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Physics of Remote SensingRemote Sensing is the science of acquiring, processing and interpreting images that record theinteraction between the electromagnetic energy and matter (Sabins, 1997). Remote sensing offersetensi!e applications in almost e!ery area of science from monitoring forest fires to geologicmapping . "lthough many aspects of remote sensing are comple and difficult to understand thebasic theory behind remote sensing is simple physics.

#here are four ma$or stages of remote sensing. #he first stage is the source of energy, usually thesun, which sends energy to a target. #he second stage is the interactions that the energy will gothrough as it passes through a !acuum and the earth%s atmosphere. #here is then interactions thatoccurs with the body on earth%s surface. #he energy again, goes through the atmosphere and finallythe sensor is able to detect and record the electromagnetic energy.

&lectromagnetic &nergy

&lectromagnetic energy is a dynamic form of energy that is caused by the acceleration oroscillation of a charged particle. "ll substances abo!e absolute 'ero ( el!in) emit a range ofelectromagnetic energy. #he sun emits electromagnetic energy and practically all of the naturalelectromagnetic energy in$ected into the earth is produced by the sun (*ra+ush, ).

&lectromagnetic Radiation

&lectromagnetic Radiation is the streams of mass-less particles, tra!eling in a harmonic, sinusoidalfusion at the !elocity of light each possessing a specific amount of energy. #he distance from onepea+ to the net is the wa!elength and the number of pea+s passing through a fied point per unittime is the wa!e frequency (illesand and iefer, 199/). &lectromagnetic radiation is&lectromagnetic energy in motion and can be described by the basic wa!e theory.

&lectromagnetic Spectrum

&lectromagnetic wa!es are characteri'ed by their wa!elength location within the electromagneticspectrum which is most commonly measured in micrometers. 0ames are often assigned to regionsof the electromagnetic spectrum, but there is no clear cut di!iding lines from one region to the

net (illesand and iefer, 199/).

Stefan - olt'mann aw

2ow much energy any ob$ects radiates is a function of its surface temperature.

#he Stefan - olt'mann equations tells one that as a temperature of a body increase the totalradiance of the body will also increase. (Sabins, 1997).

3nteractions

#he way electromagnetic radation interacts with matter can be detected with different sensors.2ow the radation interacts depends upon the properties of the medium, the wa!elength of the

incedent radation and the incident angle. #here are four ma$or types of interactions that occur4transmission, reflection, scattering and absorption (illesand and iefer, 199/).

#he atmosphere also has interactions with electromagnetic radiation as it passes through theatmosphere. "tmospheric scattering occurs when electromagnetic radiation entering theatmosphere interacts with particles in the atmosphere and the direction of the energy change isnot predictable (*ra+ash, ). #here are three ma$or types of atmospheric scattering which aredependent on the wa!elength of radiation and the si'e of the atmospheric particles.Rayleigh scattering is the most common type of scattering and occurs when the electromagneticradiation is much larger than the particles in the atmosphere. Rayleigh scattering occurs in the bluesection of the electromagnetic spectrum and is the reason that the s+y appears blue (*ra+ash,).5ie Scattering occurs when the wa!elength of the incoming electromagnetic radiation iscomparable in si'e to the atmospheric particle. 5ie scattering occurs in the red and orange parts of the spectrum and eplains why the s+y appears orange and red at dus+ and dawn. #he water !aporand fumes in the atmosphere cause the electromagnetic radiation to scatter(*ra+ash, ).0on- Selecti!e Scattering occurs when the wa!elength is smaller than the particles in theatmosphere. 0on-selecti!e scattering affects all of the parts of the spectrum equally and eplains

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why clouds appear white. 6hite clouds are a result of all of the !isible wa!elengths being scatteredequally (*ra+ash, ).

etection of &lectromagnetic Radiation

#he radiation that is emitted reflected or scattered from a body generates a radiant flu density inits surrounding space which contains information about the bodies properties. #o measure the

properties of this radiation a collector and detector are used. #he collector is a collectingaperature which intercepts the radiant field and focuses the energy into a detector. #he collectorfor !iisual, infrared and ultra!iolet remote sensing is usually a lens or a reflecting surface. #hedetector then transforms the electromagnetic radiation into another form of energy such as heat,electric current or state charge (&lachi, 1987). #hese forms of energy are measured and con!ertedinto digital numbers that can be transformed into images that can be processed.

*lan+s aw

*lan+s aw determines the emission pattern spectra of electromagnetic radation of a blac+body asa function of its wa!elength and temperature

*lan+s law shows that as the temperature of a body rises the pea+ of the emitted radiation shiftstoward shorter wa!elengths (figure 1)#he pea+ of the suns radiation is in the !isible part of theelectromagnetic spectrum and the earths pea+ of radiation is in the thermal part of theelectromagnetic spectrum.

Satellite and "irborne Sensors

#here are many different satellite sensors that are used today. ifferent sensors ha!e differentspatial and spectral resolutions therefore the information they obtain ha!e different uses.

