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ESSENTIALS O F
Applied
Physics
ESSENTIALS OF
Applied
Physics
A FOUNDATION
COURSE
FOR
TECHNICAL, INDUSTRIAL,
AND
ENGINEERING
STUDENTS
By
ROYAL M.
FRYE,
Ph.D.
Professor
of
Physics,
Boston
University
NEW YORK

P R E N
T I
C
E
-
H
A
L
L
,
INC.
1947
COPYRIGHT, 1947,
BY
PRENTICE-HALL,
INC.
70
FIFTH
AVENUE,
NEW
YORK
ALL
RIGHTS RESERVED.
NO
PART
OF
THIS
BOOK
MAY
BE REPRODUCED IN

ANY
FORM,
BY
MIMEO-
GRAPH
OR
ANY
OTHER
MEANS,
WITHOUT
PER-
MISSION IN WRITING
FROM
THE PUBLISHERS.
PRINTED
IN
THE
UNITED
STATES
Of
AMERICA
Preface
Physics
is a
prerequisite
for
courses
in
the
curriculum of

junior
colleges,
evening engineering
schools,
technical
institutes,
and
advanced
trade
schools,
owing
to the
fundamental
position
of
the
subject
in
all branches of
engineering
work.
This
book is one of
a
series
of
applied
science
textbooks
designed

to meet the
needs of
schools
where
a more
concise course is
given
than is
found
in
the
average college
physics
textbook,
and where
numerous
topics
not
found
in
a
preparatory
course
in
physics
are
essential.
The
orthodox
arrangement

of, first, mechanics,
then
sound, heat,
electricity,
and
light
is followed.
Numerous illustrative
problems
are
completely
worked
out.
A
summary
of the
irreducible
minimum
of
algebra,
geometry,
and
trigonometry
necessary
for
a
clear
under-
standing
of

physics
is
included
in
the
appendices.
Modern
viewpoints
on
light
have
been
employed,
while
at the
same
time the full
advantage
of the
wave
theory
of
light
has been
retained. The electron current
is
used
exclusively,
rather
than the

conventional
positive
current. The
practical
electrical
units
are used
instead
of the two
c.g.s.
electrical
systems
of
units. As
preparation
for
this,
the
kilogram-meter-second
system,
as
well as
the
English
system
of
units,
is used
in
mechanics. Likewise

the
kilogram-calorie
is used instead
of
the
gram-calorie.
This
work is
the
outgrowth
of
the
author's
experience
in
teaching
engineering
physics
to
many groups
of
students
in
evening engi-
neering
schools.
The
material was
developed
and

tested
in
the
class
room over a
period
of
many years.
It has
proven
effective
for
students
whose
needs for
practical
and
applied
knowledge
of
mechanics,
heat,
light,
and
electricity
were
paramount.
ACKNOWLED9MENTS
The
pen

sketches
at the heads of
the
chapters
and some of
those
in
the
body
of
the
text are
the
contributions
of
Louise
A.
Frye.
The
diagrams,
in
addition
to
many
of the
pen
sketches,
were done
by
Ralph

E.
Wellings.
A
great many
of the
illustrative
problems,
as
vi
PREFACE
well as
the
index,
were
prepared
by Virginia
M.
Brigham,
who
also
typed
the
manuscript.
The author is indebted to
Robert E.
Hodgdon
for
numerous
suggestions
made

during
the
course of
many years
7
association
in
the
teaching
of
the
physics
of
engineering.
It
is
impossible
for the author to make
adequate
acknowledge-
ment
to a
long
line of
predecessors
in
the
field of
physics
to whom

he
is
indebted.
ROYAL
M. FRYE
Boston
Contents
CHAPTER
PACE
PREFACE
V
1.
INTRODUCTION
1
Why study
physics?
What
is
the
territory
of
physics?
Why
is
physics
the
basis of all
engineering
training?
Physical

facts.
Physical
theories.
Units.
2.
NEWTON'S
LAWS
6
Historical.
Newton's first law.
Technical
terms. Newton's
second law.
Newton's third
law.
Examples
of
forces
which
do
and do not
illustrate
Newton's third
law. Newton's
law
of
gravi-
tation.
How the
law

was discovered.
3.
FORCE;
WORK;
ENERGY;
POWER
14
Forces.
Work.
Energy;
Conservation
of
energy.
Illustrations
of
energy.
Potential
energy.
Kinetic
energy.
Power.
Units
of
energy.
4.
EFFICIENCY;
MECHANICAL
ADVANTAGE;
COEF-
FICIENT OF

