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Forces of Nature
an you explain the difference between centrifugal and centripetal
force? Are you well versed in entropy and its effects? If your
knowledge needs a bit of dusting off, the Forces of Nature eBook
from Motion System Design is a thorough yet entertaining look at some of
the most important physical forces in the universe. From microgravity to
inertia, this handy eBook is designed to refresh you on the following topics:
Entropy, inertia, microgravity, and the four universal forces — gravity,
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Forces of Nature
table of contents
4
The four forces: Four fundamental forces appear to be
holding the Universe together: the electromagnetic force,
two nuclear forces, and gravity. They’re all caused by
matter’s absorption or emission of energy-carrying particles called
bosons.
8
Physical constants: These are numbers, so important
to engineering work, that you once committed to memory.
Let’s review.
10
Entropy: From the erosion of a grain
of sand off a cliff to the unbounded expansion of
the Universe, Nature tends towards disorder. This
tendency has a name — entropy. The phenomenon has specific
scientific meaning.
This arrangement also has relatively low
multiplicity — as there not many
permutations for which only two molecules
are found in the left side of the chamber.
isolate some of the more fundamental properties,
forces, and processes of nature, scientists create a
=
=
=
14
Microgravity: To peel away the cloak of gravity and
condition called “microgravity.”
18
Inertia: Matter tends to resist change. Around
=
2
FORCES of NATURE eBook
moving masses, inertia acts like a stabilizer, pushing
against any accelerating or decelerating force.
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utomationDirect announced the opening of the new
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campus of Northern Illinois University (NIU). As the field
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During the past few years, AutomationDirect has provided
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Technology. AutomationDirect has now cooperated with
the Department to help fund a well-equipped automation
laboratory. In return, the Department named the lab the
“AutomationDirect Automation Laboratory” and created the
AutomationDirect Professorship. The laboratory is designed
to support the Departmental Programmable Logic Controller
(PLC) course and the Automation course. The Programmable
Logic Controller (PLC) course teaches students basic and
advanced concepts and applications for PLC programming. In
addition, the students learn to integrate various components
with the PLC, such as sensors, switches, and output devices.
As a final project, student teams design automation systems
which sort parts, using the integration of vision, PLCs, sensors,
and pneumatics. This level of experimental interaction produces
Manufacturing Engineering Technology graduates who excel in
industry.
With AutomationDirect’s support, the school will have a
very strong laboratory facility in which the next generation of
manufacturing engineering technologists will be educated.
The Department of Technology has been the cornerstone of
technical education at Northern Illinois University for over 80
years. The department has evolved from vocational education
to an organization supporting the needs of industry and
the region. A component of the College of Engineering and
Engineering Technology, with approximately 1,500 students,
the Technology Department has over 400 students participating
in Electrical Engineering Technology (EET), Manufacturing
Engineering Technology (MET), and Industrial Management
and Technology programs. The department is accredited by
the National Association of Industrial Technologists (NAIT)
and the Accreditation Board for Engineering and Technology
(ABET).
AutomationDirect supports education
nationwide primarily through product
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uo
Gl
ns
The four forces
Bosons are
particles that carry force.
i to
F
ns
Gr
av
our fundamental forces
a
appear to be holding
Z
-
forces,
and
gravity.
They’re all caused by matter’s
Ph
absorption or emission of energy-
o
ot
W+W
the electromagnetic force, two
ns
St
ro
carrying particles called bosons.
ng
For this reason, all might be more
aptly called interactions.
Most physicists today believe
the four forces are actually just
aspects of one Force of the
universe. That’s why many are
working on a Unified Theory
to explain how they all relate.
Gravity
—
the
renegade of the bunch — is the
ro
m
only one that remains unlinked.
FORCES of NATURE eBook
Leptons:
c le a r
Electrons
Muons
Neutrinos
W
ea
k
nuc
le a r
t
experiments.
nu
ec
have already been linked with
The Grand Unification Theory says that
because the strong nuclear gets weaker while
the electromagnetic and weak nuclear forces
get stronger at high energies, they could eventually
be considered one and the same. However,
creating an energy environment high
enough to verify this is currently impossible.
Quarks
always collect into Hadrons.
There are two kinds:
Mesons
Baryons
El
In fact, three of the force types
4
nd
...
the universe together:
nuclear
Fermions are particles
that make up matter.
