Follow this and additional works at:

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "Follow this and additional works at:"

Transcript

1 Indiana University - Purdue University Fort Wayne Opus: Research & Creativity at IPFW Manufacturing & Construction Engineering Technology and Interior Design Senior Design Projects School of Engineering, Technology and Computer Science Design Projects Rugby Ball Launcher Joel Kumfer Indiana University - Purdue University Fort Wayne Mitchell Olney Indiana University - Purdue University Fort Wayne Follow this and additional works at: Opus Citation Joel Kumfer and Mitchell Olney (2017). Rugby Ball Launcher. This Senior Design Project is brought to you for free and open access by the School of Engineering, Technology and Computer Science Design Projects at Opus: Research & Creativity at IPFW. It has been accepted for inclusion in Manufacturing & Construction Engineering Technology and Interior Design Senior Design Projects by an authorized administrator of Opus: Research & Creativity at IPFW. For more information, please contact admin@lib.ipfw.edu.

2 Project Report Rugby Ball Launcher Joel Kumfer & Mitchell Olney MET 494

3 TableofContents DESIGN' 3 VELOCITY'A'TRAJECTORY'CALCULATIONS' 16 DRAG'AND'LIFT' 27 DEFLECTION'ANALYSIS' 32 ACQUIRED'COMPONENTS' 34 ASSEMBLY' 38 GANNTT'CHART' 41 TESTING'OBSERVATIONS' 42 TESTING'ASSESSMENT' 42 POSSIBLE'IMPROVEMENTS' 42 CONCLUSION' 43 REFERENCES' 43

4 Design Image1.1

5 Image1.2 Image1.3

6 Image1.4 Image1.1isourcurrentdesign;the2motorsareconnectedtoaquarterinchsteel plate(image1.2)whichisthanmountedtoanotherquarterinchsteelplate(image 1.3).Thesecondplateismountedtotwo15seriesaluminumt?slottedbars12.9 inchesinlength(image1.4).herewecalculatedthedeflectionfromjusttheweight ofthemotorhangingfromthe15seriesbars.

7 Image1.5 Image1.6

8 Image1.7 Thetwo15seriesbarsaretappedateachendandconnectedtotwounbearding s (Image1.5)ateachendwithastarhandlebrakekit(Image1.5)whichisconnected totheframe.theframeismadeofa15?seriesdoublewidebar10inchesinlength (Image1.6),thishastapedendsforendfastenerstobefitted(Image5).Theend fastenersaretightenedinonthethroughholesonthetwo15seriesbars15.75 inchesinlength(image1.7)whichareconnectedbyendfastenersandcorner brackets(image1.5).thisallowsustomovethemotorsclosertooneanotherto launchdifferentsizeballsandpossiblyflatballs.herewecalculatedthedeflection ofthemotorhangingfromtofixedends.

9 Image1.8 Image1.9

10 Thelastpartoftheframeisa15?series13inchbar(Image1.8)isconnectedto15? seriesdoublewidebar(image1.6)bythet?nutanda5/16?181.75inchlongbolt (Image1.5).Next,a10?inchlinearbearingpad(Image1.9)isboltedtothe15?series 13?inchlongbarwiththet?nutsand5/16?18bolt(Image1.5).Thisactsasatrackso thecradlecanslideforwardmovingtheballintocontactwiththetires. Image1.10

11 Image1.11 Image1.12

12 Image1.13 Image1.14

13 Image1.15 Image1.16 Thehinge(Image1.5)attachestheframetothebaseallowingustolifttheopposite endtoachievethedesiredangletoproceed.thebottompartoftheframe(image

14 1.10)ismadeoftwo15series13inchinlength(Image1.11).Thereatthree3.5inch 15seriesbars(Image1.12)onewhichhasathroughholeinthecenterofthet?slot (image1.13)whicharetapedoneachendandfittedwithanendfastener(image 1.5)tobetightenedtothe13inchbars.The13?inchbarshavefourthroughholesin themiddleoftheframetoallowtheendfastenerstobetightenedproperly.next,we attachedthelegs(image1.14)tothebottomofthebaseusingcornerbrackets (Image1.5).Weattachedtwotothefrontandonetotherearunderthehingewith twocornerbrackets.thanweaddedtwomorecornerbracketstobothsidesofthe frontofthebaseandaddedasupport(image1.16)itissecuredby5/16?18inch threadednutstokeepitinplace.thesewhereaddedforextrasupportfortheframe tokeepthemotorfromshakingtheframeduringuse. Image1.17

15 Image1.18 Image1.19 Thelastpartiswheretheballswillbeplacedandpushedtowardthespinningtires (Image1.17);thisisallsubjecttochangesimplybecausewearelookingfortheright material.the15?serieslinearbearingpad(image1.9)allowsforthe15series.75?

16 inchlitebar18inchesinlengthwhichiscappedatoneend(image1.18)tobeslide on.thenextthroughholeabovetheoneforthegripisforaballholder(image1.19). Thisisslideontothelinearbearingpad. Image1.20 Thisisthefirstdesignwecameupwith,butdecidedagainstit(Image1.20).Atthe timethemotorsweplannedtousewheremuchsmaller. Ifwehadmoretime,wewouldagaingowithadifferentdesign.Themotorsattheir highestrpmsshaketheframe,toavoidthiswewouldmaketheangledassembly attachedtothemotorsmuchbiggerandextenditpastthemotors.anothersolution wewantedtotrywasshockabsorbersonthebaseandonthemotorsthemselves. Whenwetriedtochangethepositionofthemotorstocreatedifferenttypesofspin ontheballthemotorsdidnotexactlylineupandtheballwouldgofromonewheel totheother,thisendedwiththeballspinninginseveraldirectionsmakingit difficulttocatch.inordertoavoidthiswewouldcalculatethenecessarydistance andadjustthemotorsaccordingly.thismayhavetobesituationspecificduringuse. Theentirelauncherisparticularlyheavyanddifficulttomovearound,thisis somethingweplannedforintheoriginaldesignbutdidnothavetimetoaddtoour seconddesign.thebasewouldbedesignedtodetachandcarryseparately,andthey wouldaddwheelstotheendsofthebasetoallowtheusertomovethelauncher withlittleeffort.

17 VelocityaTrajectoryCalculations Image2.1

18 Table2.1 constant' R'(wheel)' 0.127' meter' Gravity' :9.8' m/s' RPM'of'motor' 3500' '' enter'angle'of'guide=θ' 10' degree' Inputs' enter'angle'of'left'wheel=α1' 35' degree' enter'angle'of'right'wheel=α2' 0' degree' Hight'of'launcher' 1' meter' ball'radius' 0.09' meter' ω=(2*π*rpm)/60' ' rad/sec' Vtan=ω*r' ' m/s' Vx'of'left'wheel=cos(α1)*Vtan' ' m/s' Vy'of'left'wheel=sin(α1)*Vtan' ' m/s' Vx''of'right'wheel=cos(α2)*Vtan' ' m/s' Vy'of'right'wheel=sin(α2)*Vtan' 0' m/s' Outputs' intial'velocity'of'ball=vi=max'vx' ' m/s' tanget'velocity'of'ball=max'vy' ' m/s' spin'of'ball=(vy*60)/(rball*2π)' ' rpm' Vh=horizontal'velocity=cos(θ)*vi' ' m/s' Vv=vertical'velocity=sin(θ)*vi' ' m/s' time' ' sec' distance=vh*(t)' ' meter' Thegroupmadeaspreadsheettocalculateandplotthetrajectoryoftheballafterit leavesthelauncherbecauseoftheadjustabilityoftherugbyballlauncherthereare manyfactorsthatgointocalculatingtheflightpathoftheballafteritleavesthe launcher.