FRICTION;
SIMPLE
MACHINES

23
Efficiency.
Mechanical
advantage.
Coefficient
of
friction.
Simple
machines;
compound
machines.
The lever.
The
pulley.
The inclined
plane.
The
jackscrew.
The
hydraulic
press.
Pres-
sure. Pressure
energy.
5. FLUIDS
36

Boyle's
law.
Density
and
specific
gravity.
Pascal's
principle.
Hydrostatic
pressure.
Buoyant
force;
Archimedes'
principle.
,
Determination of
specific gravity.
Bernoulli's
principle.
'
6.
ELASTICITY
45
Elasticity.
Stress.
Strain.
Modulus
of
elasticity.
Hooke's

law.
Bulk modulus. Shear
modulus.
Bending
of
beams;
twisting
of
rods.
Ultimate
strength.
7,
VECTORS
53
Scalars and
vectors.
The
triangle
method
of
adding
vectors.
The
parallelogram
method
of
adding
vectors.
Resolution
of

forces
into
components.
Properties
of certain
triangles.
vii
viii
CONTENTS
CHAPTER
PACE
8.
MOMENT
OF
FORCE;
CENTER OF
GRAVITY

64
Translatory
versus
rotatory
motion. Causes
of
motion.
Moment
of
force.
Equilibrium.
Rules for

solving
an
equilibrium
problem.
Center
of
gravity.
9. ACCELERATION
73
More
general
conditions. Acceleration.
Uniform
acceleration.
The
two
fundamental
equations.
Graphical
representation.
Derived
equations.
Summary
of
equations.
The
acceleration of
gravity.
Hints
concerning

the
solution of
problems
involving
uniform
acceleration.
10.
PROJECTILES;
CENTRIPETAL
ACCELERATION .
.
83
Velocities
and
accelerations are
vector
quantities.
Projectiles.
A
simple
'projectile
problem.
A
more
general
projectile problem.
Centripetal
acceleration.
11.
NEWTON'S

SECOND
LAW
90
The
cause
of acceleration. Newton's second law.
Formulation
of
Newton's
second
law. Mass.
Inertia.
Engineering
units
and
absolute
units.
Systems
of
units.
Kinetic
energy.
12.
ANGULAR
ACCELERATION;
GYROSCOPE
103
Units
of
angle.

Angular speed.
Rotatory
motion.
Angular
velocity.
Equations
of
angular
acceleration.
Relations
between
linear
magnitudes
on
the
circumference and
the
corresponding
angular
magnitudes
at
the center.
The
gyroscope.
13.
DYNAMICS
OF ROTATION
Ill
Moment
of

inertia. Derivation
of
formula of moment of
inertia.
Units
of
moment of inertia. Work and
energy
of
rotation.
Moment
of
inertia about
axis other
than center of
gravity.
14. CONSERVATION
LAWS
119
General
survey
of
the
field
of
mechanics.
Impulse
and
momen-
tum.

