Elementary Mechanics Including Hydrostatics and Pneumatics

Front Cover
Chambers, 1879 - Hydrostatics - 203 pages
 

Contents

b Curvilinear Motion 13 Change in direction of motion and curvature
22
The translation of an extended body
23
Definition of angular acceleration
25
Discussion of the equations separately
27
Discussion of the equations together
29
Return to the more general case
30
SECT PAGE 23 Polygon of motions
35
Composition of velocities
36
Composition of accelerations
37
ON QUANTITY OF MATTER AND QUANTITY OF MOTION 1 Motion of a Particle Inertia and Momentum 29 Motion of matter and quantity of ...
41
Quantity of matter measured by inertia
42
Definitions of density and mass
43
Unit of massPopular confusion of masses and weights
44
Definition of momentum
45
Definition of particle and rigid body composition of momenta
46
Notion of the quantity of motion of a rotating body
47
Moment of momentum or angular momentum
48
Definition of moment of inertia
49
ON FORCE AND MOTION Dynamics 1 On the speed of Motion as affected by Force or Force and Rectilinear Motion 41 The measure of a force
50
Unit of forceThe poundalThe dyne 5I 44 Illustration of the use of the fundamental equation F ma
52
Newtons second law of motion in Maxwells language
53
Composition of forces
54
SECT PAGE 50 Effect of force on an extended but rigid piece of matter
56
Or the angular acceleration is the ratio of the moment of the force to the moment of inertia of the body
57
Action of a force on a particle perpendicular to its motion
59
Determination of the magnitude of this force
61
ON FORCE AND MOTIONcontinued The Force of Gravitation 58 Gravity is a practically uniform force in mechanics
65
The weight of a body is independent of its material
66
Weight is proportional to mass the ratio being g
67
Modes of diluting gravityAtwoods machine
68
Measure of g by Atwoods machine
69
Experimental verification of the laws of falling bodies
70
Experimental verification of the velocity of falling bodies
73
Generality of the equation F ma
74
The composition of motions illustrated by falling bodies
75
And by Morins machine
76
On pendulums as illustrating the rotation of a rigid body
77
WORK AND ENERGY 74 Object of the chapter
79
Definition of energy
80
Enumeration of the forms of energy
81
Newtons third law of motion 55
82
When work is done energy is always transformed
85
Potential energy of strain illustrated by a
92
Examples of the parallelogram of forces
99
SECT PAGE 109 Case of two forces in a plane
106
Reason why position is important
107
Complete construction for finding the resultant and proof
108
Composition of Parallel Forces 113 Magnitude and direction of resultant of parallel forces
110
Position of the resultant of parallel forces IIO 115 Constructions for finding the resultant of two parallel forces III
113
A ladder by calculation
125
A stick rail and wall
126
A body sliding on an inclined plane
127
Stability of Equilibrium 132 Stable equilibrium and measures of stability
129
Unstable and neutral equilibrium
130
Equilibrium of things rolling on a plane
131
SECT PAGE 136 Object of a machinePrinciple of virtual velocities
133
Pulley inclined plane lever wheel and axle
134
Combinations of these machines
136
Definition of the term power
140
Compound pendulumCentre of oscillation and per cussion
141
Ballistic pendulum
143
PROPERTIES AND STATES of Matter 144 The effects of a force depend on the sort of matter it acts on
145
Solids may be elastic or plastic
146
Limits of elasticityTenacity
147
The three elements of any strain
148
LimpidityA nonviscous plastic body is called a fluid
149
Special mechanics required for special states of matter
150
Fluid friction depends on velocity and vanishes with it
152
Pressure of gravitating liquids
154
Pressure on the base of a cylindrical vessel full of liquid
155
Weight of a cubic unit or specific weight
156
Pressure on any area immersed under a liquid
157
Hydrostatic bellows 159
159
SECT PAGE 166 Meaning of intensity of pressure variation with depth
160
Centre of pressure
161
A solid immersed in a liquid displaces its own bulk
162
Loss of weight of a solid in a liquid
164
Floating of a light solid
165
Methods of obtaining the relative specific gravities of liquids
166
Determination of absolute specific weight of substances
168
Four methods of obtaining the specific gravity of solids
169
Hydrometers of both classes
170
Equilibrium of floating bodies as regards rotation
172
General conditions for stabilityMetacentre
173
ON THE PRESSURE OF THE ATMOSPHERE AND ON THE PROPERTIES OF GASES Pneumatics 180 Many properties of liquids are possessed al...
177
Intensity of pressure of the atmosphere
178
Modes of removing air from vesselsPumps
179
Modes of measuring the pressure of the airBarometers
181
Pressure gauges in general
183
Pressure on the piston of a pump
185
Modes of lowering waterPipette Siphon
186
Buoyant power of airSpecific weight of airBalloons
188
Properties peculiar to Gases 189 Law that product of pressure and volume is constant
189
Decrease of atmospheric pressure with elevation
191
Airpump
192
Mercury gauge for pump
193
Compressedair manometers
194

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Common terms and phrases

Popular passages

Page 199 - Prove that the algebraic sum of the moments of two concurrent forces about any point in their plane is equal to the moment of their resultant about the same point.
Page 55 - Reaction is always equal and opposite to action ; that is to say, the actions of two bodies upon each other are always equal and directly opposite.
Page 42 - Every body perseveres in its state of rest or of moving uniformly in a straight line, except in so far as it is made to change that state by external forces.
Page 199 - Two bodies start together from rest, and move in directions at right angles to each other. One moves uniformly with a velocity of 3 feet per second ; the other moves under the action of a constant force. Determine the acceleration due to this force if the bodies at the end of 4 seconds are 20 feet apart.
Page 166 - The density of a body is measured by its specific gravity, which represents the weight of a substance compared with the weight of an equal volume of water. It is a useful property in comparing relative weights of bodies.
Page 198 - Find the tension on a rope which draws a carriage of 8 tons weight up a smooth incline of 1 in 5, and causes an increase of velocity of 3 ft.
Page 2 - ... naturally adopted in what is to be studied without a teacher, so far from being a drawback in a school-manual, will, it is believed, be a positive advantage. Instead of a number of abrupt statements being presented, to be taken on trust and learned, as has been the usual method in school-teaching ; the subject is made, as far as possible, to unfold itself gradually, as if the pupil were discovering the principles himself, the chief function of the book being, to bring the materials before him,...
Page 53 - Tfte change of momentum of a body is numerically equal to the impulse which produces it, and is in the same direction," or momentum (mass x velocity) = impulse (force x time).
Page 200 - The value attached to each question is shown in brackets after the question. But a full and correct answer to an easy question will in all cases secure a larger number of marks than an incomplete or inexact answer to a more difficult one.

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