19 Image2.2 Table2.1startswiththeconstantsofthelauncher,whicharethewheeldiameter andgravity.thenitasksfortheinputs(rpmofmotor,angleofguide,angleofleft wheel,angleofrightwheel,heightoflauncher)theseinputsareusedtocalculatethe trajectoryoftheballthelocationoftheinputscanbeseenonimage2.2. Firstitcalculatestheangularvelocityinradianspersecondusingtheequation below = (2 "#)/60

20 Image'2.3' This'angular'velocity'is'then'used'to'find'the'tangent'velocity'of'the'wheel'at'the'point' that'it'will'strike'the'ball'this'can'be'seen'in'image'2.3.'the'two'tangent'velocities'look' like'different'magnitudes'but'they'are'not.'the'tangent'velocities'are'just'at'different' angles'because'of'the'change'in'angle'of'the'wheel.'using'the'equation'below'with'the'r' being'the'radius'of'the'wheel'we'are'able'to'find'the'tangent'velocity'at'each'side'of'the' ball.' "# = ω r '

21 Image2.4 TheCalculatedVtangentisthenbrokendownintoitscomponentsvelocityinthe lateraldirectionvxandvelocityintheverticaldirectionvydependingontheangleof thewheelandthetangentvelocitythesecomponentscanbeseeninimage2.4.the VxandVywillbecalculatedforbothwheels.Theangleofthewheelisinrelationto theangleoftheguide,whichcanbeseenonimage2.4. = "#() "# = "#() "#

22 Image2.5 VxisthenusedastheinitialvelocityoftheballasitleavestheguideandVyisused asthetangentvelocityoftheball,whichcanbeseeninimage2.5.thetangent velocityoftheballisthenusedtocalculatetherpmofthespinoftheballwiththe equationbelow. spinofball = (V 60)/(r "## 2π)

23 Image2.6 Usingtheinitialvelocityoftheballandtheangleoftheguidewhichisinreference tothebasewhichisparalleltothegroundwhichcanbeseeninimage2.6through thisweareabletocalculatethecomponentsofthevelocityintheverticaland horizontaldirection. = cos(θ) = sin(θ) Theverticalvelocityisusedtocalculatethetimetheballistravelingintheairwith theequationbelow. 0 = "#$%h"#h = ± 4. 5 "#$%h"#h 2. 5g Thehorizontalvelocityandthetimeisthenusedtocalculatethedistancetraveled usingtheequationbelow. distance = (t)

24 Thisgivewheretheballwilllandbuttobeabletopredictwherethepersonwill standtocatchtheballweneededtomakeagraphoftheheightversusthedistance oftheballtodothiswemadeatabletocalculatetheheightanddistanceevery.1 second.giveninthetablebelow. Table 1.2 t'sec calculated'value'y' (meter) y'meter calculated'value'x'(meter) x'meter ' ' ' : On'Ground This is then put into a graph that can be seen in figure 2.1 below to show the flight pattern of the ball after it leaves the launcher.

25 Figure 2.1 Flight'Pattern' vertical'hieght'(meters)' Horizontal'Distance'Traveled'(meters)' The inputs on table 2.1 can be changed to get the desired distance and height for example to get a relatively short pass flatter more direct pass can be achieved by lowering the guide angle and increasing the RPMs of the motors and the angle wheel can be decreased like in table 2.3 to make the flight path have less of an arch. This can be seen in figure 2.2 below. If the desired height to catch the ball is approximately 1.4 meters off the ground and the pass has to go 20 meters before the player catches it then then the launcher will be passing the ball with the motors at there max speed of 3500 RPM and a short guide angle of 4 degrees with a small wheel angle of 5 degrees giving it a slower spin of 430 revolutions per minute. This will give the flight of the ball a max height of 1.53 meters and at 20 meters away the ball is 1.4 meters above the ground. Which are the desired results for a perfect pass.

26 Table 2.3 constant Inputs Outputs R'(wheel)' meter' Gravity' :9.8 m/s' RPM'of'motor' 3500 '' enter'angle'of'guide=θ' 4 degree' enter'angle'of'left'wheel=α1' 5 degree' enter'angle'of'right'wheel=α2' 0 degree' Hight'of'launcher' 1 meter' ball'radius' 0.09 meter' ω=(2*π*rpm)/60' rad/sec' Vtan=ω*r' m/s' Vx'of'left'wheel=cos(α1)*Vtan' m/s' Vy'of'left'wheel=sin(α1)*Vtan' m/s' Vx''of'right'wheel=cos(α2)*Vtan' m/s' Vy'of'right'wheel=sin(α2)*Vtan' 0 m/s' intial'velocity'of'ball=vi=max'vx' ' m/s' tanget'velocity'of'ball=max'vy' m/s' spin'of'ball=(vy*60)/(rball*2π)' rpm' Vh=horizontal'velocity=cos(θ)*vi' m/s' Vv=vertical'velocity=sin(θ)*vi' m/s' time' sec' distance=vh*(t)' meter' Table 2.4 t' sec' calculated' value'y' (meter)' y'meter' calculated' value'x' (meter)' x'meter' 0' 1' 1' 0.00' 0.00' 0.1' ' ' 4.64' 4.64' 0.2' ' ' 9.29' 9.29' 0.3' ' ' 13.93' 13.93' 0.4' ' ' 18.57' 18.57' 0.5' ' ' 23.22' 23.22' 0.6' ' ' 27.86' 27.86' 0.7' ' ' 32.50' 32.50' 0.8' ' ' 37.15' 37.15'

27 Figure 2.2 Flight'Pattern' vertical'hieght'(meters)' Horizontal'Distance'Traveled'(meters)'

28 DragandLift FindingdragandliftforceactingontheballandMagnuseffect Thedragandliftforcecanbecalculatedbyusingtheformulabelow = ""#$% 2 = "#$% = "#$$%%#&' = "#$%&'"#""#$% = "#$%&'( = "#"#$%&' TocalculatetheSurfaceareaeffectedbythedragandliftcoefficientwehadtouse thedimensionsofaninternationalrugbyballwhichwasacquiredthroughtherugby unionlawswhichcanbeseeninimage3.1. Image3.1

29 Image3.2 Referenceimage3.2fordecidingwhichdimensionisAandBontheballtheshorter radiusisalwaysbforthesurfaceareaofanellipsoid. circumference = π Diameter = ("#/)/2 =." /2 = meters =.15meters m = sqrt(1 (B/A)^2) m=sqrt(1?( /.15)^2) m= meters Surfacearea = 2 pi Surfacearea = 6.09meters arcsin ^2 EffectedSurfacearea = 3.045meter Thisisbecausetheairresistancewillonlybe actingonhalftheballasitfliesthroughtheairbecauseafterthatitgetsoverthe curve of the ball there will actually be a significant drop in pressure causing cavitation. Thevelocitycanbetakenfromtable2.1 TheCoefficeintofliftanddragisgiveninMartinPetersComputationalFluid DynamicsforSportSimulationonpages112?114.Thecalculatedforcescanbeseen