"pplications

:eologic 5apping

"S#&R images are often used for geologic mapping.0ot only does this image show different strata in differentcolors, but it also show the topography of the region

;orest ;ires

<ne of 5<3Ss main uses is to help monitor forest fires.#his 5<3S image shows forest fires in 3daho during the summerof .#he red area on the image show are that were buriningduring image aquisition while the gray area depict burn scares.

=olcano 5onitoring

"n "S#&R imagae of a !olcanic eruption o!er 5t. &tna 3taly.0ot only can "S#&R detect the thermal properites of la!a flows italso has the capability of detecting gas emmisions from the !olcano.

Sea 3ce > :laciers

" andsat 7 image of the largest glacier in "las+a.5alaspina :lacier is located west of ?alcutat ay and is@,88 +m squared. 5o!ement of glaciers and sea ice is oftenstudied using remote sensing.

Arban :rowth" andsat 7 image of etroit, 5ichigan.Remote Sensing is often used to study changesto urban area along with the effects of that growth.

=egetation 5apping

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#his S*<# image is mapping diifernt type of agricultural area.Remote sensing is often used to detect changes in !egetaionespecially due to deforestation

References

illesand and iefer, 199/, Remote Sensing and 3mage 3ntrpretaion, @rd &dition, Bohn 6iley and Sons

3nc., 0ew ?or+.

&lachi, C. 1987 3ntroduction to the *hysics and #echniques of Remote Sensing, 6iley D 3nterscience*ublications, 0ew ?or+.

Sabins, ;, 1997, Remote Sensing *rinciples and 3nterpretations, @rd &dition, 6. 2. ;reeman andCompany, 0ew ?or+.

"S#&R 6eb *age4 http4EEasterweb.$pl.nasa.go!E

andsat 6eb *age4 http4EElandsat7.usgs.go!Einde.php

5<3S 6eb *age 4 http4EEmodis.gsfc.nasa.go!E

*ra+ush, "nupma, 6eb *age and Class notes4http4EEwww.gi.alas+a.eduEFpra+ashEteachingEundergraduateEmaterialEinde.html

Physics of Submarines5ost people ha!e some sort of familiarity with submarine craftsG most of which are most li+elyrelated to the na!y. #his is a !ery accurate depiction of submarines, as they are primarily used forthis, howe!er, they are used in areas of scientific research as well. #he purpose of this web page isto go into the history of the submarine to see how it has de!eloped o!er time. 6e will also loo+ athow a submarine wor+s, from a physics standpoint.

#he 2istory of Submarines

@@ C "ristotle described a type of submersible chamber used by the sailors of "leander the:reat during the loc+ade of #iros.

C #here is e!idence that there was a primiti!e submarine in China that was able to mo!e by

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the bottom of the sea.

1H78 " 5uch later in time, the first actual design for a submarine was presented by 6illiam orne.3n this design was the concept of ballast tan+s (3 will go into more depth on these later) used tosubmerge and surface. #his design, howe!er, was ne!er actually built.

1I " " utchman, named Cornelis rebel, built the first successful submarine with a woodenframe that was encased in leather. #his craft was able to carry 1 rowers and eight additionalpeople, totaling the people in the craft to . #his !essel was capable of di!ing to depths of meters and could tra!el 1 +ilometers at a time. #his submarine was tested in the #hames Ri!er,and would often remain submerged for hours. #his submarine was the first to address the problemof oygen shortage.

177H " a!id ushnell, an engineering student at ?ale, in!ented the J#urtleK. #his egg shapedsubmarine was dri!en by two, hand-cran+ed screw propellersG one controlling forward mo!ement,and the other for side-to-side motion. #his submarine only held one person, and was intended to beused in warfare. #his craft was equipped with a detailed system of !al!es, air !ents, ballast pumps,

lead weights to +eep upright, and a mine that was to be attached to enemy%s ships with adetachable screw.

#his was the first combat submarine and on September I, 177I it was put to test against a ritishflagship, 25S &agle in 0ew ?or+ 2arbor. 6hen the J#urtleK attempted to attach the mine to theship, it was deflected by the copper sheathing on the ship.

1798 " Robert ;ulton used the same concepts eercised in the design of the J#urtleK to build hisown submarine, the J0autilisK. 3t used two forms for power for mo!ement, di!ing planes, shape,armament, and air replenishment. #here was a sail to use while on the surface, and a hand-cran+edpropeller to use while submerged. #his craft was streamline to increase agility and featured di!ingplanes to control the angle of descent. 3t was / feet long and carried a crew of four. 3t had oneweapon, called the torpedoG which at the time, eisted as a bo of dynamite. 3t is unclear how long

this !essel could stay submerged (somewhere around 1 hours). #he J0autilisK was the firstsubmarine to eperiment with compressed oygen.

18H " :ermans constructed a submarine called the JSea e!ilK. #his craft made o!er a hundreddi!ing%s and held a crew of 1/.

18I/ " <!erloo+ed during the ci!il war is the fact that the first successful use of a submarine inbattle was eecuted during this time. #he confederates built four submarines, the 2unley being themost famous for its ad!enture. #his Submarine rammed into ASS 2ousatonic in Charleston 2arbor,South Carolina. " torpedo on the 2unley eploded, consequently sin+ing both !essels.

