An Elementary Treatise on Mechanics, Embracing the Theory of Statics and Dynamics, and Its Application to Solids and Fluids

Portada
Harper & Brothers, 1863
 

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Resultant of any number of opposite Forces
12
Point of Application at any Point in its Direction
13
Direction of the Resultant of several Forces
14
Direction of the Resultant of two equal Forces
15
Direction of the Resultant of two unequal Forces
16
Variation of the Magnitude of the Resultant and its Components
17
Equilibrium of three equal Forces
18
Resultant of two equal Forces at an Angle of 120
20
Parallelogram of Forces
21
Triangle of Forces
22
Resolution of Forces
23
Polygon of Forces
24
Representation of equilibrated Forces
25
Graphical determination of Resultant
26
Parallelopiped of Forces
27
Ratios of three equilibrated Forces
28
Expression for the Resultant of two Forces
29
Definition of Moment of a ForceOrigin of Moments
30
Equality of the Moment of the Resultant with the Sum of the Moments of
31
Equality of the Moment of the Resultant with the Sum of the Moments of
32
number of Components 33 When the Origin of Moments is fixed 34 When the Forces are in Equilibrium
33
Examples
35
Definition of Arms of Forces
37
Equilibrium of two Parallel Forces by a third Force
38
Point of Application of the Resultant
39
When the Forces act in opposite Directions
40
When the Forces are Equal and Opposite
41
Such Forces constitute a Statical Couple
42
Resultant of any Number of Parallel Forces
43
Definition of Center of Parallel Forces
44
Equality of the Moment of the Resultant with the Sum of the Moments of the Components
45
Definition of Moment of a Force in reference to a Plane
46
Conditions of Equilibrium of any Number of Parallel Forces
47
Condition of Rotation
48
When in Equilibrium each Force equal in Magnitude to the Resultant of all the others
49
Equilibrium independent of their Direction
50
Examples CHAPTER III
51
Definition of a Statical Couple
52
Definition of the Arms of a Couple
53
Definition of the Moment of a Couple
54
A Couple may be turned round in its own Plane
55
A Couple may be removed parallel to itself in its own Plane
56
A Couple may be removed to a Parallel Plane
57
Couples are equivalent when their Planes are Parallel and Moments are Equal
58
Couples may be changed into others having Arms of a given Length
59
Definition of the Axis of a Couple
60
Properties of an Axis
61
Definition of the Resultant of two or more Couples
62
Equality of the Moment of the Resultant with the Sum of the Moments of the Components
63
Equality of the Axis of the Resultant with the Sum of the Axes of the Com ponents
64
The Resultant of two Couples inclined to each other
65
Representative of the Axis of the Resultant of two Couples
66
Parallelogram of Couples
67
Resultant of any Number of Concurring Forces
68
Directions of the Rectangular Components involved in their Trigonometrical Values
69
Conditions of Equilibrium of Concurring Forces
70
Resultant Force and Resultant Couple when the Forces do not concur
71
Construction of the Results
72
Equation of the Resultant
73
Equilibrium of nonconcurring Forces
74
Equilibrium when there is a fixed Point in the System
75
Equilibrium of a Point on a Plane Curve
76
Definition of Virtual Velocities
78
Principle of Virtual Velocities Page
79
Principle of Virtual Velocities obtains in Concurring Forces in the same Plane
80
Principle of Virtual Velocities obtains in nonconcurring Forces in the same Plane
81
Definition of Gravity
83
Laws of Gravity CHAPTER V
84
Definition of a Heavy Body
85
Definition of the Weight of a Body
86
Definition of its Mass
87
Expression for Weight
88
Definition of Density
89
Another Expression for Weight
90
Relations of Masses to Volumes of the same Density
91
Relations of Densities to Volumes of the same Mass
92
Relations of Densities to Masses of the same Volume
93
Definition of Center of Gravity
94
Connection of the Center of Gravity with the Doctrine of Parallel Forces
95
Definition of a Body symmetrical with respect to a Plane
96
Position of its Center of Gravity
97
Definition of a Body symmetrical with respect to an Axis
98
Position of its Center of Gravity
99
Center of Gravity of a Body symmetrical with respect to two Axes
100
Definition of Center of Figure
101
Center of Gravity of any Number of heavy Particles
102
Their Center of Gravity when their Positions are given by their Coordinates
103
Their Center of Gravity when they are all in the same Line
104
Their Center of Gravity when they are Homogeneous 43
105
The Center of Gravity of the Whole and a Part given to find that of the other Part
106
Examples1 Of a Straight Line2 Triangle3 Parallelogram4 Polygon 5 Triangular Pyramid6 Any Pyramid7 Frustum of a Cone8 Perimeter of a Triangle...
107
When the Body has a Fixed Point in
108
Definition of Stable Unstable and Neutral Equilibrium 54