30 belowintable3.1. Table3.1 θ' Drag' Coefficient' Lift' Coefficient' Drag'force' (N)' Lift'Force'(N)' 0' 0.18' 0' ' 0' 1' 0.183' 0.01' ' ' 2' 0.186' 0.02' ' ' 3' 0.189' 0.03' ' ' 4' 0.192' 0.04' ' ' 5' 0.195' 0.05' ' ' 6' 0.198' 0.06' ' ' 7' 0.201' 0.07' ' ' 8' 0.204' 0.08' ' ' 9' 0.207' 0.09' ' ' 10' 0.21' 0.1' ' ' 11' 0.212' 0.108' ' ' 12' 0.214' 0.116' ' ' 13' 0.216' 0.124' ' ' 14' 0.218' 0.132' ' ' 15' 0.22' 0.14' ' ' 16' 0.222' 0.148' ' ' 17' 0.224' 0.156' ' ' 18' 0.226' 0.164' ' ' 19' 0.228' 0.172' ' ' 20' 0.23' 0.18' ' ' 21' 0.237' 0.19' ' ' 22' 0.244' 0.2' ' ' 23' 0.251' 0.21' ' ' 24' 0.258' 0.22' ' ' 25' 0.265' 0.23' ' ' 26' 0.272' 0.24' ' ' 27' 0.279' 0.25' ' ' 28' 0.286' 0.26' ' ' 29' 0.293' 0.27' ' ' 30' 0.3' 0.28' ' ' 31' ' 0.288' ' ' 32' 0.319' 0.296' ' ' 33' ' 0.304' ' ' 34' 0.338' 0.312' ' ' 35' ' 0.32' ' ' 36' 0.357' 0.328' ' '

31 37' ' 0.336' ' ' 38' 0.376' 0.344' ' ' 39' ' 0.352' ' ' 40' 0.395' 0.36' ' ' 41' ' 0.373' ' ' 42' 0.416' 0.386' ' ' 43' ' 0.399' ' ' 44' 0.437' 0.412' ' ' 45' ' 0.425' ' ' 46' 0.458' 0.438' ' ' 47' ' 0.451' ' ' 48' 0.479' 0.464' ' ' 49' ' 0.477' ' ' 50' 0.5' 0.49' ' ' 51' 0.511' 0.493' ' ' 52' 0.522' 0.496' ' ' 53' 0.533' 0.499' ' ' 54' 0.544' 0.502' ' ' 55' 0.555' 0.505' ' ' 56' 0.566' 0.508' ' ' 57' 0.577' 0.511' ' ' 58' 0.588' 0.514' ' ' 59' 0.599' 0.517' ' ' 60' 0.61' 0.52' ' ' 61' 0.617' 0.521' ' ' 62' 0.624' 0.522' ' ' 63' 0.631' 0.523' ' ' 64' 0.638' 0.524' ' ' 65' 0.645' 0.525' ' ' 66' 0.652' 0.526' ' ' 67' 0.659' 0.527' ' ' 68' 0.666' 0.528' ' ' 69' 0.673' 0.529' ' ' 70' 0.68' 0.53' ' ' 71' 0.673' 0.515' ' ' 72' 0.666' 0.5' ' ' 73' 0.659' 0.485' ' ' 74' 0.652' 0.47' ' ' 75' 0.645' 0.455' ' ' 76' 0.638' 0.44' ' ' 77' 0.631' 0.425' ' '

32 78' 0.624' 0.41' ' ' 79' 0.617' 0.395' ' ' 80' 0.61' 0.38' ' ' Thiscanthenbeusedtoadjustthetrajectoryoftheballdependingontheangleof theguide. Westillneedtheaccelerationoftheballtofinditsforcetocalculatehowmuchthe ballisactuallybeingeffectedbyairresistance. WewillalsohavetotakeintoconsiderationtheManguseffectbecauseofthespiral ontheballcausingadifferenceinairpressureactingononesideoftheballcausing aslightcurveinthepassdependingonthedistanceandrpmoftheball.

33 DeflectionAnalysis Thedeflectionofthemotoratthecantileverfixedtothe15series13?inchbaris veryslightgiventheweightofthemotor.itisthesameinthexandydirection,but itisonlyonehundredofaninch.thistellsusthemotorswillrotatethebarout slightly.thiscanbeseenintable4.1 Table ;ULSCantileverMiddle' Variables Measurements Units ' ' ' ' Profile'Length' 13' in' ' Maximum'Length'of'Profile' 242' in' D'='(L^3*W)/(48*E*I)' Profile'load' 30' lbs' Profile'weight/foot' 0.936' lbs' ' Deflection'x' ' ' Cross'Sectional'Area' 0.781' in^2' Moment'of'Inertia'X' ' in^4' ' Deflection'y' ' ' Moment'of'Inertia'Y' ' in^4' Yield'Strength'' 35000' lbs/in^2' ' ' Modulus'of'elasticity' ' lbs/in^2' ' ' ' ' Next,wecalculatedthedeflectionofthesamebarbutfixedatbothends.Themotor restinginthecenterasasingleload.thedeflectionisagainthesameinthexandy direction,butatseventensthousandsaninch.thebarwilldeflecttowardsthe groundattheplacementofthemotorbutonlyslightly.thiscanbeseenintable4.2 Table ;ULSFixed2Ends' Variables Measurements Units ' ' Profile'Length' 13' in' ' ' Maximum'Length'of'Profile' 242' in' ' D'='(L^3*W)/(48*E*I)' ' Profile'load' 30' lbs' Profile'weight/foot' 0.936' lbs' ' Deflection'x' ' ' Cross'Sectional'Area' 0.781' in^2' Moment'of'Inertia'X' ' in^4' ' Deflection'y' ' ' Moment'of'Inertia'Y' ' in^4' Yield'Strength'' 35000' lbs/in^2' ' ' Modulus'of'elasticity' ' lbs/in^2' ' ' ' '

34 Next,wecalculatedthedeflectionofthe15series15.776inchbarswiththeweight ateachendofthebarsbutfixedinthecenter.thebarswillhavesomedeflectionin thexandydirectionboththesame2hundredofaninch.theweightofthemotors atthefurthestpointonthebarswilldeflectslightlytowardstheground.thiscanbe seenintable4.3 Table ;ULSCantileverends' Variables Measurements Units ' ' Profile'Length' ' in' ' ' Maximum'Length'of'Profile' 242' in' ' D'='(L^3*W)/(3*E*I)' ' Profile'load' 30' lbs' ' Deflection' ' Profile'weight/foot' 0.936' lbs' x' ' Cross'Sectional'Area' 0.781' in^2' ' Deflection' ' Moment'of'Inertia'X' ' in^4' y' ' Moment'of'Inertia'Y' ' in^4' Yield'Strength'' 35000' lbs/in^2' ' ' Modulus'of'elasticity' ' lbs/in^2' ' ' ' '

35 AcquiredComponents Image5.1 Wehavepurchasedtherequiredfootageofbarsfrom80?20seeninImage5.1

36 Image5.2 Wehavetwo10indiameter2inthicksolidrubberwheelsthatneedtohavethe bearingsweldedtokeepthemsteadywiththemotorshaft.seeimage5.2.