Conservation
of momentum. Conservation
of
angular
momentum.
Illustrations.
Variation of
mass with
speed.
"Law
of
conservation
of mass"
no
longer
held
to
be true.
Conservation
of
energy.
15.
SIMPLE
HARMONIC
MOTION;
SIMPLE
PENDULUM;
'
COMPOUND
PENDULUM

126
Radial
acceleration.
Simple
harmonic motion. The
velocity
in
simple
harmonic motion. The acceleration
in
simple
harmonic
motion. Technical
terms associated
with
simple
harmonic
motion.
Force
in
simple
harmonic motion. The
simple
pendulum.
The
physical
or
compound
pendulum.
Derivation of

fundamental
equation
of the
compound
pendulum.
Use
of
compound
pendu-
lum
equation
to
measure moments
of
inertia.
Energy
of a
body
executing
simple
harmonic motion.
CONTENTS
ix
CHAPTER
PAGE
16. PROPERTIES
OF WAVES
139
Essential
characteristics

of
a wave
transmitting
medium.
Trans-
verse waves.
Longitudinal
waves.
Technical terms.
Reflection.
Refraction.
Diffraction. Interference.
Polarization.
Stationary
waves.
17.
SOUND
148
Definitions.
No sound
in
a
vacuum.
Speed
of
sound.
Depen-
dence
of
speed

of
sound on
temperature.
Pitch, loudness,
and
quality.
Harmonics.
The
Doppler
effect. Reflection
of
sound.
Sound
represents
energy.
Time
of reverberation.
Diffraction
of
sound. Interference
of
sound. Kundt's tube.
Organ
pipes.
Violin
strings.
18.
HEAT AND TEMPERATURE:
THE
TWO

LAWS OF
THERMODYNAMICS
161
Heat
as a form
of
energy.
Theoretical
basis of
temperature.
Conversion
of
energy
of
motion
into
heat.
Orderly
motion
tends
to
become
chaotic,
but chaotic motion does
not
tend to
become
orderly.
Distinction between
heat

and
temperature. Properties
that
depend
on
temperature. Temperature
scales. How
to
change
from
one scale to another.
The
first
two
laws
of
thermo-
dynamics.
Generalization
of
the second
law.
Entropy; efficiency
of a heat
engine.
19.
HEAT
TRANSFER
170
Three

general
methods
of
heat transfer.
Conduction;
Com-
putation
of transfer
of
heat
by
conduction.
Numerical
values
of
heat conductivities.
More
complicated
cases.
Convection.
Radiation.
Computation
of
transfer
of
heat
by
radiation.
An
illustration

of heat
insulation.
Perfect reflectors and
perfect
absorbers.
Thermal
equilibrium.
20. EXPANSION 178
Linear
expansion
of
solids.
Coefficients of
linear
expansion.
Balance
wheel on
a watch. Volume
expansion
of
solids
and
liquids.
Volume
expansion
of
gases.
21.
CALORIMETRY
184

Measurement
of
heat.
Definition
of
specific
heat.
States
of
matter.
Energy
is
required
to
separate
molecules.
The
triple
point
diagram.
Artificial
refrigeration.
Heat
of
vaporization.
Heat
of fusion.
22. MAGNETISM
192
Elemetary

facts
of
magnetism.
The
underlying
theory.
The
earth
as a
magnet.
Magnetic
lines of force.
Quantitative
aspects
of
magnetism.
Demagnetization.
Additional evidence of
the
identification
of
magnetism
with
arrangement
of
elementary
magnets.
Magnetism
not
confined

to
iron.
x
CONTENTS
CHAPTER
PAGE
23.
STATIC
ELECTRICITY 202
How atoms
are
put
together.
Conductors
and insulators. Static
electricity.
Coulomb's
electrostatic law.
Condensers;
capaci-
tance.
Voltage.
Comparison
of
magnetic
and electrostatic effects.
24.
ELECTRICITY
IN
MOTION;

HEATING
EFFECT .
.
210
Electric
currents.
Drift
speed
of
the electrons
versus
signal
speed.
Electromotive force. Ohm's
law.
Distinction between
electro-
motive force and
voltage. Resistivity.
Heat
produced by
an
electric
current. Hot wire
ammeters.
Electric
light.
Electric
power.
Thermoelectricity.