109
Position of the Center of Gravity when the Equilibrium is Stable and when Unstable
110
Pressure on the Fixed Point
111
Position and Pressure when there are two Fixed Points
112
Position and Pressure when there are three Fixed Points
113
Position and Pressure when a Body touches a Horizontal Plane in one Point
114
Position and Pressure when a Body touches a Horizontal Plane in two Points
115
Position and Pressure when a Body touches a Horizontal Plane in three Points
116
Position and Pressure when a Body touches a Horizontal Plane in any Number of Points
117
Measure of the Stability on a Horizontal Plane
118
Case of a Body on an Inclined Plane
119
Examples
120
General differential Expressions for the Center of Gravity of a Plane Curve
122
General differential Expressions for the Center of Gravity of a Plane Area
123
General differential Expressions for the Coordinates of a Surface of Revolution
124
General differential Expressions for the Coordinates of a Solid of Revolution
125
Determination of a Surface of Revolution
126
Determination of a Solid of Revolution
127
Examples1 Of a Circular Arc2 Circular Segment3 Surface of a Spherical Segment4 Spherical Segment
128
Examples on the preceding Chapters CHAPTER VI
129
Classification of the Mechanical Powers Ó I THE LEVER
130
Definition of a Lever
131
Kinds of Lever
132
Conditions of Equilibrium when the Forces are Parallel
133
Conditions of Equilibrium when the Forces are Inclined
134
Conditions of Equilibrium when the Lever is Bent or Curved 76
135
Conditions of Equilibrium when any Number of Forces in the same Plane act on a Lever of any FormExamples II WHEEL AND AXLE
136
Definition of Wheel and Axle 86
137
Conditions of Equilibrium when two Forces act Tangentially to the Surface of the Wheel and Axle
138
Conditions of Equilibrium when there are three Forces
147
Conditions of Equilibrium when the Ends are fixed 91
148
Conditions of Equilibrium when the Ends are fixed and a third Force applied to a Running Knot
149
Conditions of Equilibrium when there is any number of Forces
150
Relations of the Forces when in Equilibrium
151
Relations of the Forces when the Ends are Fixed and the Forces Parallel
152
Relations of the Forces when the Ends are Fixed and the Forces are Weights
153
Point of Application of the Resultant
154
CatenaryExamples IV THE PULLEY
155
Definition of the PulleyFixed and Movable
156
Use of Fixed Pulley
157
Equilibrium in single Movable Pulley
158
Systems of Pulleys
159
Equilibrium in first System
160
Equilibrium in the second
161
Equilibrium in the thirdExamples
162
Velocity lost when the Sides are Infinite in Number 287 Direction and Intensity of an Impulse at each Angle to make a Body describe a Polygon with...
174
Direction and Intensity when the Polygon becomes a Circle 289 Definition of Centrifugal and Centripetal Force 290 Discussion of the Motion of a B...
180
Moon retained in its Orbit by Gravitation III PENDULUM 299 Definition of a Simple Pendulum 300 The Force by which it is urged in its Path
182
Times of Descent to the Center of Force equal when the Force varies as the Dis tance
183
Expression for the Time given 303 Discussion of the Vibrations of Pendulums 304 Pendulum used to determine the Figure of the Earth 305 Lengths ...
184
Conditions of Equilibrium in a Combination of Levers
186
Conditions of Equilibrium in the Endless Screw
187
Conditions of Equilibrium in any Combination of the Mechanical Powers
188
Conditions of Equilibrium in the Knee CHAPTER VII
189
Preliminary Considerations
190
Application to the Wheel and Axle
191
Application to Toothed Wheels
192
Application to Movable Pulley with Parallel Cords
193
Application to the first System of Pulleys
194
Application to the second System 116
195
Application to the third System
196
Application to the Inclined Plane
197
Application to the Wedge
198
Application to the Lever of any Form
199
Application to the single Movable Pulley with inclined Cords
200
Definition of FrictionKinds CHAPTER VIII
201
Measurement of Friction
202
Laws of Friction
203
Limits of the Ratio of the Power to the Weight in the Screw
206
94 Value of the Coefficient of Friction 124
207
DYNAMICS INTRODUCTION
208
In Dynamics Time an Element
209
Definition of Motion
210
Definition of Absolute Motion
211
Definition of Relative Motion
212
Definition of VelocityIts Measure
213
Definition of Variable VelocityIts Measure 15 Definition of Relative Velocity
214
CONSTRAINED MOTION OF A POINT
215
Velocity of a Point on a given Curve 355 Time of its Motion 356 The Reaction of the Curve
216
16 Definition of InertiaFirst Law of Motion 217 Definition of Center of Inertia
217
Definition of the Path of a Body
218
Definition of Free and Constrained Motion
219
Definition of an Impulsive Force
220
Definition of an Incessant Force
221
Definition of a Constant ForceIts Measure
222