37 Image5.3 ThisisourThreePhaseinductionmotortoturnthewheels(Image5.3)ithas 3500rpm.5hpwitha5/8indiametershaft.Weareworkingonthecircuitdiagrams forthewiringonallelectricalcomponents.wehopetohavethemotorandvariable frequencyacdrive(image5.4).motorschematicswillbeattachedatendofreport.

38 Image5.4 ThisisthevariablefrequencyACdriveitwillconverttheDCinputintoaACoutput forthemotorandalsoallowustovarythespeedofthemotorwithaspeedcontrol. SeeImage5.4.

39 Assembly Image6.1 The80?2015seriesbarshavebeencuttotheneededsizethe3.5inchbarsseenin image1.12havealsobeentapedwitha5/16tap,andthe15?30seriesbarhashad allholestapedwitha5/16tap.cutthree3?footbarswith45?degreeanglesonthe toptoattachtothebasetocreatethetripod.

40 Image6.2 ThemotorsseeninImage5.3havebeenwiredtoaspeedcontrolwhichis connectedtothevariablefrequencyacdrive(image5.4),whichisthenconnected toapowersourcethisassemblycanbeseeninimage6.2.

41 Image6.3 Thisisthefinishedassembly.Itisplacedonatripodsupportedby2X4woodboards topreventthebarsfrommovingatall.theangleofthelauncherischangedby crewingupanddownonthethreadedrodsonbothsidesofthefrontproviding supporttothemotors.thewheelsanglescanalsobechangedandthedistance betweenthewheelscanbeextendedandreduceddependingonthesizeoftheball. Theassemblydoeseverythingthatweneeditto.

42 GannttChart Plan Actual didn't,do 1/1/17 1/8/17 1/15/17 1/22/17 1/29/17 2/5/17 2/12/17 2/19/17 2/26/17 3/5/17 3/12/17 3/19/17 3/26/17 4/2/17 4/9/17 4/16/17 4/23/17 Form,group Find,project Write,proposal find,motor create,parts, list,from,80/20 complete, velocity, calculations Order,wheels order,80/20, parts Machine,Bars Assemble, electrical, components Weld,Wheels create,speed, marks,on, speed,control Assemble, Launcher Test,Launcher

43 TestingObservations Ourtestingstartedoutverywellthelauncherwasabletolaunchsmall20meter passeswithconstantprecisionwithaleftandrightspiraldependingonwhich wheelwasatanangle.itconsistentlyhookedtowhicheverside swheelwastilted. Werealizedthisisbecauseithitsthewheelsatdifferenttimessotheballactually shootsawayfromtheflatwheelbecauseitisactuallyalmostaninchaheadofthe tiltedwheel. Aswespedupthelaunchertoahigherrpmwerealizedthewheelsweren tperfectly circularcausingcentrifugalforceonthemotorsandmakesthembegintovibrate evenwiththespacersweputontopreventthat.asweacceleratedtherevolutions ofthemotorstheassemblywouldbegintovibrateatthehinge.thiscausedtheball tobegintoshakeandbounceontheguideplatemakingitnearlyimpossibletofeed theballstraightthroughthewheels.thismadeitsowecouldnotlaunchtheballat thehighspeedsthatwewantedandstillgetacleanspiral.theballwouldflyout veryhardbutinanerraticandunpredictablespiral. Wealsorealizedafterlaunchingasmallamountofballsthemotorsanglelocking systemwouldbecomeloosefromthevibrationandimpactandwouldstarttotryto settlebacktoparallelwiththebase.thiscausedustohavetoretightenourlocking systemeveryfewlaunches. AswewerestartingtoactuallyrecordourteststhevariablefrequencyACdrive seeninimage5.4failedduetoashortcircuiterrorindicatedbyaflashingredlight. WetriedtocorrecttheproblemandfriedthevariablefrequencyACdriveultimately endingourtesting. TestingAssessment TheRugbyBallLauncherworkedatlowspeedsverywellandlaunchedconsistent spirals.highspeedscausevibrationsinourassemblyandmakeiterratic. PossibleImprovements Wewouldconsiderthisagoodprototype.Withmoretimewecouldmakemany improvementstothisproject.wewouldliketousehydrauliccylinderstochange theanglebecausetheywillmovefasterandwontfalldownaftermultiplelaunches theywouldalsobeabletorotatefreelywheretherodsgetstuckatthehigher degrees.wewouldalsomakethehingeandslidingactionmorestabletoprevent somevibratingwhilealsomakingthebasebiggertoencompassthemotorsandhold themsteady.anotherchangewewouldmakeisapeggingsystemwiththemotors angletopreventslip.andalsomakesurethatthewheelslineupwhentheyare rotatedstilltopreventtheballfromcomingouttoonesideortheotherdepending onwhichwheelisatanangle.alsoifweusedlargerwheelsthenwewouldn'tneed asmanyrpmsfromthemotorssothemotorscouldbesmaller.another improvementwouldbehavingdcmotorssowewouldn tneedthevariable frequencyacdriveseeninimage5.4becausethecomponentsinthecircuitare opentotheelementsandwiththisbeingconsideredsportingequipmentithastobe abletowithstandabitofmistreatment.

44 Conclusion Wemademanyimprovementsthroughoutourconstructionandformationofour seniordesignprojectandusedmanyskillslearnedindynamicsclasswhilecreating atrajectorypathfortheballsflightpattern.wealsousedmachiningskillslearnedin basicmachiningtoconstructthefinalassembly.andweusedtheskillslearnedin strengthsandmaterialstocalculateourdeflectionofthematerialsunderthestress ofthemotors.thisprojectusedmanyskillslearnedthroughoutbothofour educationalcareersatipfw. References (1)Peters,Martin.Computationalfluiddynamicsforsportsimulation.Springer, (2)Beer,JohnstonandFlori.MechanicsforEngineers,Dynamics.FifthAddition, December3,2007

Robust Network Interdiction with Invisible Interdiction Assets

Robust Network Interdiction with Invisible Interdiction Assets University of Arkansas, Fayetteville ScholarWorks@UARK Theses and Dissertations 5-2014 Robust Network Interdiction with Invisible Interdiction Assets Nail Orkun Baycik University of Arkansas, Fayetteville

Διαβάστε περισσότερα

Development and Verification of Multi-Level Sub- Meshing Techniques of PEEC to Model High- Speed Power and Ground Plane-Pairs of PFBS

Development and Verification of Multi-Level Sub- Meshing Techniques of PEEC to Model High- Speed Power and Ground Plane-Pairs of PFBS Rose-Hulman Institute of Technology Rose-Hulman Scholar Graduate Theses - Electrical and Computer Engineering Graduate Theses Spring 5-2015 Development and Verification of Multi-Level Sub- Meshing Techniques

Διαβάστε περισσότερα

the total number of electrons passing through the lamp.

the total number of electrons passing through the lamp. 1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy

Διαβάστε περισσότερα

Review Test 3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Review Test 3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Review Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. 1) sin - 11π 1 1) + - + - - ) sin 11π 1 ) ( -