"fter the war was o!er, two men began to wor+ with submarines. Simon a+e came up with the idea

of submersing and surfacing using buoyancy, which is used in today%s submarines. Bohn *hilip2olland wor+ed on de!eloping adequate means of propulsion. oth of these men also wor+ed withcompressed air, steam, and electricity as means of power in the submarine.

187 " " man by the name of 6hittehead contributed to the rapid success of submarines in ma$orcountry%s na!y%s, when he in!ented the first automobiled torpedo, gi!ing submarines a lethalweapon.

188I " #he na!al country of :reece acquired a submarine built by the Swiss. #he J0ordenfeltKwas steam powered and could tra!el as fast as nine +nots. #his craft measured @@ meters in lengthand weighed 1I tons. #he submarine was equipped a torpedo and was not retired from use until191.

1898 " #he Anited States 0a!y%s first submarine, the ASS 2olland, built by B.*. 2olland, waslaunched. #his craft was H@ feet long and weighed 7H tons. #he ASS 2olland used a gas-powered

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engine while on the surface and an electric motor once submerged.

Anited States was in!ol!ed in 6orld 6ar 3, partly due to the :erman%s unruly use of submarines.#hey would use their !essels to sin+ any allied ships, including passenger and merchant ships. #heuse of a periscope and self-propelled torpedoes allowed submarines to play a ma$or role inwarfare.

3n between wars, submarines were impro!ed, and gi!en a thic+er hull, allowing them to increasedepths by 1 feet. #here was 1 submarines of this class built.

19/@ " uring 6orld 6ar 33, the :erman 0a!y in!ented a snor+el mast. #his feature allowed thesubmarines to run on diesel power while slightly submerged, while recharging their batteries. #he:ermans were also able to come up with an alternati!e power sourceG which they found to behydrogen peroide.

#he A.S. 0a!y remodeled their submarines by streamlining them more, and increasing batterypower, so they could run longer and faster. uring this war submarines pro!ed to play a +ey role inthe 0a!y, as they were credited with sin+ing HL of Bapanese na!al and merchant ships.

19H@ " " new submarine with a hull resembling a blimp was launched called the ASS albacore. #hehull design on this craft was so successful that nearly all submarines built afterward followed in itsfootsteps.

19H/ " #he ASS 0autilus was launched an was the most technologically ad!anced submarine of itstime. 3t was the first nuclear powered submarine. 3t could tra!el +nots while submerged andremained underwater for an indefinite period of time.

19I " Submarines began using solid-propellant ballistic missiles with nuclear warheads in the AS.#hese missiles were capable of reaching targets H miles away when launched from a submerged

submarine.

197 " " new class of submarines were built with / launching tubes for 3C5s (inter-continentalballistic missiles), each ha!ing a range of /I milesM

Submarine Ases

0aturally, as has been discussed, submarines ha!e played a ma$or role in our country%s na!y. #heyma+e up o!er L of na!al !essels. Submarines are effecti!e in our military because they allow astealth way to enter into enemy waters and possible attac+. "nd because other countries ha!e alsoepanded their na!ies to include submarines, it is an absolute must for the AS to also ha!esubmarines to counteract.

Submarines are most prominent in na!iesG howe!er, they are also used in other !enues. 3n recentdecades, they ha!e become much more commonly used as a research tool as well. #hey allowscientists to tra!el deep into the see and study deep water sea life. 0ot long ago, the depths of theoceans were a mystery, no one had been deep enough to see what really eisted beneath thesurface. 6ith submarines, howe!er, researchers are allowed a safe way to study the deep sea, without ha!ing to die doing so. 6hat a concept.

Submarines ha!e also become more popular in tourism. 5ostly in warm climates, these !essels willta+e tourists close to the ocean floor, in a dry, safe medium. #hese submarines use the sameconcepts as those used in the na!y, howe!er, they are produced on a much smaller scale, with outsome of the cool gadgets, li+e torpedoes.

Submarines are great tools that can be used for !arious different things. #hey are used by the na!y,researchers and tourism companies to eplore, and na!igate areas that are not accessible with ascuba tan+ and a wet suit. "lthough 3 ha!e ne!er actually been on a submarine, 3 can still saywithout a doubt, they are coolM

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2ow Submarines 6or+

Submerging and Surfacing

" Submarine can float on water because the weight of the water displaced is equal to the weight of the craft. #he upward force that the water has on the !essel is +nown as they buoyant force. #he+ey to controlling a submarine%s di!ing and resurfacing, is to control the buoyancy.

Submarines are equipped with ballast tan+s and trip tan+s that can be filled with either water orair. #o ha!e the submarine sitting on the surface, the ballast tan+s must be emptyG to descend, theair in the tan+s is replaced with water. #he density of a submarine then becomes greater than thewater and it will submerge. #here is a supply of compressed air on board that is used for both lifesupport and to fill the ballast tan+s.