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ag
net
ic
G rav
ita tio n a l
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5
ar force
Strong nucleattra
ctive
Direction: Always
Affects: Quarks, binding them into 1)
s
unstable pairings of quarks and antiquark
le
stab
to form mesons or more commonly 2)
quark triplets called baryons. Protons and
neutrons are two kinds of baryons.
Carried by: Gluons
only
Claim to fame: This force groups quarks
,
ition
into neutrally “colored” particles. In add
e
the gluons (through and on which this forc
acts) also stay grouped in these special
arrangements. Atomic bombs and nuclear
e
reactors cash in on the strong nuclear forc
rt.
apa
stored in atomic nuclei by knocking them
Relative strength: 1
rc e
o
f
l
a
n
atio
ctive
Gravicttion: Always attrnaything with
Dire
, all
fects a
avity af in other words
r
G
:
s
t
Affec
rg y —
/or ene ticles.
d
n
a
r ved
s
s
ma
par
et obse
y
t
o
n
exist.
o ns —
: Gravit lly believed to d the
y
b
d
ie
nera
Carr
idere
, but ge
ly cons
in a lab me: Alternate force field, or
o fa
r the
-time, a
Claim t
f space gravity is by fa use
o
e
r
tu
cur va
ange,
t (beca t
on exch forces, and ye
it
ies
v
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g
a
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the eas
th
’s
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it
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o
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p
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Relativ
Weak nu
c
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Direction
: T h ou g h
not direc
sense, th
tional in th
e force a
e usual
ffects ma
in two dis
tt
er or anti
tinc
matter
why the u t, nonsymmetrica
l
niverse c
ontains m ways. This is
ore matte
antimatte
r than
Affects:
r.
Particles
w
ith a spin
multiple th
of 1
ereof —
in other w /2 or some
ords, ma
particles
tter
Carried b
only.
y: Ver y h
eavy W+, (which ac
W , and Z
t just like
b oso ns
photons
Claim to
at high e
fame: Un
n
e
rgy).
li
ke the oth
weak nuc
lear force
er forces
,
a
th
particles
into comp ctually changes m e
letely diffe
atter
allowing
rent parti
all
cles by
antipartic leptons and quark
les to inte
s and
rchange
energy, m
ass, elec
tric
charge, a
nd flavor.
Relative
strength
:
10 -5
Electromagn
e
etic force
Direction: Att
ractive or repu
lsive
Affects: Elect
ric
al
ly charged part
Carried by: V
icles
irtual photons
— called virtua
they’re imagin
l not because
ar y, but becaus
e they’re exch
charged partic
an
ged between
les (like electr
ons) so quickl
Claim to fame:
y.
Macroscopical
ly useful, this fo
the basis of al
rce is
l electrical desi
gns today. The
released when
ph
otons
electrons chan
ge shells also
allow
human sight.
Relative stren
gth: 7×10 -3
6
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Planck’s constant
Physical constants
Permittivity
Gravitational acceleration
Gas constant
Avogadro’s number
Electron charge
Permeability
Gravitational constant
Particle mass
Boltzmann’s constant
Bohr radius
Speed of light
Also see page 13 about the
Boltzmann relationship to entropy.
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9
Tomato, tomaaato
Call me irreversible
Courtesy Kyle May
Shattering a glass, scrambling an egg, sending an
unfortunate reply-all email — what is it about these
actions that makes them impossible to reverse? Well,
that’s complicated; the orderly reassembly of atoms or
restoring of situations breaks a few rules of our universe,
not the least of which have to do with directionality of
space-time.
Suffice it to say that irreversible events are in
effectively closed systems, and it’s a law of physics
(the Second Law of Thermodynamics, to be exact)
that entropy, sometimes also called the Arrow of Time,
always increases in such situations. In theory, reversible
processes do exist — for example, squeezing air from
one end of a balloon to another — but in reality, even
these create friction and other nonreversible results.
[
What’s more, the entropy of two joined systems is greater than the pair’s two entropies
if they remain separated — as the removal of
a boundary to allow mixing makes for a less
organized situation.
Courtesy Great War Primary
Document — gwpda.org
Entropy
Just as light can be defined as a particle
or as a wave, so too can entropy be scientifically described in two different ways. The first
way is in terms of heat — a view developed
by Frenchman Nicolas Léonard Sadi Carnot
in 1824.