Διαβάστε περισσότερα

Calculating the propagation delay of coaxial cable

Calculating the propagation delay of coaxial cable Your source for quality GNSS Networking Solutions and Design Services! Page 1 of 5 Calculating the propagation delay of coaxial cable The delay of a cable or velocity factor is determined by the dielectric

Διαβάστε περισσότερα

UDZ Swirl diffuser. Product facts. Quick-selection. Swirl diffuser UDZ. Product code example:

UDZ Swirl diffuser. Product facts. Quick-selection. Swirl diffuser UDZ. Product code example: UDZ Swirl diffuser Swirl diffuser UDZ, which is intended for installation in a ventilation duct, can be used in premises with a large volume, for example factory premises, storage areas, superstores, halls,

Διαβάστε περισσότερα

Rational Ligand Design for Potential Applications in Transition Metal Catalysis

Rational Ligand Design for Potential Applications in Transition Metal Catalysis University of Missouri, St. Louis IRL @ UMSL Dissertations UMSL Graduate Works 10-25-2011 Rational Ligand Design for Potential Applications in Transition Metal Catalysis Sergey L. Sedinkin University of

Διαβάστε περισσότερα

Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1

Main source: Discrete-time systems and computer control by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1 Main source: "Discrete-time systems and computer control" by Α. ΣΚΟΔΡΑΣ ΨΗΦΙΑΚΟΣ ΕΛΕΓΧΟΣ ΔΙΑΛΕΞΗ 4 ΔΙΑΦΑΝΕΙΑ 1 A Brief History of Sampling Research 1915 - Edmund Taylor Whittaker (1873-1956) devised a

Διαβάστε περισσότερα

Assalamu `alaikum wr. wb.

Assalamu `alaikum wr. wb. LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump

Διαβάστε περισσότερα

«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE

«ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE «ΨΥΧΙΚΗ ΥΓΕΙΑ ΚΑΙ ΣΕΞΟΥΑΛΙΚΗ» ΠΑΝΕΥΡΩΠΑΪΚΗ ΕΡΕΥΝΑ ΤΗΣ GAMIAN- EUROPE We would like to invite you to participate in GAMIAN- Europe research project. You should only participate if you want to and choosing

Διαβάστε περισσότερα

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11

Potential Dividers. 46 minutes. 46 marks. Page 1 of 11 Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and

Διαβάστε περισσότερα

Reforming the Regulation of Political Advocacy by Charities: From Charity Under Siege to Charity Under Rescue?

Reforming the Regulation of Political Advocacy by Charities: From Charity Under Siege to Charity Under Rescue? Chicago-Kent Law Review Volume 91 Issue 3 Nonprofit Oversight Under Siege Article 9 7-1-2015 Reforming the Regulation of Political Advocacy by Charities: From Charity Under Siege to Charity Under Rescue?

Διαβάστε περισσότερα

10/3/ revolution = 360 = 2 π radians = = x. 2π = x = 360 = : Measures of Angles and Rotations

10/3/ revolution = 360 = 2 π radians = = x. 2π = x = 360 = : Measures of Angles and Rotations //.: Measures of Angles and Rotations I. Vocabulary A A. Angle the union of two rays with a common endpoint B. BA and BC C. B is the vertex. B C D. You can think of BA as the rotation of (clockwise) with

Διαβάστε περισσότερα

Section 8.2 Graphs of Polar Equations

Section 8.2 Graphs of Polar Equations Section 8. Graphs of Polar Equations Graphing Polar Equations The graph of a polar equation r = f(θ), or more generally F(r,θ) = 0, consists of all points P that have at least one polar representation

Διαβάστε περισσότερα

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)

Phys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required) Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts

Διαβάστε περισσότερα

DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.

DESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0. DESIGN OF MACHINERY SOLUTION MANUAL -7-1! PROBLEM -7 Statement: Design a double-dwell cam to move a follower from to 25 6, dwell for 12, fall 25 and dwell for the remader The total cycle must take 4 sec

Διαβάστε περισσότερα

Οδηγίες Αγοράς Ηλεκτρονικού Βιβλίου Instructions for Buying an ebook

Οδηγίες Αγοράς Ηλεκτρονικού Βιβλίου Instructions for Buying an ebook Οδηγίες Αγοράς Ηλεκτρονικού Βιβλίου Instructions for Buying an ebook Βήμα 1: Step 1: Βρείτε το βιβλίο που θα θέλατε να αγοράσετε και πατήστε Add to Cart, για να το προσθέσετε στο καλάθι σας. Αυτόματα θα

Διαβάστε περισσότερα

Approximation of distance between locations on earth given by latitude and longitude

Approximation of distance between locations on earth given by latitude and longitude Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth

Διαβάστε περισσότερα

Decision-Making in the Dark: How Pre-Trial Errors Change the Narrative in Criminal Jury Trials

Decision-Making in the Dark: How Pre-Trial Errors Change the Narrative in Criminal Jury Trials Chicago-Kent Law Review Volume 90 Issue 3 Juries and Lay Participation: American Perspectives and Global Trends Article 8 6-23-2015 Decision-Making in the Dark: How Pre-Trial Errors Change the Narrative

Διαβάστε περισσότερα

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1

Practice Exam 2. Conceptual Questions. 1. State a Basic identity and then verify it. (a) Identity: Solution: One identity is csc(θ) = 1 Conceptual Questions. State a Basic identity and then verify it. a) Identity: Solution: One identity is cscθ) = sinθ) Practice Exam b) Verification: Solution: Given the point of intersection x, y) of the

Διαβάστε περισσότερα

derivation of the Laplacian from rectangular to spherical coordinates

derivation of the Laplacian from rectangular to spherical coordinates derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used

Διαβάστε περισσότερα

Section 8.3 Trigonometric Equations

Section 8.3 Trigonometric Equations 99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο

Διαβάστε περισσότερα

Section 9.2 Polar Equations and Graphs

Section 9.2 Polar Equations and Graphs 180 Section 9. Polar Equations and Graphs In this section, we will be graphing polar equations on a polar grid. In the first few examples, we will write the polar equation in rectangular form to help identify

Διαβάστε περισσότερα

Volume of a Cuboid. Volume = length x breadth x height. V = l x b x h. The formula for the volume of a cuboid is

Volume of a Cuboid. Volume = length x breadth x height. V = l x b x h. The formula for the volume of a cuboid is Volume of a Cuboid The formula for the volume of a cuboid is Volume = length x breadth x height V = l x b x h Example Work out the volume of this cuboid 10 cm 15 cm V = l x b x h V = 15 x 6 x 10 V = 900cm³

Διαβάστε περισσότερα

Study on Re-adhesion control by monitoring excessive angular momentum in electric railway traction

Study on Re-adhesion control by monitoring excessive angular momentum in electric railway traction () () Study on e-adhesion control by monitoring excessive angular momentum in electric railway traction Takafumi Hara, Student Member, Takafumi Koseki, Member, Yutaka Tsukinokizawa, Non-member Abstract

Διαβάστε περισσότερα

Homework 3 Solutions

Homework 3 Solutions Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For

Διαβάστε περισσότερα

Lifting Entry (continued)

Lifting Entry (continued) ifting Entry (continued) Basic planar dynamics of motion, again Yet another equilibrium glide Hypersonic phugoid motion Planar state equations MARYAN 1 01 avid. Akin - All rights reserved http://spacecraft.ssl.umd.edu

Διαβάστε περισσότερα

The Nottingham eprints service makes this work by researchers of the University of Nottingham available open access under the following conditions.