#he speed of descent is additionally helped with a set of di!ing planes or JwingsK on the top of thesubmarine. #he angle of the wings is controlled, thus influencing the angle of descent.

#o +eep the submarine le!el at any depth, the submarine maintains a balance of air and water inthe trip tan+s, so that the o!erall density is equal to the surrounding water. #he di!ing planes alsohelp +eep the depth of the submarine constant. #he rudder on the bac+ of the craft helps steer it.

*ower Supply

0uclear submarines use nuclear reactors, steam turbines, and reduction gearing to dri!e the mainpropeller shaft. &lectric power is also used to operate equipment, this is made from diesel enginesand nuclear reactors. atteries may also be used for electric power, and they may be charged usingeither a diesel engine or a nuclear reactor.

0uclear submarines ha!e an ad!antage to diesel submarines because they can stay submerged forwee+s at a time. iesel engines can only be used while the submarine is surfaced, or at least usinga snor+el, to recharge the batteries. <nce the batteries are charged, the submarine can descendusing electric power. ecause nuclear fuel lasts much longer than diesel fuel, nuclear submarinescan stay under water or at sea for long periods of time, without ha!ing to port to refuel.

0a!igation

Submarines na!igate using global positioning system while on the surface, howe!er, this will notwor+ while the !essel is submerged. Anderwater, the crafts use inertial guidance systems that +eeptrac+ of the ship%s motion from a fied starting point using gyroscopes. #hese systems are !erycomple and difficult to use, and !ery accurate at the same time. #hey are accurate up to 1Hhours at a time.#o locate targets, submarines use passi!e sonar. #his wor+s by emitting sound wa!es through waterand allowing the sound wa!es to reflect off the target and returnG by +nowing the speed of sound inwater and the time it too+ for the sound wa!e to tra!el bac+, submarines can calculate thedistance to the target. #his is the same technique that bats, dolphins, and whales use. #hese

systems can also help recalibrate the inertial guidance systems.

"ir Supply

<ygen is supplied from either compressed tan+s, or an oygen generator, which wor+s byelectrolysis. <ygen can either be released in periods throughout the day, or whene!er a computersenses the oygen le!el is low. Carbon ioide must be remo!ed from the air as well. #his can bedone chemically using soda lime in JscrubbersK. #he carbon dioide is trapped and remo!ed fromthe air in chemical reactions. 5oisture is remo!ed by a dehumidifier, this pre!ents condensationbuildup within the ship.

6ater Supply

5ost submarines can ta+e in seawater and turn it into fresh water through a distillation process.#he distillation plant on submarines can produce 1, to /, gallons of water per day. #hewater is mainly used for cooling equipment and for the crews% personal use.

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References

;ruedenrich, Craig, *h., and 5arshall rain. 2ow Submarines 6or+. 1 "pr. @

:uilmartin, Bohn ;, Br. "bout Submarines. 1 "pr. @

about.htmlN.

#he 0ational 5useum of "merican 2istory. 1 "pr. @ .

Serway, Raymond ", and Robert B eichner. *hysics4 ;or Scientists and &ngineers. Anited States of

"merica4 #homson earning, 30C, .

#he Anited States 0a!y. #he &!olution of Submarine esign. 1 "pr. @

Physics of Magnets

5agnets are one of the fundamental items in physics. #his page is designed in order to pro!ide ageneral o!er!iew of magnets and their uses as well as an in depth loo+ into certain aspects ofmagnetism.

6e all +now certain situations where magnets are used, hanging things on a refrigerator foreample. ut other applications are much more useful in our society. #hey are used in all +inds ofspea+ers, and in many computer parts including hard dri!es and floppy dri!es ( for recording andreading purposes). *erhaps a more common use that goes unnoticed is the magnetic strip on creditand debit cards. #hese ha!e a certain magnetic ma+eup, that is why you are to +eep them awayfrom other magnets. 5agnets are also used in many motors, in such items li+e a dishwasher, =and =2S players, and a pager or cell phone !ibrator.

5agnets are all dipoles, that is they all ha!e both a north and a south pole. 0o +nown magnetic

monopoles eist. oo+ing at magnets from a basic point of !iew, opposites attract and similarsrepel. 5agnetic field lines always mo!e from the north pole to the south pole, we will discuss thislater.

Some of the ma$or contributors to magnets are men li+e 2ans Christian <ersted, Bames Clar+5awell, 6illiam Scoresby, 5ichael ;araday and Boseph 2enry.

2ans Christian <ersted eperiment with a wire carrying a current and a compass led to much ofwhat we +now about 5agnetic ;ields.

Bames Clar+ 5awell disco!ered relationships between electricity and magnetism many of whichare used in the &lectromagnetic #heory. 5ore information on the relationship between magnets and

electricity can be found here.

6illiam Scoresby used the &arths magnetic fields to produce powerful magnets.

5ichael ;araday and Boseph 2enry are reported to ha!e simultaneously disco!ered electromagneticinduction, which is the effect whereby the relati!e motion of a magnet and an electric coilproduced a current.