Assume that we have a two-chambered insulated tank; ideal gas fills one half. If we remove the barrier between the two chambers,
our ideal gas will expand to fill both evenly.
The increase in entropy for an isothermal process is:
Q
T
where Si = Initial entropy
S = Sf
Si =
S f = Final entropy
Q = Heat to or from system
V final
Vinitial
T = Temperature, kelvins
= nRT ln
F
rom the erosion of a grain of sand off a
cliff to the unbounded expansion of the
Universe, Nature tends towards disorder.
This tendency has a name — entropy. The
!
Measured in Joules per Kelvin, this entropy
change does not need to be expressed as the
integral, as it is equal to that of a reversible
process with the same initial and final states.
phenomenon has specific scientific meaning, but
in everyday popular culture, is described succinctly
and wittily by the infamous Murphy’s Law — What can
go wrong, will go wrong.
Murphy’s Law:
Correlates and functions
If left alone, things tend to go from bad to worse. • If a series of events can go wrong, they
will do so in the worst possible sequence. • Nothing is as easy at it looks. • If everything
seems to be going well, you have obviously overlooked something.
Entropy and black holes
Mexican-born Israeli Jacob Beckenstein proposed in 1972
that even black holes obey the Second Law of Thermodynamics,
and have a definable amount of entropy. This implies that black
holes also have a temperature, and emit the associated radiation
and particles — something that Stephen Hawking reluctantly
confirmed a year later. Today it is generally accepted that a
black hole’s event-horizon area is a measure of its entropy.
10
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Fan of the flames: Sadi Carnot wrote his short book,
Reflections on the Motive Power of Fire, in 1824. It
details how motion can be generated from the “fall” of
heat from one object to another colder body. It also first
outlined the Second Law of Thermodynamics.
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11
A
Spread, sprinkled, or expanded systems in general possess
higher relative entropy: Mustard in a neat line on a hotdog is
less entropic than mustard splattered on a shirt; similarly, the
carbon in a diamond is more orderly and less entropic than
that in graphite.
Speaking of allotropes, if systems tend towards increasing
entropy, then why do materials freeze into orderly crystal
lattices? Even here, the Second Law of Thermodynamics
holds. Entropy coexists with forces that drive atoms and
molecules to lower energy states; even where crystals
themselves are lower in entropy and energy, they form in
non-isolated systems that interact with the environment, its
kinetics, and greater energy.
The first way to describe entropy is in terms of thermodynamics
or heat. The second way to describe entropy is with statistics.
This arrangement (with all 12 of
our molecules collected in one side
of the tank) is possible but unlikely —
and has low multiplicity.
Courtesy Jon Sullivan
The densest lattices (as the face-centered cubic here) are most efficient
for packing spherical atoms. Researchers at the University of
Pennsylvania led by Randall D. Kamien have shown that though they’re
more unique, systems of oddly shaped molecules also freeze into efficient
and predictable lattices for maximum overall system entropy.
In a paper published in the American Journal of Physics,
Daniel F. Styer proposes that the hard association of
entropy with notions of disorder is troublesome, and that
the scientific definitions deserve more distinction. He also
proposes the simile entropy as freedom.
In this case, two suddenly joined (and possibly less
“organized”) systems might also be called less bounded.
12
FORCES of NATURE eBook
Common — tendency to entropy
Odds are even
s a measurement of a system’s
randomness, entropy has
specific scientific meaning.
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 Assume that we now have a single-chamber insulated
tank that contains one dozen identical molecules of an ideal
gas.
At any instant, each of our molecules has a 50/50 chance
of being on one half of the chamber. However, the position
permutations for which all 12 of the molecules are on one side
at once are miniscule; rather, probability is highest that at any
given moment, the molecules will be spread evenly throughout
the chamber. This unfurled arrangement has higher entropy
and is expressed by a relationship developed by Austrian Louis
Boltzmann:
Configurations with higher multiplicity
and probability of occuring (as the below
arrangements, in which the molecules
are spread equally over chamber halves,
for example) also have higher entropy, as
there are more channels for free energy.
S = k lnW
where k = Boltzmann contant
Boltzmann’s constant relates the macroscopic
Gas constant
ideal gas law (of pressure, mass, volume, and
=
temperature) to the microscopic physics of our 12
Avogadro's number
identical molecules. Multiplicity is the number of
J
ways
that the molecules can rearrange to make one
!