The Nottingham eprints service makes this work by researchers of the University of Nottingham available open access under the following conditions. Luevorasirikul, Kanokrat (2007) Body image and weight management: young people, internet advertisements and pharmacists. PhD thesis, University of Nottingham. Access from the University of Nottingham repository:

Διαβάστε περισσότερα

EE512: Error Control Coding

EE512: Error Control Coding EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3

Διαβάστε περισσότερα

Problem Set 9 Solutions. θ + 1. θ 2 + cotθ ( ) sinθ e iφ is an eigenfunction of the ˆ L 2 operator. / θ 2. φ 2. sin 2 θ φ 2. ( ) = e iφ. = e iφ cosθ.

Problem Set 9 Solutions. θ + 1. θ 2 + cotθ ( ) sinθ e iφ is an eigenfunction of the ˆ L 2 operator. / θ 2. φ 2. sin 2 θ φ 2. ( ) = e iφ. = e iφ cosθ. Chemistry 362 Dr Jean M Standard Problem Set 9 Solutions The ˆ L 2 operator is defined as Verify that the angular wavefunction Y θ,φ) Also verify that the eigenvalue is given by 2! 2 & L ˆ 2! 2 2 θ 2 +

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:

HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch: HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying

Διαβάστε περισσότερα

Εγκατάσταση λογισμικού και αναβάθμιση συσκευής Device software installation and software upgrade

Εγκατάσταση λογισμικού και αναβάθμιση συσκευής Device software installation and software upgrade Για να ελέγξετε το λογισμικό που έχει τώρα η συσκευή κάντε κλικ Menu > Options > Device > About Device Versions. Στο πιο κάτω παράδειγμα η συσκευή έχει έκδοση λογισμικού 6.0.0.546 με πλατφόρμα 6.6.0.207.

Διαβάστε περισσότερα

Approach: Romancing the Inanimate

Approach: Romancing the Inanimate Georgia State University ScholarWorks @ Georgia State University Art and Design Theses Ernest G. Welch School of Art and Design Summer 8-1-2013 Approach: Romancing the Inanimate Julia Gray Hines Georgia

Διαβάστε περισσότερα

Διπλωματική Εργασία του φοιτητή του Τμήματος Ηλεκτρολόγων Μηχανικών και Τεχνολογίας Υπολογιστών της Πολυτεχνικής Σχολής του Πανεπιστημίου Πατρών

Διπλωματική Εργασία του φοιτητή του Τμήματος Ηλεκτρολόγων Μηχανικών και Τεχνολογίας Υπολογιστών της Πολυτεχνικής Σχολής του Πανεπιστημίου Πατρών ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ:ΗΛΕΚΤΡΟΝΙΚΗΣ ΚΑΙ ΥΠΟΛΟΓΙΣΤΩΝ ΕΡΓΑΣΤΗΡΙΟ ΗΛΕΚΤΡΟΝΙΚΩΝ ΕΦΑΡΜΟΓΩΝ Διπλωματική Εργασία του φοιτητή του Τμήματος Ηλεκτρολόγων

Διαβάστε περισσότερα

Δημιουργία Λογαριασμού Διαχείρισης Business Telephony Create a Management Account for Business Telephony

Δημιουργία Λογαριασμού Διαχείρισης Business Telephony Create a Management Account for Business Telephony Δημιουργία Λογαριασμού Διαχείρισης Business Telephony Create a Management Account for Business Telephony Ελληνικά Ι English 1/7 Δημιουργία Λογαριασμού Διαχείρισης Επιχειρηματικής Τηλεφωνίας μέσω της ιστοσελίδας

Διαβάστε περισσότερα

DuPont Suva 95 Refrigerant

DuPont Suva 95 Refrigerant Technical Information T-95 ENG DuPont Suva refrigerants Thermodynamic Properties of DuPont Suva 95 Refrigerant (R-508B) The DuPont Oval Logo, The miracles of science, and Suva, are trademarks or registered

Διαβάστε περισσότερα

EE 570: Location and Navigation

EE 570: Location and Navigation EE 570: Location and Navigation INS Initialization Aly El-Osery Kevin Wedeward Electrical Engineering Department, New Mexico Tech Socorro, New Mexico, USA In Collaboration with Stephen Bruder Electrical

Διαβάστε περισσότερα

is like multiplying by the conversion factor of. Dividing by 2π gives you the

is like multiplying by the conversion factor of. Dividing by 2π gives you the Chapter Graphs of Trigonometric Functions Answer Ke. Radian Measure Answers. π. π. π. π. 7π. π 7. 70 8. 9. 0 0. 0. 00. 80. Multipling b π π is like multipling b the conversion factor of. Dividing b 0 gives

Διαβάστε περισσότερα

Homework 8 Model Solution Section

Homework 8 Model Solution Section MATH 004 Homework Solution Homework 8 Model Solution Section 14.5 14.6. 14.5. Use the Chain Rule to find dz where z cosx + 4y), x 5t 4, y 1 t. dz dx + dy y sinx + 4y)0t + 4) sinx + 4y) 1t ) 0t + 4t ) sinx

Διαβάστε περισσότερα

EE101: Resonance in RLC circuits

EE101: Resonance in RLC circuits EE11: Resonance in RLC circuits M. B. Patil mbatil@ee.iitb.ac.in www.ee.iitb.ac.in/~sequel Deartment of Electrical Engineering Indian Institute of Technology Bombay I V R V L V C I = I m = R + jωl + 1/jωC

Διαβάστε περισσότερα

Strain gauge and rosettes

Strain gauge and rosettes Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified

Διαβάστε περισσότερα

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds!

b. Use the parametrization from (a) to compute the area of S a as S a ds. Be sure to substitute for ds! MTH U341 urface Integrals, tokes theorem, the divergence theorem To be turned in Wed., Dec. 1. 1. Let be the sphere of radius a, x 2 + y 2 + z 2 a 2. a. Use spherical coordinates (with ρ a) to parametrize.

