responsible for most of the problems and illustrations and for the examination papers which appear in the following pages, I feel also that I am solely responsible for the faults that will be found in them.
Whatever portion of the work has any merit may be safely reckoned as coming from the pen of my friend, whatever is weak and obscure as coming from my own.
It will perhaps be felt that some important points have been omitted which ought to have found a place in this Treatise, and that others have not been considered with sufficient fulness. The absence of any explanation of the Principle of Virtual Velocities - a principle of which, I think, great use might be made in an Elementary Treatise on Statics - and the want of a larger collection of Problems, and of advice and guidance in their solution, are doubtless blemishes. But I have been in a measure constrained to brevity. The work is published at the charge of Her Majesty's Government, and I have not felt myself justified in exceeding, more than could be avoided, the space and expense which, in the estimate previously supplied by the Publishers, was deemed sufficient for printing the manuscript as it was left by Mr Rawlinson.
Whatever portion of the work has any merit may be safely reckoned as coming from the pen of my friend, whatever is weak and obscure as coming from my own.
It will perhaps be felt that some important points have been omitted which ought to have found a place in this Treatise, and that others have not been considered with sufficient fulness. The absence of any explanation of the Principle of Virtual Velocities - a principle of which, I think, great use might be made in an Elementary Treatise on Statics - and the want of a larger collection of Problems, and of advice and guidance in their solution, are doubtless blemishes. But I have been in a measure constrained to brevity. The work is published at the charge of Her Majesty's Government, and I have not felt myself justified in exceeding, more than could be avoided, the space and expense which, in the estimate previously supplied by the Publishers, was deemed sufficient for printing the manuscript as it was left by Mr Rawlinson.
EDWARD STURGES.
CONTENTS
CHAPTER I.
PRELIMINARY NOTIONS
- Definition of force
- Numerical estimate of force,
- Units of weight and length,
- How to represent forces by straight lines
- The use of the signs + and - before symbols representing forces
- Axioms
- Examination on Chap
CHAPTER II
ON THE COMPOSITION AND RESOLUTION OF FORCES ACTING AT ONE POINT
- Any number of forces acting on a point in any directions must have a resultant To find the resultant of any number of forces acting on a particle along the same line, 2, 3. If any number of forces act upon a particle and keep it at rest, any one of them is equal and opposite to the resultant of all the rest, The direction of the resultant of two equal forces acting on a particle in different directions
- The enunciation of the parallelogram of forces, 9. Examples on the composition of two forces,
- The trigonometrical formulae for finding the magnitude and direction of the resultant of two forces
- On the resolution of a force into a pair of component forces
- Resolution of a force when the directions of the component forces are given, Examples,
CHAPTBR III.
ON THE COMPOSITION AND RESOLUTION OF FORCES ACTING ON A POINT
- Proof of the parallelogram of forces
- The triangle of forces
- The polygon of forces
- Extension of the parallelogram of forces by geometry
- To find the magnitude and direction of the resultant of any number of forces acting on a point
- To find the conditions of equilibrium of any number of forces acting on a particle
- Problems
CHAPTER IV.
ON THE COMPOSITION AND RESOLUTION OF FORCES ACTING ON A RIGID BODY
- How the investigation of forces in equilibrium acting on a particle is extended to a rigid body
- The resultant of two parallel forces
- Definition of Centre of Gravity. Centre of Gravity of a uniform beam
- Two equal and parallel forces acting in opposite directions can have no single resultant. Definition of a couple
- Definition of moment of a force about a point
- How any number of forces acting on a rigid body at different points in the same plane may be supposed to act all at one point by the Introduction of couples
- The effect of a couple is not altered by turning its arm through any angle about one extremity in its own plane
- Two couples whose arms have a common extremity and whose moments are equal have the same statical effect
- To find the resultant of any number of couples whose arms have a common extremity
- To find the conditions of equilibrium of any number of forces acting on a rigid body,
- Problems
CHAPTER V.
ON THE COMPOSITION AND RESOLUTION OF FORCES ACTING ON A SYSTEM OF TWO OR MORE RIGID BODIES
- Action and reaction
- Contact of smooth surfaces
- Problems
- Contact of rough surfaces
- Problems
CHAPTER VI.
ON THE CENTRE GRAVITY AND EQUILIBRIUM,
- Property of the centre of gravity
- The centre of gravity may sometimes be determined by inspection
- Given the centres of gravity of two parts of a body to find the centre of gravity of the whole
- To find the centre of gravity of a system of material particles
- The centre of gravity of a triangle
- Of a triangular pyramid
- Of a cone, ib, Of the surface of a cone
- Problems, 8, 9, 10. On equilibrium
- To determine the centre of gravity of a body by experiment
- Stable and unstable equilibrium
CHAPTER VII.
ON MACHINES
- Preliminary remarks
- The Lever. The three different kinds
- Examples
- The modulus
- The modulus obtained geometrically
- The common balance, the requisites for a good one; the measure of sensibility, 6. The common steelyard
- The Danish steelyard
- The compound lever
- The Wheel and Axle
- The modulus
- The windlass
- Wheels and axles in combination
- Toothed wheels
- The Pulley
- The angle moveable pulley
- The first system of pulleys
- The second system
- White's pulley
- The third system of pulleys
- Remarks on some of the causes of inaccuracy in our results
- The inclined plane, description of, and modulus
- The Screw, description of, and modulus
- The Wedge, description of, and modulus
- Machines with friction. The Lever
- The wheel and axle
- The inclined plane
- The screw
- The wedge
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