8.314
essentially identical situation.
mol
K
=
1
6.022 10 23
mol
23
= 1.38 10 J/K
W = Multiplicity of the situation
Note that this statistical definition is related to the
thermal definition, as molecules must have the energy to
spread through the chamber — and any resulting entropy
results from their interactions.
Two on the left
N!
nL! nR!
Total molecules (factorial)
In left (factorial) In right (factorial)
12!
=
2! 10!
479,001,600
=
2 3,628,800
= 66
W =
This arrangement also has relatively low
multiplicity — as there not many
permutations for which only two molecules
are found in the left side of the chamber.
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13
y
v
a it
g
r
o
M icr
Einstein on trial
The Satellite Test of the Equivalence Principle
(STEP) will carry concentric test masses
into orbit to test a fundamental assumption
underlying Einstein’s theory of general relativity:
that gravitational mass is equivalent to inertial
mass. During the experiment, four pairs of test
masses will be falling, and their accelerations
will be measured a million times more accurately
than in any ground-based test.
G
ravity, the attractive force between two masses, keeps us oriented in
more ways than one. Without gravitational influences, we’d barely be
able to recognize our world, let alone function in it.
Sometimes gravity gets in the way, however, blinding us to how things actually
work. Even our mechanical aptitude possesses a certain near-sightedness; we
understand things based on the way they behave in the Earth’s gravitational
field, and that, only at the surface.
Newton’s apple
To peel away the cloak of gravity and isolate some of the more
fundamental properties, forces, and processes of nature, scientists create a
condition called “microgravity.”
Microgravity is relative rather than absolute. It’s created by free-fall; the entire
experiment accelerates at 1g, nullifying the effect of Earth’s gravity. Otherwise,
you’d have to travel almost 17 times farther than the Moon, or 6.37 million km, to
reach a point in space where gravity is one-millionth of that on Earth’s surface.
If you drop an apple on Earth, it falls to the ground at a rate of 1g. If an astronaut
drops an apple on the space shuttle, it falls too; it just doesn’t look like it’s falling.
That’s because the apple, astronaut, and shuttle are all falling together. But they’re
not falling toward the earth, they’re falling around it — in orbit.
Newton developed a “thought experiment” to demonstrate this concept: Imagine
placing a cannon atop a mountain. Once fired, a cannonball immediately
begins falling toward the Earth. The greater the
speed, the farther it travels. If fired with enough
speed, the cannonball could circle, or orbit, the
Earth in a state of continuous free-fall.
By conducting experiments in microgravity, researchers hope to uncover new
information previously masked by the effects of Earth’s gravitational field.
Primary areas of investigation range from fundamental and fluid physics to
biotechnology, combustion science, and materials science. NASA even hopes to
test Einstein’s theory of general relativity and Newton’s law of gravity.
14
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Look out below
The STEP experiment is a 21st-century version of a test Galileo
performed by dropping a cannonball and a musket ball from atop the
Tower of Pisa to compare their accelerations.
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The familiar teardrop-shaped
yellow candle flame is the
result of gravity-driven buoyant
convection, which carries soot
to the flame’s tip. In microgravity,
where convective flows are
absent, the flame is spherical,
soot-free, and blue. The study of
combustion is vitally important
today as it accounts for 85% of
the world’s energy use.
Bubble bath
When a liquid is heated from
the bottom, small bubbles of
hot gas form and are carried
upward
by
gravity-driven
convective flows. In the same
setup in microgravity, the
heated gas bubbles grow
larger and remain attached to
the bottom for a longer period
of time because of the lack of
convection and buoyancy.
Crystal clear
Proteins grown in microgravity
are many times longer than
those grown on Earth. The
raf kinase crystals, below, the
largest ever produced, were
grown during the second U.S.
Microgravity Laboratory (USML2) mission in November 1995. In
general, the larger the crystal,
the more structural information
it reveals.
(Photos courtesy Dr. Jean-Pierre Wery and Eli Lilly and Co.)
No more tears
Breaking the law of gravity
Space station
The International Space Station is a semipermanent facility that lets scientists conduct
research in microgravity over a period of months,
without having to return the test setup to Earth
after every experiment.