#here are three types of magnets. *ermanent, temporary, and electromagnets. *ermanent magnetsare the most common ones. <nce they are magneti'ed they stay so (although they can lose much of their magnetic force). #hey can be metals found in nature. #emporary magnets hold the propertiesof a magnet while in a magnetic field, but lost these properties once the field goes away. "neample of this would be a paper clip that is charged and can act li+e a magnet for a short while.&lectromagnets are wires wrapped around a metal center(usually iron). #he wires ha!e a currentflowing through them. "n eample of this would be a nail with wires wrapped around it andconnected to a battery. #he nail would then be able to pic+ up metallic ob$ects.

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3t is important to note that these magnetic fields always tra!el from the north pole to the southpole. 5agnetic fields always radiate out of the north pole and magnetic fields always go in to thesouth pole. 6e define a magnetic field with the symbol . O#he direction of the magnetic field atany location is the direction in which the compass needle points at that locationO (Serway).

6ith regard to the !elocity of a particle mo!ing through a magnetic field, its direction can bechanged by the field but speed and +inetic energy of the particle cannot be altered by the

magnetic field. 3t is also important to note that Owhen a charged particle mo!es in a magnetic field,the wor+ done by the magnetic force on the particle is 'ero.O 6e +now thisO because thedisplacement is always perpendicular to the direction of the forceO(Serway). #hin+ of it as if youwere wal+ing. #he wor+ done while wal+ing is 'ero because you are displacing forward and thedirection of the force is down (your feet stri+ing down on the ground pushing you up).

3f we are dealing with a charged particle in a magnetic field, the particle mo!es in a circleperpendicular to the magnetic field. 3t mo!es in this way because Othe magnetic force ; sub b is atright angles to ! and and has a constant magnitude q!O (Serway). #he force is deflecting ! and ;sub b continuously. 2owe!er, note that again although the direction of the !elocity changes, it doesnot change its magnitude. " really cool webpage related to magnetic forces on mo!ing charges canbe found here. epending on weather the magnetic field goes into or out of the OcircleO determineswhich direction the particle mo!es. 3f the field is coming out of the page the particle mo!es in a

cloc+wise fashion. 3f the field is going into the page the particle tra!els countercloc+wise. #hispage pro!ides a real time demonstration of this. Same is true depending on the charge. 3f thecharge is positi!e(and the force is pointing inward) it would mo!e countercloc+wise, and if the thecharge is negati!e (and the force is pointing inward) it would mo!e cloc+wise.

3t is important to note that earths true magnetic north (the pole that attracts the south pole) isntthe geographical north pole. "s http4EEdeeptow.whoi.eduEnorthpole.html says O&arths magneticnorth pole is where the magnetic field lines are oriented !ertically and plunge into the surface ofthe earthO. 6e +now that the field lines tra!el from north to south, so it must be that the earthsgeographical magnetic north is true magnetic south. 3n the picture below the eact location ofearths geographical north magnetic pole. ocated in northern Canada.

"lthough this can seem weird at first it ma+es logical sense to call it the Onorth poleO. #hin+ of a

compass for eample. #he needle OpointsO to the north pole. 6hat is really happening is the metalin the compass needle is being attracted to the earths magnetic south pole. 3t is easier to thin+ ofpointing northPnorth, instead of actually understanding the compass isnt pointing, but insteadbeing pulled.

O#he =an "llen radiation belts consist of charged particles (mostly electrons and protons)surrounding the &arth in doughnut-shaped regionsO (Serway). #hese particles are trapped by &arthsmagnetic field. #he =an "llen belts Ospiral around the field lines from pole to pole...O(Serway).#hecause for the aurora is particles colliding with atoms in the atmosphere. #he reason the "urora ismostly confined to the polar regions is because this is where the =an "llen belts are closest to the&arths surface. #he &arths surface is where the field lines enter or eit the planet. 3t is at thislocation where the =an "llen belts interact with the &arths atmosphere causing the collisionsdiscussed abo!e.

"s you can now hopefully see magnetic fields not only play a role in physics but are also !eryapplicable to our e!eryday li!es. 5agnetic fields are !ery comple and 3!e onlytouched the surface.

#he relationship between magnetism and electricity is !ery close. #his page is dedicated to howmagnetism and electricity interact in fields but before we discuss that 3 feel it is important to +nowa little bit about the electromagnetic force.

"ccording to this physics page OQthe electromagnetic force one of the four fundamental forces theelectromagnetic force manifests itself through the forces between charges (Coulombs aw) and themagnetic force, both of which are summari'ed in the orent' force law.O

0ow that we +now how closely related the electric and magnetic forces are it is appropriate todiscuss further the interaction between electricity and magnetism in fields.

#he first interaction is a magnetic force acting on a current carrying wire. #his situation actssimilar to the situation of a charged particle mo!ing through a magnetic field. #here is a force on

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the wire. 3t is simply a collection of charges in motion. O2ence the resultant force eerted by thefield on the wire is the !ector sum of the indi!idual forces eerted on all the charged particlesma+ing up the currentO (Serway). #he total 5agnetic force on a wire is equal to the current(3) times(length of wire) cross (magnetic field). 3f we ha!e a closed current loop the net magnetic forceacting on it is .

