Applied Mechanics, Volume 1

Couverture
John Wiley, 1913
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Table des matières

Problems Involving Balanced Systems of Forces Acting through the Same Point and Lying in the Same Plane 24 1
24
General Condition of Equilibrium of a System of Forces
29
Equilibrium of Two Couples
30
Resultant of Any Number of Couples Acting in the Same Plane
31
Resultant of a Single Force and a Couple
32
Resolution of a Single Force into an Equal and Parallel Force and a Couple
33
Conditions of Equilibrium of a System of Parallel Forces
34
Resultant of any System of Forces Acting at Different Points and Situated in the Same Plane
37
Conditions of Equilibrium of any System of Forces Acting in the Same Plane
39
Problems Involving Systems of Forces Acting in the Same Plane but not through the Same Point
40
Method of Sections
55
Statically Indeterminate Cases
59
3 FORCES WHOSE LINES OF ACTION ARE NOT CONFINED TO A SINGLE PLANE 57 Resolution of a Force into Components in Three Directi...
60
Composition of Forces Applied at the Same Point
61
Conditions of Equilibrium for any System of Forces Acting at a Point
62
Moment of a Force with Respect to any Line
67
A Condition of Equilibrium for any System of Forces Acting through a Point
68
Characteristics of a Couple
69
Compositions of Two Couples in Planes Inclined to Each Other
70
Composition of Any System of Couples
71
Composition of Parallel Forces not Confined to the Same Plane
72
Conditions of Equilibrium of any System of Parallel Forces
74
Conditions of Equilibrium of any System of Forces
77
DISTRIBUTED FORCES 74 Types of Distributed Forces
84
Resultant of a Distributed Force
85
Stress
88
Intensity of Stress
89
Uniform Stress
90
Problems Distributed Forces
91
Gravity
94
Problems Attraction at a Point
96
Determination of the Constant K
105
CHAPTER III
107
Center of Gravity of a Body
108
Center of Gravity of a Homogeneous Body
109
Center of Gravity of a Slender Rod of Uniform Section and Ma terial
110
ART PAGE 94 Center of Gravity of a Line
111
Problems Centers of Gravity of Lines
112
Center of Gravity of a Thin Plate of Uniform Thickness and Ma terial
113
Center of Gravity of a Plane Surface
114
Centers of Gravity of Surfaces not in the Same Plane
115
Pappuss Theorems
125
Centers of Gravity of Homogeneous Solids and Systems of Solids
126
Experimental Methods of Determining Centers of Gravity
130
CHAPTER IV
132
Units of Moments of Inertia of Areas
133
Radius of Gyration
134
Problems Deduction of Formulas for Moments of Inertia of Plane Areas
136
Summary of Formulas for Moments of Inertia of Areas
141
Method of Determining the Moments of Inertia of Areas by
142
Moments of Inertia of Structural Shapes
144
Moments of Inertia of Builtup Sections
146
Product of Inertia
148
Relation between Products of Inertia of Areas with Respect to Parallel Axes
149
Problems Products of Inertia
150
Product of Inertia of an Area with Respect to a Pair of Axes one of which is an Axis of Symmetry
153
Relations between the Moments and Products of Inertia of an Area about Different Pairs of Coördinate Axes Passing through the Same Point
155
Principal Moments of Inertia of Areas and Principal Axes
156
Axes of Symmetry of Areas are Principal Axes
157
ART PAGE 127 Ellipse of Inertia
158
Problems Moments of Inertia about Inclined Axes
160
Moment of Inertia of a Solid
162
Units of Moments of Inertia of Solids
163
Radius of Gyration of a Solid
164
Relations between Moments of Inertia of Solids about Parallel Axes
165
Problems Deduction of Formulas for Moments of Inertia of Homogeneous Solids
167
Summary of Formulas for Moments of Inertia of Solids
172
Method of Determining Moments of Inertia of Solids by Dividing into Finite Parts
173
Problems Moments of Inertia of Solids
174
Product of Inertia of a Solid
175
Resolution and Composition of Accelerations
191
Momentum
194
Moment of Momentum
195
Centripetal and Centrifugal Forces
196
Work and Energy
198
Motion of a Particle under the Action of the Force of Gravity
199
Motion of a Particle on a Frictionless Inclined Plane under the Action of Gravity
200
Motion of a Particle along a Curve under the Action of Gravity 201 а 156 Simple Circular Pendulum
203
Simple Cycloidal Pendulum
205
Harmonic Motion
207
Composition and Resolution of Simple Harmonic Motions
211
Problems Kinetics of the Particle
216
Work POWER AND ENERGY ART PAGE 162 Work
223
Work Done by a Rotating Force
225
Work Done by a System of Forces
227
Work Done by a Rotating Couple
229
Units of Work
231
Power
232
Units of Power
233
Power Diagram
234
Kinetic Energy of a System of Particles
236
Potential Energy
237
Conservative System
239
The Potential
242
Problems Work Energy Power
245
3 FRICTION 179 Sliding Friction
250
Laws of Sliding Friction
252
The Weight on the Inclined Plane
254
The Wedge
255
Axle Friction
256
Friction of an Axle Bearing at Two Elements
257
Friction of an Axle Bearing over a Surface
258
Pin Friction
260
Pivot Friction
261
Friction of Screw Threads
264
ction Cones and Friction Discs
265
Belt Friction
266
Rope Drives
270
Maximum Power which can be Transmitted by a Belt or Rope
272
Rolling Friction
273
Weight on Rollers
275
Roller Bearing
276
Mechanical Efficiency
278
4 KINETICS OF Rigid Bodies HAVING PLANE Motion ONLY 199 Motion of a Rigid Body
285
Translation of a Rigid Body a
286
ART PAGE 203 Kinetic Energy of a Body having a Motion of Translation
289
Momentum of a Body having a Motion of Translation
290
Angular Momentum
302
Kinetic Energy of a Rotating Body
303
Centripetal and Centrifugal Forces
304
Interchangeability of the Center of Percussion and the Center of Rotation
305
Center of Oscillation
306
Rotation and Translation Combined Instantaneous Axes
307
Momentum Due to Combined Translation and Rotation
315
Kinetic Energy Due to Translation and Rotation Combined
316
Problems Kinetics of Rigid Bodies
317
IMPACT 215 Impact or Collision
347
Direct Central Impact
348
Coefficient of Restitution
349
Kinetic Energy of the Colliding Bodies
350
Experimental Determination of the Coefficient of Restitution
351
Oblique Central Impact
352
Direct Eccentric Impact
353
Loss of Energy
354
Oblique Eccentric Impact
355
Examples of Direct Central Impact
356
Recoil of a Gun
357
Ballistic Pendulum
358
Problems Impact
360
Droits d'auteur