Some
practical
aspects
of an
electric
circuit.
25. VOLTAIC
AND
ELECTROLYTIC
CELLS;
SIMPLE
CIRCUITS
221
Voltaic
cells.
Dry
cells.
Storage
batteries.
Chemical
effect of
the
electric
current.
Hill
diagram.
Series and
parallel
circuits.
Cells

in
parallel
and
in series.
26.
MAGNETISM
AND THE
ELECTRIC
CURRENT
. .
231
Some
of the
effects
of
an electric current are
not
inside
the
wire.
Magnetic
fields around a current
in a wire.
The
electromagnet.
The
electric bell.
Comparison
of
fields

produced
by
currents
and
by
magnet
poles.
Flux
density.
Flux. Dimensions.
Effect
of a
magnetic
field
on a
current.
Comparison
of forces
exerted
by
a
magnetic
field on
poles
and currents.
Motors
and meters.
In-
duced
electromotive

force. Induction
coil;
transformer.
In-
ductance.
Lenz's
law.
27. ALTERNATING
CURRENTS
249
Qualitative
description
of
an
alternating
current.
Mechanical
analogies.
Effect
of
resistance
alone. Effect
of
inductance
alone.
Effect
of
capacitance
alone.
The

joint
effect of
resistance,
in-
ductance,
and
capacitance.
The
rotating
vector
diagram.
The
alternating
current
equation.
Resonance. Power.
Alternating
current
meters.
Parallel circuits.
28.
RADIO;
RADAR
260
Speed
of transmission
of
a
telephone
message

versus
speed
of
sound.
Electromagnetic
waves. Four
reasons
why
radio at
one
time
seemed
impossible.
Amplification by
means of
the
radio
tube.
Oscillation
produced
by
the
radio
tube.
Modulation
pro-
duced
by
the radio
tube.

Rectification
produced by
the
radio
tube.
Alternating
current radio
sets.
Electronics,
Radar.
Radar
in
war.
Radar
in
peace.
CONTENTS
xl
CHAPTER
PAGE
29.
PHOTOMETRY;
REFLECTION
AND REFRACTION
OF
LIGHT
271
Brief
history
of

the
theory
of
light.
The
"wave
mechanics"
theory
of
the
nature of
light. Meaning
of
"frequency"
and
"wave
length"
in
photon
theory. Speed
of
light.
Electromagnetic
radiation.
Units of
length.
Photometry.
Reflection
of
light.

Images.
Curved
mirrors. Refraction
of
light.
30.
LENSES;
MISCELLANEOUS
PROPERTIES
OF LIGHT
.
283
Lenses.
Formation of
a real
image
by
a
converging
lens.
Alge-
braic
relationships.
Formation
of
virtual
images. Dispersion
by
refraction.
Diffraction

and
interference.
Dispersion
by
dif-
fraction.
Measurement
of "wave
lengths."
Spectra.
Polarization
of
light.
APPENDIX 1:
Common
physical
constants
and conversion
factors
293
APPENDIX 2:
Significant
figures
and
computation
rules .
. 295
APPENDIX
3:
Abbreviated

multiplication
and
division
. .
299
APPENDIX 4:
Summary
of essentials
of
algebra

301
APPENDIX
5:
Geometrical
propositions
essential to this
book
. 304
APPENDIX
6:
Definition of sine and
cosine;
sine
law,
cosine law
305
APPENDIX 7:
Table of sines and
cosines

307
APPENDIX 8:
Three-place logarithm
table
308
APPENDIX 9:
The
two
fundamental
theories
of
physics
.
.311
APPENDIX
10:
List of
symbols
used
in
this
book
313
INDEX
315
ESSENTIALS
O
F
Applied