Soon after <ersteds disco!ery that a compass needle is reflected by a current-carrying wire two

scientist by the name of Bean-baptiste iot and ;eli Sa!art performed eperiments dealing withthe force eerted by a current on a nearby magnet (Serway). #heir eperiments lead to the iot-Sa!art law. O#he iot-Sa!art aw relates magnetic fields to the currents which are their sourcesO.

#here are !ariants of magnetic fields and wires. "mperes law can be used in many of these!ariants. See "mperes law applications.

#he last sub$ect 3 will touch on here is &lectromagnetic ;ields. &lectromagnetic wa!es (whichnaturally in!ol!e magnetic fields and electric fields) are predicted by 5awells equations. #heseequations are 3. :auss law for electricity 33. :auss law for magnetism 333. ;aradays law of induction3=. "mperes law.

#he reason 3 mentioned the electromagnetic fields is so we could discuss the energy in electric and

magnetic fields. 6e +now both fields store energy. &lectric fields store energy in capacitors andmagnetic fields store energy in inductors. #he equations for the energy densities are shown below.

0ature is !ery symmetric as you may or may not ha!e +nown. #his is why many scientists belie!e!ery strongly that there are such things as magnetic monopoles. "s to date, howe!er, Oa singlemagnetic pole has ne!er been isolatedO (Serway). <ne of the reasons they are so had to find orma+e is shown below. "s the pictures show if you ta+e a magnet, say a bar magnet, and cut it inhalf, instead of getting a south pole and a north pole, we are left with two new magnets.

" positi!e magnetic monopole is an isolated magnetic north pole.O #his is a good picture to +eep inmind because you can ha!e an isolated electric charge that is either positi!e or negati!e. #his isnot the case with magnets.

"s we can see the monopole magnets would act li+e an isolated charge. #he fields radiate radiallyoutward from the north pole (positi!e charge) and go radially in to the south pole (negati!echarge). "lthough magnetic monopoles are belie!ed to eist, they ha!e ne!er been obser!edeperimentally. #his results in 5awells equation.(Clic+ the lin+ to the left for an etensi!e loo+ atthe 5awell equations). 3t is predicted, according to grand unified theories(:A#), that O#he chargeon magnetic monopoles predicted by :A#s is either 1 or g(Beon and ongo 199H). O and O#heupper limit on the monopole mass is 1I e=, or .ug.O

5uch time and many resources are gi!en to people trying to find magnetic monopoles as Serway-eichner says Oattempts to detect Qmagnetic monopoles currently ma+e up an acti!e eperimentalfield of in!estigationO. 3t is important to find these monopoles because it would change the theoryaround some of the methods sol!ing magnet related problems. ;or eample the 5awell equationswould be shown to be flawed and possibly obsolete.

References

1. Serway, Raymond ", and Robert B. eichner. *hysics for Scientists and &ngineers. 0.p.4 #hompsonearning, 3nc, .

. http4EEmy.eecpc.comEFrhoadleyEmaginde.htm

@. http4EEscienceworld.wolfram.comEphysicsE- &cellent Source for 3nformation dealing withanything physics related.-http4EEscienceworld.wolfram.comEphysicsEtopicsE&lectromagnetism.html-http4EEscienceworld.wolfram.comEphysicsE5agnetic5onopole.html-http4EEscienceworld.wolfram.comEphysicsE5agnetic5onopole.html

/. http4EEwww.mmem.spschools.orgE-http4EEwww.mmem.spschools.orgE;.9798E5agnetsE5agnetClipsE5agneticomain5o!ie.html

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- http4EEwww.mmem.spschools.orgE;.9798E5agnetsE5agnetClipsEestroy5agnet5o!ie.html

H. http4EEwww.sciencetech.technomuses.caEinde1.cfm-http4EEwww.sciencetech.technomuses.caEenglishEschool'oneE3nfo5agnets.cfmTwhatare

I. http4EEwww.wondermagnet.comEde!Emagfaq.htmlTq1H

7. http4EEfarside.ph.uteas.eduEFrfit'pEteachingE@lElecturesEnodeI.html8. http4EEhyperphysics.phy-astr.gsu.eduEhbaseEmagneticEmagfor.htmlhttp4EEhyperphysics.phy-astr.gsu.eduEhbaseEhframe.html coolestEmain pageM

Physics of FirearmsSo you are into reloading and you wonder how well that little pac+age with 77 grains of 35R /@Hpowder behind a @ grain round nose, full metal $ac+et bullet will do. 6ell, you can do two things,a little bit of physics calculations, or go out and touch it off, hoping that it doesn%t eplode in thebarrelM 3 would choose to do a little physics myselfU y using some basic physics equations, you canfigure out $ust about any part of the rifles ballistics data. ;or instance, if you +now a few !ariables,you can predict range with physics, or if you li+e you can figure things li+e drag on the bullet,pressure and epansion !alues inside the gun, on the bullet and much more, all from physics.