Space shuttle
By maintaining a consistent orbit, a space
shuttle can provide up to 17 days of high quality
microgravity conditions. Shuttles can accommodate
a wide range of equipment, functioning as a
laboratory in which scientists can conduct longterm investigations.
Sounding rockets
An experiment placed in a rocket and launched
along a parabolic trajectory experiences
microgravity for several minutes prior to re-entering
Earth’s atmosphere as the rocket is in free-fall.
Reduced gravity aircraft
Flying a plane over a parabolic arc can
produce microgravity conditions lasting 20
to 25 sec. NASA uses a modified KC-135
four-engine jet transport for such tests,
performing as many as 40 trajectories
during a 2-hr flight.
Level best
A gallium-doped germanium crystal grown aboard a
sounding rocket demonstrates the effect of gravity on
material properties. The random striations visible in the
bottom portion, which solidified under gravity, are an
indication of variations in gallium concentration. The top
portion grew in microgravity, where the lack of buoyancyinduced convection allowed the mixture to remain uniform
as the melt solidified.
16
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Drop tower
Drop towers are long vertical shafts where test
objects achieve microgravity through free-fall.
Glenn Research Center in Cleveland operates two
drop towers — one above ground (24 m tall), one
underground (132 m deep). Here, scientists can
perform microgravity experiments lasting 2.2 to 5.2
sec.
Thanks to NASA for technical support and graphics, and Steve Lambing for technical input.
AUTOMATIONDIRECT.COM • FORCES of NATURE eBook
17
Inertia is matter’s tendency to resist
change. Around moving masses it
acts like a stabilizer, pushing against
any accelerating or decelerating force.
Galileo first defined the principle of
inertia in the 16th century; it states that
every object persists in its state of rest
or uniform motion unless compelled
by outside forces. Isaac Newton later
=
Stuck in its ways
Point of view
=
Inertia
=
Classifying
“rest”
as just zero-motion
leads to the concept of
=
nonaccelerating inertial
frames: As long as
frames move uniformly
they’re like stationary
references, so masses
in these frames all observe the same laws of physics. (On
the other hand, accelerating objects encounter fictitious
forces such as the Coriolis effect.)
Ernst Mach first proposed that any system’s inertia is the
result of its interaction with the rest of the universe; Albert
Einstein later vouched for this statement’s refutation of
absolute reference frames — and differentiating rest and
motion — by reasserting the equivalence of all inertial
frames.
adopted this principle as his First Law
of Motion.
Related concept: Momentum
z
Take it for a spin
x
18
y
Also called rotational inertia, an object’s moment
of inertia is its tendency to continue rotating free of
angular acceleration unless an external torque is
applied. The strength of this tendency is measured in
kg-m2 and varies with the object’s shape.
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Inertia depends only on mass, but momentum
depends on mass and speed. The same amount
of momentum might be found in a faster/small
mass as in a slower/large mass. Similarly, when
a twirling skater draws her arms inward, her
moment of inertia decreases so her angular
velocity must increase. That’s because angular
momentum is also conserved, so the product
of angular velocity times moment of inertia is
constant.
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19
Inertial = gravitational
F = G
mboat . mearth
r2
F = mboat . a
Newton’s Second Law of Motion
assumes mass is an object’s resistance
to acceleration, but Newton’s Law of
Universal Gravitation assumes mass
measures gravitational attraction. The
dichotomy is resolved in the Principle
of Equivalence, which states there
is no way to distinguish between the
effects of acceleration and gravity.
Indeed, some physicists discriminate
gravitational mass mg from inertial mass
mI. However, in our universe it appears
the two masses are always equal.
Where does inertia come from?
Truth is, no one really knows. While some
scientists argue that inertia isn’t a fundamental
property, others think it indeed relates to matter’s
essential nature — it just hasn’t been addressed by
modern theories yet.
Scientists at the California Institute for Physics
and Astrophysics, Palo Alto, Calif., and elsewhere
are exploring inertia’s possible origins. They’re
trying to reformulate older concepts within more sophisticated quantum field
(QFT) and superstring theories to link inertia to the Higgs field. Why? It’s
believed that inside this Higgs field live Higgs bosons which impart mass by
“dragging down” all particles with which they interact. One catch: Even if the
Higgs particle causes inertial behavior, it still won’t prove whether inertia is an
intrinsic or extrinsic property.
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