Physics
CHAPTER
I
Introduction
*-2^
1-1.
Why
Study
Physics?
By
far the
larger
group
of
subjects
in
the
curriculum
of
the
average
school is that
containing
history,
psychology,
biology,
sociology, languages,
and
philosophy,

which
de-
pend
for their
importance
on their
direct
relations to
living,
intelli-
gent
beings.
The smaller
group
contains,
for
example,
physics,
chem-
istry,
astronomy,
and
geology,
all
of which
deal
with
inanimate
nature;
we

study
these
either
out of
a
sheer
desire
for
knowledge
for
its own
sake,
or be-
cause
of
possible
applications
of
this
informa-
tion
in
our
daily
lives.
Mathematics
occupies
something
of
a middle

position;
it consists
of
a
set
of rules in
accordance with which a
series
of
operations
are
performed,
but
in
this
case
it
is we
who
devise the rules. All
we
ask
of
these rules is
consistency.
Most
of
us
hope
that the

mathematical
rules
will
also be
use-
fill
(and
it
is true
that
they
usually
are)
;
yet
there
is
gossip
to the
effect
that
certain
mathematicians
have been
guilty
of
praying
that
no
practical

use
would
ever be
found for their
particular
creations.
^
2
INTRODUCTION
[1-2
But
mathematics
is
a
subject
that
requires
rigorous
concentration
for
its
mastery,
and
therefore
is not
overpopular.
Much
of
physics
is

hidden
from
the nonmathematician.
The
demand
for
physicists
considerably
exceeds
the
supply.
This
book
contains
a
minimum
of
mathematics.
It is written for
those
who
quite
frankly
intend
to
use
physics
as
a
prerequisite

for
engineering.
1-2.
What
Is the
Territory
of
Physics?
Pure
physics
con-
cerns
itself
with
things
that our
senses
reveal to us :
heat,
electricity,
natural
forces,
forms
of
energy,
properties
of
matter,
sound,
and

light;
we also
find
it convenient to
add to
this
list
all
sorts of
devices
made
by
man
which
depend
on a
knowledge
of natural
phenomena.
By
means
of
the
telescope
and
spectroscope,
the
sense
of
sight

is
extended
to
such enormous
distances that we are
enabled to
tell
the
sizes,
chemical
constitutions,
temperatures,
physical
states,
amount,
and
direction
of
motion of
objects
completely
invisible
to
the
naked
eye.
We
also
have
knowledge

of
particles
so small
that
they
are
beyond
the
power
of
being
made
visible
by
the
best
optical
or
electron
microscope
that
man has
yet
invented.
And the science
of
physics
is
still
growing.

We
continue
to observe facts
about nature.
We
are
still
inventing
theories
to
fit these facts. The
theories often lead
us to
suspect
the
existence
of
new facts as
yet
undiscovered. Then
we
carry
out
ex-
periments
in
search
of
these
supposed

new facts.
Sometimes we
discover
that the "facts"
do
not
exist,
and
as
a
result we
have to
throw
away
the
theory
which
involved
them.
If
on
the
other
hand
the
facts
are
there,
our
respect

for
the
theory
increases.
Physics
is
a
study of
the
facts
of
the
nonliving part of
nature
together
with those
interconnecting
theories
that
so
far
have stood
the
test
of
experiment.
1-3.
Why
Is
Physics

the Basis
of
All
Engineering
Training?
Engineering
schools
train students to be civil
engineers,
mechanical
engineers, metallurgical
engineers,
electrical
engineers,
illuminating
engineers, biological
engineers,
chemical
engineers,
sanitary
engi-
neers,
marine
engineers,
torpedo
engineers,
public
health
engineers,
naval

engineers,
and
aeronautical
engineers.
Almost
anyone reading
this
list
will
take
pleasure
in
adding
to it. But all
of
these
branches
of
engineering grow
directly
from the
subdivisions of
physics
itself
or
from
the
closely
associated sciences of
chemistry

and
biology.
Phys-
ics itself includes at
present
the
subjects
of
mechanics, sound,
heat,
magnetism,
electricity,
and
light.
Formerly
all
the
natural
sciences
combined,
including
physics, chemistry,
astronomy,
and
biology,
were
considered
to
be
within

the
capabilities
of
single
individuals to
master.
But as
these
sciences
grew
in
scope,
it
became
increasingly
1-4]
INTRODUCTION
3
difficult
for
any
one man to
master them
all,
or even
any
one
of them.
Today
it is the