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So, lets ta+e a loo+ at both the potential and +inetic energies of the .@@8 6inchester magnum. 3will use a load gi!en by the 6inchester Reloading manual, which can be found online at4http4EEwww.winchester.comEreloaderEinde.html

#his load is a @ grain bullet, using H9.8 grains of 6inchester 7I powder, and this gi!es a mu''le!elocity of 8H ftEsec.

;or potential energy we +now that *&Pmgh, where *&P *otential &nergy, mPmass, gPaccelerationdue to gra!ity, and hPheight.

So for a @-grain bullet, the potential energy is calculated by first finding the mass. #o do this,ta+e @grainsE7grainsEpound. #his gi!es you a !alue of ./8H7lbs. #hen we need to con!ertpounds to slugs (slugs are the units of massU) ./8H7lbE@.ftEsVP.1@@1slugs. 0ow we cancalculate the potential energy of our @-grain bullet. 6e will assume that hPsi feet, since that isroughly the height of the barrel when 3 shoot from a standing position. So, since *&Pmgh, we get*&P(.1@@slugs)(@.ftEsecV)(Ift)P.HI9HIlbft. #he answer is pretty much nothing and so we canpretty much ignore the potential energy of that bullet sitting at si feet in the air, but now lets loo+at the inetic energy of this bullet when shot. Since this bullet will be twisting when it flies, it willha!e rotational +inetic energy, but 3 really don%t want to get into those calculations and from what 3

ha!e read, the amount of energy gi!en by rotation !ersus that of the charge behind the bullet isreally insignificant so 3 will only calculate the & as if the bullet is not rotating. #he formula is&P1Em!V. 6e +now the !alues for m and the mu''le !elocity so all we do is plug in numbers,pretty simpleM &P(1E)(.1@@slugs)(8HftEsec)VP@/7.11ftlbsM #hat is a lot of energy for thatlittle chun+ of leadM So with $ust a little bit of physics we ha!e calculated the potential and +ineticenergies of a .@@8 6inchester magnum.

So you ha!e your rifle or pistol at the range and you wonder what type of range you can epect toget. 3f you +now the !elocity as the bullet lea!es the barrel and the angle at which you fire thegun, you can calculate range. ?es it is that simpleM #he range equation for pro$ectile motion isRP(=oVEg)sinq,where RPRange, =oP3nitial =elocity, gP"cceleration due to gra!ity, and q is theangle at which the gun is fired. So for our .@@8, fired at an angle of 1E degree, we would epect arange of4 RP((((8HftEs)V)E(@.ftEsV))W(sin((1E))))P89.9ftM #hat is impressi!e range. Since

we +now that firing an ob$ect at /H degrees will gi!e you maimum range, we can calculate whatour .@@8 would do. Asing the range equation, we get a range of 1I,1/9.8Hft or roughly @ milesM#his is of course neglecting things such as drag, but it is still impressi!e figure.

Asing 6inbalistics, the tra$ectory for my .@@8 6inchester 5agnum with a @-grain bullet, and inideal conditions (standard temp, pressure, no wind... this of course 0&=&R occurs when you are outin the woods with the sight on a mooseMMM) So as you can see from the data, this rifle is sighted in at yards, and a significant drop occurs at ranges past H yards or so. So while the rangecalculation may gi!e you a big number, this shows that the effecti!e range is much smaller. 3f youare interested in the 6inballistics program, it can be found athttp4EEthor.prohosting.comEFbyeaterEwbdwnld.htm

;or some !ery ecellent ballistics calculations, chec+ out

http4EEwww.lascruces.comEF$bmEballisticsEballistics.html. 3n here you will find calculations foralmost e!ery aspect of small arms ballisticsM &!en if you dont understand all of what is in!ol!ed inballistics, this site lays it out !ery nicely and tells you eactly what you are calculating, and how. 3ha!e to say that 3 am impressed with the amount of information in their ballistics area. 3 ha!en%tyet spent much time on their site, but they ha!e software and many other useful resources too, sofor the hand loader out there, 3 would recommend their site as a starting point for gatheringinformation.

http4EEwww.winchester.comEreloaderEinde.html

Physics of ;encingefore 3 begin my discussion about how physics effects fencing and how fencers use physics formore effecti!e fencing, 3 will briefly discuss the origins of the sport of fencing. #he first twofencing manuals were created and published in 1/71and 1/7/. #hese emerged from an attempt atde!eloping a system to teach people how to weild a light sword more effecti!ely inbattle and duelsin ;ran+furt, :ermany. <!er the years, two distinct styles emerge. #hey were ;rench and 3talian.#he french style relied mostly on strategy while 3tialian used mostly physical strenght(Roswell).

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#he first foils emerged during the se!enteenth century for a more effecti!e way of teachingstudents  the OartO of dueling. 3n the eighteenth century, the rules were created for fencing  as asport. 3t is from these rules that todays rules for fencing were created (Roswell)

3n fencing there are three types of weapons that are taught. #hey are the epee, foil, and sabre. ;orthe sa+e of this paper, the weapon being demonstrated is foil and the style is modern 3talian.