Διαβάστε περισσότερα

Schedulability Analysis Algorithm for Timing Constraint Workflow Models

Schedulability Analysis Algorithm for Timing Constraint Workflow Models CIMS Vol.8No.72002pp.527-532 ( 100084) Petri Petri F270.7 A Schedulability Analysis Algorithm for Timing Constraint Workflow Models Li Huifang and Fan Yushun (Department of Automation, Tsinghua University,

Διαβάστε περισσότερα

ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. «Προστασία ηλεκτροδίων γείωσης από τη διάβρωση»

ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ. «Προστασία ηλεκτροδίων γείωσης από τη διάβρωση» ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΠΟΛΥΤΕΧΝΙΚΗ ΣΧΟΛΗ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΕΡΓΑΣΤΗΡΙΟ ΥΨΗΛΩΝ ΤΑΣΕΩΝ ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ «Προστασία ηλεκτροδίων

Διαβάστε περισσότερα

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ

ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΟΔΟΝΤΙΑΤΡΙΚΗΣ ΕΡΓΑΣΤΗΡΙΟ ΟΔΟΝΤΙΚΗΣ ΚΑΙ ΑΝΩΤΕΡΑΣ ΠΡΟΣΘΕΤΙΚΗΣ ΣΥΓΚΡΙΤΙΚΗ ΜΕΛΕΤΗ ΤΗΣ ΣΥΓΚΡΑΤΗΤΙΚΗΣ ΙΚΑΝΟΤΗΤΑΣ ΟΡΙΣΜΕΝΩΝ ΠΡΟΚΑΤΑΣΚΕΥΑΣΜΕΝΩΝ ΣΥΝΔΕΣΜΩΝ ΑΚΡΙΒΕΙΑΣ

Διαβάστε περισσότερα

Study of In-vehicle Sound Field Creation by Simultaneous Equation Method

Study of In-vehicle Sound Field Creation by Simultaneous Equation Method Study of In-vehicle Sound Field Creation by Simultaneous Equation Method Kensaku FUJII Isao WAKABAYASI Tadashi UJINO Shigeki KATO Abstract FUJITSU TEN Limited has developed "TOYOTA remium Sound System"

Διαβάστε περισσότερα

[1] P Q. Fig. 3.1

[1] P Q. Fig. 3.1 1 (a) Define resistance....... [1] (b) The smallest conductor within a computer processing chip can be represented as a rectangular block that is one atom high, four atoms wide and twenty atoms long. One

Διαβάστε περισσότερα

Daewoo Technopark A-403, Dodang-dong, Wonmi-gu, Bucheon-city, Gyeonggido, Korea LM-80 Test Report

Daewoo Technopark A-403, Dodang-dong, Wonmi-gu, Bucheon-city, Gyeonggido, Korea LM-80 Test Report LM-80 Test Report Approved Method: Measuring Lumen Maintenance of LED Light Sources Project Number: KILT1212-U00216 Date: September 17 th, 2013 Requested by: Dongbu LED Co., Ltd 90-1, Bongmyeong-Ri, Namsa-Myeon,

Διαβάστε περισσότερα

DuPont Suva 95 Refrigerant

DuPont Suva 95 Refrigerant Technical Information T-95 SI DuPont Suva refrigerants Thermodynamic Properties of DuPont Suva 95 Refrigerant (R-508B) The DuPont Oval Logo, The miracles of science, and Suva, are trademarks or registered

Διαβάστε περισσότερα

CHAPTER 12: PERIMETER, AREA, CIRCUMFERENCE, AND 12.1 INTRODUCTION TO GEOMETRIC 12.2 PERIMETER: SQUARES, RECTANGLES,

CHAPTER 12: PERIMETER, AREA, CIRCUMFERENCE, AND 12.1 INTRODUCTION TO GEOMETRIC 12.2 PERIMETER: SQUARES, RECTANGLES, CHAPTER : PERIMETER, AREA, CIRCUMFERENCE, AND SIGNED FRACTIONS. INTRODUCTION TO GEOMETRIC MEASUREMENTS p. -3. PERIMETER: SQUARES, RECTANGLES, TRIANGLES p. 4-5.3 AREA: SQUARES, RECTANGLES, TRIANGLES p.

Διαβάστε περισσότερα

Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων. Εξάμηνο 7 ο

Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων. Εξάμηνο 7 ο Εργαστήριο Ανάπτυξης Εφαρμογών Βάσεων Δεδομένων Εξάμηνο 7 ο Procedures and Functions Stored procedures and functions are named blocks of code that enable you to group and organize a series of SQL and PL/SQL

Διαβάστε περισσότερα

How to register an account with the Hellenic Community of Sheffield.

How to register an account with the Hellenic Community of Sheffield. How to register an account with the Hellenic Community of Sheffield. (1) EN: Go to address GR: Πηγαίνετε στη διεύθυνση: http://www.helleniccommunityofsheffield.com (2) EN: At the bottom of the page, click

Διαβάστε περισσότερα

Section 7.6 Double and Half Angle Formulas

Section 7.6 Double and Half Angle Formulas 09 Section 7. Double and Half Angle Fmulas To derive the double-angles fmulas, we will use the sum of two angles fmulas that we developed in the last section. We will let α θ and β θ: cos(θ) cos(θ + θ)

Διαβάστε περισσότερα

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β

3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β 3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle

Διαβάστε περισσότερα

Smaller. 6.3 to 100 After 1 minute's application of rated voltage at 20 C, leakage current is. not more than 0.03CV or 4 (µa), whichever is greater.

Smaller. 6.3 to 100 After 1 minute's application of rated voltage at 20 C, leakage current is. not more than 0.03CV or 4 (µa), whichever is greater. Low Impedance, For Switching Power Supplies Low impedance and high reliability withstanding 5000 hours load life at +05 C (3000 / 2000 hours for smaller case sizes as specified below). Capacitance ranges

Διαβάστε περισσότερα

ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS

ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS ΟΜΗΡΟΥ ΙΛΙΑΔΑ ΑΛΕΞΑΝΔΡΟΣ ΠΑΛΛΗΣ SCHOOLTIME E-BOOKS www.scooltime.gr [- 2 -] The Project Gutenberg EBook of Iliad, by Homer This ebook is for the use of anyone anywhere at no cost and with almost no restrictions

Διαβάστε περισσότερα

HISTOGRAMS AND PERCENTILES What is the 25 th percentile of a histogram? What is the 50 th percentile for the cigarette histogram?

HISTOGRAMS AND PERCENTILES What is the 25 th percentile of a histogram? What is the 50 th percentile for the cigarette histogram? HISTOGRAMS AND PERCENTILES What is the 25 th percentile of a histogram? The point on the horizontal axis such that of the area under the histogram lies to the left of that point (and to the right) What

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 24/3/2007

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 24/3/2007 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Όλοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα μικρότεροι του 10000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Αν κάπου κάνετε κάποιες υποθέσεις

Διαβάστε περισσότερα

Areas and Lengths in Polar Coordinates

Areas and Lengths in Polar Coordinates Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the

Διαβάστε περισσότερα

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006

ΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 6/5/2006 Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Ολοι οι αριθμοί που αναφέρονται σε όλα τα ερωτήματα είναι μικρότεροι το 1000 εκτός αν ορίζεται διαφορετικά στη διατύπωση του προβλήματος. Διάρκεια: 3,5 ώρες Καλή

Διαβάστε περισσότερα

Technical Information T-9100 SI. Suva. refrigerants. Thermodynamic Properties of. Suva Refrigerant [R-410A (50/50)]

Technical Information T-9100 SI. Suva. refrigerants. Thermodynamic Properties of. Suva Refrigerant [R-410A (50/50)] d Suva refrigerants Technical Information T-9100SI Thermodynamic Properties of Suva 9100 Refrigerant [R-410A (50/50)] Thermodynamic Properties of Suva 9100 Refrigerant SI Units New tables of the thermodynamic

Διαβάστε περισσότερα

DuPont Suva. DuPont. Thermodynamic Properties of. Refrigerant (R-410A) Technical Information. refrigerants T-410A ENG

DuPont Suva. DuPont. Thermodynamic Properties of. Refrigerant (R-410A) Technical Information. refrigerants T-410A ENG Technical Information T-410A ENG DuPont Suva refrigerants Thermodynamic Properties of DuPont Suva 410A Refrigerant (R-410A) The DuPont Oval Logo, The miracles of science, and Suva, are trademarks or registered