business
of
chemistry
to
study
several
hundred
thou-
sand
compounds;
of
astronomy,
to
catalogue
nearly
100 billion
stars
in
our
own
galaxy
along
with
a
billion other
galaxies;
and of
biology,
to
classify

hundreds
of
thousands
of
zoological
and botanical
species.
Yet
in
these
three sciences
the
relationships
between
entities
are far
more
important
than
the
large
numbers of
entities involved.
And
even as
chemistry
and
astronomy
are
already

considered
as
separate
sciences,
it
may
well
be that other
portions
will
in
the future
be
de-
tached from
physics,
but
physics
will
still
remain
basic,
not
only
to
the
other
"physical
sciences/'
but

to
all
branches of
engineering.
1-4.
Physical
Facts. The
two
important
things
in
our uni-
verse as
we know
it are
energy
and
intelligence.
The latter
we
leave
to
psychologists,
biologists,
and
philosophers,
and confine our atten-
tion
to
the

former.
At
a
suitable
point,
we shall define
energy,
and
later
we shall
see that
one
of
the
manifestations
of
energy
is matter. For
the
present,
however,
we
shall
find
it
convenient
to
take over
a few
terms

from
everyday
life such
as time and
space,
and
by
means
of
these,
define
more
terms for
technical use.
Once
we have defined a
technical
term,
we
shall be
care-
ful
not
to
use that
word
in
any
other
way,

and
physical
facts of a
general type
(often
called
laws
or
principles)
will
be stated
using
these technical
terms.
Although
matter
is sometimes
defined
as
that
which
occupies
space,
we must remember that a vacuum
(absence
of
matter)
also
occupies
space,

and
furthermore
that
a
vacuum has
pronounced
physical
properties.
Consequently
it
will
be better at
present
to think
of matter as
the
substance
of which
physical
bodies
are
made,
and
reserve
until
later
a
discussion
of
the

method
of
measuring
quantity
of
matter,
or
mass. We
may
temporarily
think
of
energy
as
a
storehouse out
of which
comes
the
ability
to
change
either the
shape
or the state of
motion of
matter.
A
physical
fact

may
be described as
something
that
actually
can
be
demonstrated
in
the
laboratory
to a
high degree
of
precision
(although
never to a
precision
of one hundred
per
cent,
for both
practical
and
theoretical
reasons).
We
shall
not
be

surprised
at
the
necessity
of
discarding
a
theory
occasionally
for
a
better
one,
but
we
do
expect
our
physical
facts,
once
established,
to remain
physical
facts.
1-5.
Physical
Theories.
A
large

collection
of isolated
physical
facts
without
any interconnecting theory
would
be hard
to
keep
in
4
INTRODUCTION
[1-6
mind,
and
for
this reason would lose
much of
its
usefulness
to
the
engineer.
The
mathematical
network,
as
self-consistent as
geometry,

which
has
been
developed slowly
over the
years,
and which
weaves
together
the vast accumulation
of
physical
data
into one
integrated
whole,
is referred to
as
physical theory.
Thus
we talk of the
theory
of
elasticity,
electrical
theory,
theory
of
light;
or

even
in
connection
with mechanical devices
we
are
apt
to
ask,
"What
is
the
theory
back
of
that
machine?"
The
importance
of
theory,
however,
increases as
the
student becomes
more
advanced.
In
this
elementary

treatment
of
physics,
we
shall
be much more
concerned with
facts than
with
theory.
1-6. Units. In
concluding
this
chapter,
it
is
proper
to
say
a
few words
about units. Outside
of the
field of
electricity,
the
engineer
finds
that he
can

get
along very
well
with
just
three fundamental
units:
a
unit of
time,
say
the
second;
a unit of
distance,
such
as the
foot
or the meter
\
and
a
unit
of
force,
for
example
the
pound
or the

newton.
In
defining
the
second,
it is
customary
to divide
the
length
of
the
average
"solar
day"
into
86,400
equal
parts
(24
X
60
X
60).
The
second
is
common to both the
English
and