So without further ado.... et us begin our discussion of physics with basic mo!es, and then mo!eon to more ad!anced mo!es in fencing.

asic ;encing

#o begin with, we will discuss the effects of gra!ity on the body in the regular or Oon gardeOstance., and what forces are used during the OthrustO and the OlungeO.

<n :arde

oo+ at a picture of what a fencer loo+s li+e in the Oon gardeO position. "s you can see, the largerarrow shows the pull of gra!ity. #he smaller arrows show where gra!ity is pulling the limbs. Redbeing for the legs and yellow for the arms.

unge

0et, we will discuss the lunge. elow you will see two more images. ;irst it is from the thrustposition. #hen the net image shows the lunge position. #he lunge picture shows the forwardmomentum in the blue arrow. "s in the pre!ious pictures, the same colors are used for the samegra!ity applications, but the ma$or difference is the effects of gra!ity on the legs. 3n this position,the effects of gra!ity are more se!ere because the legs are again further from the center mass of the body and therefore, more of the force of gra!ity is Opushing downO on the legs.

So that will conclude the discussion of basic stances and physics of them. 0et, we will discuss themore ad!anced mo!es and how fencers use physics to their ad!antage with them.

"d!anced 5o!es of ;encing

6elcome to the continuation of the pre!ious discussion. 3n this section, a selected number of mo!esin fencing will be discussed. #hey are the cupee, incortata, pasata soto, gla'ad, and the beat > go.6hile the pre!ious section only discussed the effects of gra!ity, this section, will describe in moredetail how physics is used in fencing. Since the ongarde, lunge, and thrust position ha!e alreadybeen discussed, they wont be here.

Cupee and eat > :o

;irst, we will discuss the cupee (pronounced li+e tupee). #he cupee is actually a mo!e that is anoption after a different mo!e. #he first mo!e is called the eat > :o. ;irst, the fencer beats the

blade. #his is accomplished by stri+ing the opponents blade near the midde. #he following imageswill help illistrate the actions.#he blue arrows show the path of the fencers blade and the red arrows show the path of theopponents blade. #he purple arrows represent momentum and the force of the blade. 3n the actionof the beat, the fencer transfers the energy from his blade to that of his opponent. #he action of this will send the opponents blade out of the line (represented by the red arrow). when thishappens, the fencer lunges at the opponent. 3f the opponent +now what he is doing, he willperform a counterparry. #his is accomplished by using the energy from the beat to bring the bladearound and parry the lunge. #his is represented by the red arrow in picture two. #he cupee is theaction performed by the fencer in picture two (blue arrow). 3t is the pulling bac+ of the blade toa!oid the counterparry. #his is completed during the lunge. "fter the completion of the lunge, thefencer OpunchesO at the target sending his point under the parry and hitting target.

:la'ad

#he second mo!e we are going to discuss is called a gla'ad. #his is both an offensi!e action and adefensi!e action. #he point of a gla'ad is to send the opponents point out of line and ending the

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mo!e already in thrust for the lunge. 3f the mo!e is performed effecti!ely, a counter parry will notbe an option. ets ta+e a loo+ at our pictures.

3n the first image, the orange line represent the foil due to horrible photography. #he postion of thefencers blade, is under the opponents blade in order to Opic+ upO the blade and ma+e a circularmotion towards the opponents outside low target. #he result of this can be seen in the secondimage. #he final action is to lunge at the target where the foil is pointing. "s the third picture

shows, the opponents blade is almost completely out of his hand. #his gla'ad was performedcorrectly. 3n this mo!e, the fencer uses the friction between the two blades for Opic+ing upO theopponents blade. 6ith the combination of friction from the forward motion of the blade and themomentum build up, and because momentum is always conser!ed, 6hen the fencer ends contactwith the other blade, it sends the other blade out of line with a lot more force than the beat > gohad in it.

#he 3ncortata and *asata Soto#he net two mo!es are based upon the idea that it is better to a!oid the blade altogether andattac+ where the fencer least epects it. #he pasata soto is a mo!e when the fencer drops to theground when an opponent lunges at them. the wordsOpasata sotoO translate to literally mean to passunderneith. #he following pictures demonstrate what the pasata soto and incortata loo+ li+e.

#he first image is what a pasata soto is supposed to loo+ li+e. 3t is $ust dropping straight to theground and letting the opponent s+ewer himself on the fencers blade. #he fencer accomplishes thisby remo!ing his bac+ leg from support, and letting gra!ity force him to fall on his other leg. 3f thisis performed fast enough,the opponent wont ha!e time to react. #he second image is of anincortata. it is actually using the nonweapon hand to bring the body out of the line of theopponents lunge. #his is also done while pointing the blade at the opponent thus impaling him onthe blade. #his is accomplished because of the fact that forcePmassaccelleration. y OflingingO thearm bac+wards towards the fencers bac+. #he accelleration of the hand pulls the body along with itso that the acceleration is enought to mo!e in time to get out of the way of the opponents blade.