Definition of a Variable ForceIts Measure
223
Definition of MomentumIts MeasureOf Living Force
224
Definition of a Moving ForceIts Measure
225
The second Law of Motion
226
The third Law of Motion CHAPTER I
227
Point to which the Force must be applied
228
General Equation of Uniform Motion
229
Relation of Spaces to Velocities when the Times are Equal
230
Relation of Spaces to the Times when the Velocities are Equal
231
Relation of Velocities to the Times when the Spaces are Equal
232
Measure of an Impulsive Force
233
The Velocity resulting from the Action of several Forces
234
Parallelogram of Velocities
235
Rectangular Composition and Resolution of Velocities
236
Relations of Space Time and Velocity of two Bodies moving in the same Straigh Line
237
Relations of Space Time and Velocity of two Bodies moving in the Circumference of a Circle
238
Examples CHAPTER II
239
Definition of Direct Central and Oblique Impact
240
Definition of ElasticityPerfectImperfectIts Modulus
241
Definition of Hard and Soft
242
Velocity of two Inelastic Bodies after Impact
243
Loss of Living Force in the Impact of Inelastic Bodies
244
Velocities of imperfectly Elastic Bodies after Impact
245
APPLICATION OF THE INTEGRAL CALCULUS TO THE DETERMINATION OF THE CEN TER OF GRAVITY
247
143
254
Pressure on any Side of a Vessel or immersed Surface 387 Pressure in a definite Direction 388 Resultant Pressure on the Interior Surface of a Vessel 3...
259
The Velocity and Space from the joint Action of a Projectile and Constant Force
260
The Velocity when the Space is given
261
Velocity lost and gained by the Action of a Constant Force when the Space
262
the same
263
Scholium on the Numerical Value of the Force of Gravity
264
Weights of the Constituents of a Mechanical Mixture 408 Hydrometer 1 Of Constant Weight 2 Of Constant Volume 409 Nicholsons Hydrometer
267
Examples CHAPTER IV
268
Time of Flight on a Horizontal Plane
269
Range on a Horizontal PlaneThe same for two Angles of Elevation
270
Greatest Height
271
Range and Time of Flight on an Inclined Plane and Coordinates of Point of Impact
272
Formula for Velocity of a Ball or Shell
273
Examples
274
Relations of Space Time and Velocity
275
Velocity down the Plane and its Height
276
Times down Inclined Planes of the same Height
277
Relations of Space Time and Velocity when projected up or down the Plane
278
Time of Descent down the Chords of a Circle 169
279
Straight Line of quickest Descent from a Point within a Circle to its Circumference
280
Straight Line of quickest Descent from a given Point to an Inclined Plane
281
Motion of two Bodies suspended by a Cord over a Fixed Pulley
282
Motion of two Bodies when the Inertia of the Pulley is considered II MOTION IN CIRCULAR ARCS
283
Velocity acquired down the Arc of a Circle
284
Velocity lost in passing from one Side of a Polygon to the next
285
Velocity of a Fluid from a small Orifice in the Bottom of a Vessel 421 Horizontal Range of a Spouting Fluid 422 Quantity of Discharge from a small ...
286
Discharge from a Triangular Aperture
287
Velocity of Efflux of an Elastic Fluid 428 Motion of Fluids in Long Pipes
289
173
291
General Method of determining the Discharge from small Orifices 430 General Method of determining the Time for a Vessel to empty itself 431 Gen...
293
HYDROSTATIC AND HYDRAULIC INSTRUMENTS 433 Mariottes Flask
295
Bramahs Press
296
Hydrostatic Bellows
298
Diving Bell
299
Sea Gage
300
Siphon
301
Common Pump
302
Common Pump Conditions of Failure 441 Air Pump
305
Condenser
306
Clepsydra
307

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accelerating force action angular velocity applied apsis axes axis axle beam body is projected body moves center of gravity centrifugal force circle circumference co-ordinates component concurring forces conditions of equilibrium constant force cord couple curve density descend determine displaced fluid distance earth elastic equal and opposite equation feet fixed point fluid force of gravity forces acting friction fulcrum given Hence horizontal impact inclined plane inertia length lever magnitude mass modulus of elasticity moment of inertia motion opposite directions orbit P₁ P₂ parallel forces particle perpendicular point of application polygon position pressure principle of virtual PROP pulley radius radius of gyration ratio reaction represent Resolving respectively resultant SCHOL sides space described square substituted surface tension tion triangle uniform v₁ versin vertical line vibration weight wheel

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Informació bibliogràfica

TítolAn Elementary Treatise on Mechanics, Embracing the Theory of Statics and Dynamics, and Its Application to Solids and Fluids
AutorAugustus William Smith
EditorHarper & Brothers, 1863
Original deUniversitat de Califòrnia
Digitalitzat el5 Juny 2007
  
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