metric
systems.
As a
basis for
the
units
of
the metric
system,
there are
carefully
preserved
two
pieces
of
metal
at
as
nearly
as
possible
constant conditions.
The
distance
between two fine scratches on one
of them
is
taken
by
the

scientific
world as the definition of the
meter,
and
the mass of the
other
piece
of
metal defines the
kilogram.
A
newton is
somewhat
smaller
than
the
kilogram;
a
kilogram
weighs
about
9.8 newtons.
In
London there
exist
similarly
the standard
yard
and the
standard

pound.
Such units as
the
foot
per
second,
the
foot-pound,
and
so
on
are
obvious combinations of
these fundamental
units.
There
are
3.2808 feet
in a
meter,
and 2.2046
pounds
in a
kilogram.
In the
United
States,
we are
legally
on the

metric
system;
our
foot
is
defined
1200 ,
4
,
,
1
r i -i
as
^r^r
of a
meter,
and our
pound
as
TT-^TZTO
*
a
kilogram.
SUMMARY OF
CHAPTER
1
Technical
Terms
Defined
Physics.

Physics
is
a
study
of
the facts
of
inanimate
nature
together
with
the theories that thus far
have
stood
the test of
experiment.
Fact.
Facts,
in
physics,
are the direct
result
of
physical
experimentation
and observation.
Theory.
An
assumption
or

system
of
assumptions
not
only
mutually
con-
sistent,
but also consistent
with
all known facts.
INTRODUCTION
5
Physical
Unit. An
arbitrary
portion
of
a
physical
quantity,
of
a con-
venient
size,
and established
by
general
agreement.
Second.

5455
of
a
mean solar
day.
Meter.
Distance
at
the
temperature
of
melting
ice between
two
scratches
on a
platinum-iridium
bar
preserved
at
the
International
Bureau
of
Weights
and
Measures,
Paris,
France.
Yard. In

England,
the distance between
two
scratches
on a
standard bar
preserved
at
London.
In
the United
States
^25
of
a
meter. This
makes
one meter
equal
to
3.2808
feet.
Kilogram.
The
amount
of matter
in
a certain
platinum
cylinder

also
preserved
at
Paris,
France.
Newton. A unit of force
or
weight
which will
be
found to
tie
in
with
both
the metric
system
and the
practical system
of electrical units.
One
kilogram
weighs
about 9.8 newtons.
Pound.
The
United
States
pound
is

defined
by
law as
Tr^Trrr^
of
a

r J
2.204622
kilogram.
EXERCISES
AND
PROBLEMS
1-1. Name
ten
practical
illustrations
of
physical principles,
so
dis-
tributed that at least
one
application
will be
drawn from
each
of
the
five

branches
of
physics.
1-2. As an
illustration of the
terms
fact
and
theory,
state a
nonphysical
fact;
also
a
nonphysical
theory.
1-3.
Mention several
important
industries
of
today
which owe their
existence
entirely
to theories
developed during
the
previous century.
1-4. From

the data
in
section
1-6,
find* the
number
of
inches
in
a
meter;
also
the
number
of
kilograms
in
an ounce.
1-5. How
many
newtons are
there
in a
pound?
1-6. If
there
are
62.4
pounds
of

water
in
a
cubic
foot,
find the
number of
kilograms
of
water
in
a cubic meter.
CHAPTER 2
Newton's
Laws
2-1. Historical. One
of
the
earliest books on
physics
was
written
by
Aristotle
(385-322
B.C.)-
He
was
a
remarkable

man,
and
is
credited with
having
possessed
the
most
encyclopedic
mind in
all
history.
However,
Aristotle
lived before the
experimental era,
and
for
this reason he made
many
statements
that
could
have
been
dis-
proved easily
by simple
trial.
One

of
these
statements,
concerning
falling weights,
was not shown
to be false until
the
time of
Galileo
(1564r-1642).
Galileo
made
numerous
scientific
discoveries,
but
due
to
ecclesiastical
and civil
opposition,
he
never
reached
the
point
of
generalizing
his

findings;
on
the
contrary,
he
was
forced
to
renounce
some
of
them as
false! Sir
Isaac
Newton
(1642-1727)
was
born
in
England
the
year
Galileo
died
in
Italy.
He too
had
a
most

unusual
mind,
and
an
almost
uncanny
sense
regarding
physical
phenomena.
Moreover,
he had
the
advantage
of
living
at a
time
when it
had be-
come
customary
to
perform
scientific
experiments
before
drawing
physical
conclusions.

