or -M=^ = ". Eq. 62
/ e\ ea
From this equationit is evident that,in order to determine M
by experiment,we must measure the four quantitiesin the righthand
member of the equation. As a stretchingforce it is often
most convenient to use the \yeightof a ma
The law of the Conservation of Energy expresses the fact that
the sum total of the energy in any isolated system remains the
same. This energy can change from one form to another, it
tends constantlyto become less and less available ; but, so far
as is kn
98. We shall see later that a body may be able to do work
in consequence of
1. Its position.
2. Its speed (angularor linear).
3. Its temperature.
4. Its electrical condition.
5. Its chemical composition.
The power of doing work is called energ
DISTINCTION BETWEEN SPEED AND VELOCITY
24. Speed represents merely the rapidityof motion, while
velocityrepresents rapidity,direction, and sense. Speed is
denned by a single number, while velocitydemands three
specificatio;nsnamely, amount, direction, and
Let us denote this acceleration by a, the change in velocityby
v Defining equation
: " for average ac- Eq. 11
tn " t\ celeration.
Acceleration,then, is simply the rate at which the particleis
gaining or losing velocity. This rate is not always con
conceptionsof kinematics, namely position,velocity,
and acceleration,we proceed to the study of two highly einsteinr-g
CASE I. Motion of a Particle along a StraightLine :
Direction of VelocityConstant; Speed Variable
36. If,in Fig. 20, the v
same time, it must contain as littleuseless material as possible.
In order to secure this latter result, the engineer must have
definite and quantitativeinformation concerning the elastic
propertiesof the steel to be used in the bridge; in particular,
that this motion can be accuratelydescribed (denned) in a
manner even simplerthan this.
The student frequentlyconfounds simpleharmonic with ciulr-ar
motion, and should, therefore, at this point,carefully
distinguishbetween these two motions. The actual mo
body too high a speed, he allowed the body to roll down a
smooth inclined plane of small slope.
But first he satisfied himself that all kinds of matter would
fall the same distance in the same time. One ball might be
made of copper, another of iron ; the
to the free side of the chain coming from the large
pulley,and if any link, say P, of this chain be dpilas-ced
through one circumference of the largerfixed
pulley,the work done by the force F will be F " 2 m-R.
During this same time the work done on the w
likewise the vertical component of the initial velocitywill enter
into the equationfor the vertical motion. But these are mtaert-s
which, like the resistance of the air,must be left for later
Problems on Gravitation
In consideringthe followingquest
3. In the case of a watch, compute the angularspeedsof the second hand
and the hour hand, respectively. . TT _, tr
4. What is the angular speed of a bicyclewheel making 30 revolutions
per minute? Ans. TT radians per second.
5. The front wh
partlyfrom the fact that the acceleration of any particleewhvaert,moving at any given instant in any path,however otours,tumay
always be resolved into two components, one along
the path,and one normal to the path ; and these two cneomnptosbelong
~. .,., Shearing stress
Rigidity modulus = n "
But this subjectis somewhat intricate,and must be left for
later study. Before leaving it,however, we merely remark
that the rigiditymodulus of any material measures its strength
mind that the sense of a force is, in
general,quiteas important a factor as its
amount, or its direction.
73. Very often the resultant of a given
system of forces is zero; in this case the
body acted upon is said to be in equilibrium.
That large branch of
appreciablythe static distribution. Nevertheless, the flux
of energy dependsupon the magnetic force as well. It may,
indeed,be representedin another way, w^ithoufcintroducintghe
magnetic force,but then the formula would not be sufficiently
This force of reaction in accelerated bodies is beautifullyitlraltues-d
by the followingexperiment: "
With a pieceof lightstringsupport an iron ball, from two
to four inches in diameter, as indicated in Fig. 41. To the
lower side of the ball attach a piec
fixed heightAB (Fig. 32). The body on reaching the foot of
the planeA F with a constant and
definite velocity,is allowed to roll
up a second incline of variable
slope. Galileo observed that as
the slope of the second plane
FIG. 32. " Galileo's experimenta
When such a pendulum is pulled aside through an angle 6
(Fig.47),the particleis urged back toward its positionof eliqbuir-ium
with an acceleration which may be easilycomputed as
follows : "
The simplependulum is representedby the line OB,
^2 ^lJ'i*iat any instant.
27. The numerical value of " (in Eq. 7) togetherwith the
direction and sense of the axis about which the rotation occurs
are the three specificatiownhsich describe any angularvelocity.
It is evident, then, that o
into the box of the wagon to see whether it contains a load
Imagine three balls,each six inches in diameter, each painted
black, one a rubber football,one a wooden ball from a bowling
alley,one an iron cannon ball. Imagine them all started irnogll
^ J^l"^'^!^ : W. H. PREECE, C.B.,F.R.S.
(Late Secretary of Telegraphs,G.P.O.),
DR. JOHN HOPKINSON, F.R.S.
(Past-Presidenotf the Institution of Electrical
PROF. W. E. AYRTON
(Past-Presidenotf tlie Institution of Electrical
LORD RAYLEIGH, F.R.S.
whose mass is 20 g. What is the pull on the stringwhen the bullet is
making 1 revolution per second? Ans. 8000 7r2dynes.
5. A locomotive whose mass is 100,000 kg. is rounding a curve of
400 m. radius at a speed of 10 m. per second. What is the force which
Imagine the particleat any time to be at the pointPt in
23. The direction of the velocitywill there be perpendicular
to the radius OPt. And the same is true at any other instant,
for in circular motion the straightline which represe
sun in one focus,
(ii)at such a speed that the line from the center of the sun
to the center of the planet sweeps out equal areas in equal
(iii)while the square of the year, measured in any unit of
time, bears to the cube of the planet'sdistance fr
Derived units are defined as those which depend for their value
upon the fundamental units. In like manner, the unit of aecracetil-on,
the unit of area, and the unit of volume are all derived
units. So are all the units employed in this text-book, except
the Tables are issued with each copy.
THE DISTRIBUTION OF ELECTRICITY. By Prof. GeorgeForbes,M.A
DEVELOPMENTS OF ELECTRICAL DISTIRIBUTION. By Prof. Geor^
Forbes, F.R.S. Is.
MAY'S POPULAR INSTRUCTOR FOR THE MANAGEMENT 0
ELECTRIC LIGHTING PLANT
exert? Ans. L = 180 x 106.
2. At one end of a board which is 20 ft. long is placed a stone iwengigh40 Ib. At the other end of the board is placed a stone weighing
90 Ib. Neglecting the weight of the board, find the point at which it
must be supportedin or
where f is a proportionalityconstant which is known as the
coefficient of friction for the two materials in question.
The followingtable will give some idea of the values which
f assumes in practice: "
A helpfulpointof view from which to regard the coeffi
evident that F1 = Fz. So that
the only advantage offered by
the fixed pulley is a change of
direction ; a pulldownward can
be transformed into a pull
112. When a pulley is arar-nged
as in Fig. 59, it is
evident that at any particula