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Expressions et termes fréquents

Fréquemment cités

Page 3 - I. — Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by force to change that state.
Page 11 - If three forces acting at a point are in equilibrium they can be represented in magnitude and direction by the three sides of a triangle taken in order.
Page 3 - To every action there is always an equal and contrary reaction; or, the mutual actions of any two bodies are always equal and oppositely directed in the same straight line.
Page 20 - moment of a force" with respect to a point is the product of the force and the perpendicular distance from the given point to the line of action of the force.
Page 134 - Expressed in words, this equation states that the polar moment of inertia for an area, with respect to an axis perpendicular to its plane, is equal to the sum of the moments of inertia about any two mutually perpendicular axes in its plane that intersect on the polar axis.
Page 125 - ... solid thus generated is equal to the product of the revolving area and the path described by the center of gravity of the plane area during the revolution.
Page 18 - If three forces, acting at a point, be represented in magnitude and direction by the sides of a triangle taken in order, they will be in equilibrium.
Page 165 - Steiner. is true for bath a plane laminar body and a thin three-dimensional body, and states that the moment of inertia of a body about any axis is equal to its moment of inertia about a parallel axis through its...
Page 107 - Their points of application remain the same. 2°. Their relative magnitudes are unchanged. 3°. They remain parallel to each other. Hence, in finding the centre of a set of parallel forces, we may suppose the forces turned through...
Page 29 - The perpendicular distance between the lines of action of the two forces is called the arm, and the product of one of the forces and the arm is called the moment of the couple. A...

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