Newton
published
a
book in
1687
(written
in
Latin,
which was
then a
universal
scientific
language),
in
which
he
summarized
Galileo's work in
the form
of
three
laws
that are
known
to
this
day
as
Newton's
first,

second,
and
third
laws
respectively.
These laws
are
the
basis
of
what is
known
as
Newtonian
mechanics.
They
hold for
distances
somewhat
greater
than
those
between atoms
up
to
astronomical
distances.
(Advanced
students will
learn

that,
for
atomic
dimensions,
we
have
to
use
what
is
known
as
quantum
mechanics,
a
form
of
mechanics
which
automatically
becomes
New-
6
2-2]
NEWTON'S LAWS
7
Ionian
mechanics with
increased
distances).

Therefore,
for
the
pur-
poses
of
the
engineer,
there
is no need
of
questioning
the
exactness
of
Newton's
laws.
2-2. Newton's
First
Law.
If
we
should
pass by
a
store
win-
dow
in which
a

croquet
ball was
busily engaged
in
rolling
about
in
such a
way
as
to
describe
figure
eights,
our intuition
would tell
us,
"Something
is
wrong;
there
is
more
here
than
meets
the
eye!"
We
all

have
in
mind
a
notion
of
what
an
object
ought
to
do
when
left
to
itself,
and
it is
not
to
describe
figure
eights.
If
we start
an
object
sliding
along
a

smooth
sur-
face,
then leave
it
to
itself,
the
object
will
move
more and
more
slowly
in a
straight
line
and
finally
come
to
rest.
If
we
repeat
the
experi-
ment on
a
still

smoother
surface,
say
some
glare
ice,
the
object
will
take
much
longer
to
come to
rest,
and
still
continue to
travel
along
a
straight
line.
But
it is
not correct
in
either of
these two cases
to

say
that
the
object
is left
to itself. In
both
cases,
forces of
friction
were
slowing
down the
moving
object.
If
there
were
actually
zero
friction,
the
object
would
never
come to
rest when "left to itself."
This
statement
constitutes

a
part
of
New-
ton's first law. A
more
complete
statement
is
as
follows: A
body
left
to
itself
will remain at
rest
if
it is
already
at
rest,
and
if
it
is
already
in
motion,
it

will
continue in motion
with
uniform
velocity
in a
straight
line.
Newton's first
law
represents
such an idealization
that we
never
encounter
a
pure
case of
it
in
practice.
No
object
that
we have
ever
met
can be
said to be
"left

to itself."
Gravitation
is
always present
to
pull objects
toward
the
earth
;
friction
or
air
resistance is
always
acting
to
slow
down
the motion of
bodies.
In
fact,
it would even
be
difficult
to
say just
what
we mean

by
"at rest."
Any
table
in
front
of
us
which
appears
to
be at
rest
is
moving
about
700
miles
per
hour
due to
the rotation
of
the
earth,
about
66,000
miles
per
hour

due to
the
earth's orbital motion about the
sun,
and
faster
yet
on
account
of
galactic
rotation.
In
general
we consider
it
a
sufficiently good
illustration of
Newton's first
law
if we
find ourselves
nearly
plunging
over
the
seat
in
front

of
us
on a
trolley
when the
motorman
suddenly
applies
the brakes. We were
in motion
and
physical
law does
its
best
to
keep
us
in
motion! Another
illustration
is
the
possibility
of
re-
moving
a book
from under
a

pile
of books
by
means
of
a
quick
jerk.
The
books
on
top
were at
rest
and
they
therefore
tend
to remain
so.