Διαβάστε περισσότερα

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016

Section 1: Listening and responding. Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Presenter: Niki Farfara MGTAV VCE Seminar 7 August 2016 Section 1: Listening and responding Section 1: Listening and Responding/ Aκουστική εξέταση Στο πρώτο μέρος της

Διαβάστε περισσότερα

Χρειάζεται να φέρω μαζί μου τα πρωτότυπα έγγραφα ή τα αντίγραφα; Asking if you need to provide the original documents or copies Ποια είναι τα κριτήρια

Χρειάζεται να φέρω μαζί μου τα πρωτότυπα έγγραφα ή τα αντίγραφα; Asking if you need to provide the original documents or copies Ποια είναι τα κριτήρια - University Θα ήθελα να εγγραφώ σε πανεπιστήμιο. Stating that you want to enroll Θα ήθελα να γραφτώ για. Stating that you want to apply for a course ένα προπτυχιακό ένα μεταπτυχιακό ένα διδακτορικό πλήρους

Διαβάστε περισσότερα

Η βραχόπτωση της 17/12/09 στα Στενά των Τεµπών, σε σχέση µε τις δονήσεις των ανατινάξεων διάνοιξης της νέας οδικής Σήραγγας

Η βραχόπτωση της 17/12/09 στα Στενά των Τεµπών, σε σχέση µε τις δονήσεις των ανατινάξεων διάνοιξης της νέας οδικής Σήραγγας Η βραχόπτωση της 17/12/09 στα Στενά των Τεµπών, σε σχέση µε τις δονήσεις των ανατινάξεων διάνοιξης της νέας οδικής Σήραγγας The rockfall of 17/12/09 at Tempi Valley in correlation to the blast vibrations

Διαβάστε περισσότερα

ΑΚΑ ΗΜΙΑ ΕΜΠΟΡΙΚΟΥ ΝΑΥΤΙΚΟΥ ΜΑΚΕ ΟΝΙΑΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ

ΑΚΑ ΗΜΙΑ ΕΜΠΟΡΙΚΟΥ ΝΑΥΤΙΚΟΥ ΜΑΚΕ ΟΝΙΑΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΑΚΑ ΗΜΙΑ ΕΜΠΟΡΙΚΟΥ ΝΑΥΤΙΚΟΥ ΜΑΚΕ ΟΝΙΑΣ ΣΧΟΛΗ ΜΗΧΑΝΙΚΩΝ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΘΕΜΑ :ΤΥΠΟΙ ΑΕΡΟΣΥΜΠΙΕΣΤΩΝ ΚΑΙ ΤΡΟΠΟΙ ΛΕΙΤΟΥΡΓΙΑΣ ΣΠΟΥ ΑΣΤΡΙΑ: ΕΥΘΥΜΙΑ ΟΥ ΣΩΣΑΝΝΑ ΕΠΙΒΛΕΠΩΝ ΚΑΘΗΓΗΤΗΣ : ΓΟΥΛΟΠΟΥΛΟΣ ΑΘΑΝΑΣΙΟΣ 1 ΑΚΑ

Διαβάστε περισσότερα

Advanced Subsidiary Unit 1: Understanding and Written Response

Advanced Subsidiary Unit 1: Understanding and Written Response Write your name here Surname Other names Edexcel GE entre Number andidate Number Greek dvanced Subsidiary Unit 1: Understanding and Written Response Thursday 16 May 2013 Morning Time: 2 hours 45 minutes

Διαβάστε περισσότερα

ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ. Ψηφιακή Οικονομία. Διάλεξη 7η: Consumer Behavior Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών

ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ. Ψηφιακή Οικονομία. Διάλεξη 7η: Consumer Behavior Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Ψηφιακή Οικονομία Διάλεξη 7η: Consumer Behavior Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών Τέλος Ενότητας Χρηματοδότηση Το παρόν εκπαιδευτικό υλικό έχει αναπτυχθεί

Διαβάστε περισσότερα

The Great Recession and the Pressure on Workplace Rights

The Great Recession and the Pressure on Workplace Rights Chicago-Kent Law Review Volume 88 Issue 2 The Supreme Court and the American Public Article 13 April 2013 The Great Recession and the Pressure on Workplace Rights Katherine S. Newman Follow this and additional

Διαβάστε περισσότερα

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3)

(1) Describe the process by which mercury atoms become excited in a fluorescent tube (3) Q1. (a) A fluorescent tube is filled with mercury vapour at low pressure. In order to emit electromagnetic radiation the mercury atoms must first be excited. (i) What is meant by an excited atom? (1) (ii)

Διαβάστε περισσότερα

Dynamic types, Lambda calculus machines Section and Practice Problems Apr 21 22, 2016

Dynamic types, Lambda calculus machines Section and Practice Problems Apr 21 22, 2016 Harvard School of Engineering and Applied Sciences CS 152: Programming Languages Dynamic types, Lambda calculus machines Apr 21 22, 2016 1 Dynamic types and contracts (a) To make sure you understand the

Διαβάστε περισσότερα

TMA4115 Matematikk 3

TMA4115 Matematikk 3 TMA4115 Matematikk 3 Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet Trondheim Spring 2010 Lecture 12: Mathematics Marvellous Matrices Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet

Διαβάστε περισσότερα

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού)

Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Οι αδελφοί Montgolfier: Ψηφιακή αφήγηση The Montgolfier Βrothers Digital Story (προτείνεται να διδαχθεί στο Unit 4, Lesson 3, Αγγλικά Στ Δημοτικού) Προσδοκώμενα αποτελέσματα Περιεχόμενο Ενδεικτικές δραστηριότητες

Διαβάστε περισσότερα

Queensland University of Technology Transport Data Analysis and Modeling Methodologies

Queensland University of Technology Transport Data Analysis and Modeling Methodologies Queensland University of Technology Transport Data Analysis and Modeling Methodologies Lab Session #7 Example 5.2 (with 3SLS Extensions) Seemingly Unrelated Regression Estimation and 3SLS A survey of 206

Διαβάστε περισσότερα

Fractional Colorings and Zykov Products of graphs

Fractional Colorings and Zykov Products of graphs Fractional Colorings and Zykov Products of graphs Who? Nichole Schimanski When? July 27, 2011 Graphs A graph, G, consists of a vertex set, V (G), and an edge set, E(G). V (G) is any finite set E(G) is

Διαβάστε περισσότερα

Appendix to On the stability of a compressible axisymmetric rotating flow in a pipe. By Z. Rusak & J. H. Lee

Appendix to On the stability of a compressible axisymmetric rotating flow in a pipe. By Z. Rusak & J. H. Lee Appendi to On the stability of a compressible aisymmetric rotating flow in a pipe By Z. Rusak & J. H. Lee Journal of Fluid Mechanics, vol. 5 4, pp. 5 4 This material has not been copy-edited or typeset

Διαβάστε περισσότερα

The Probabilistic Method - Probabilistic Techniques. Lecture 7: The Janson Inequality

The Probabilistic Method - Probabilistic Techniques. Lecture 7: The Janson Inequality The Probabilistic Method - Probabilistic Techniques Lecture 7: The Janson Inequality Sotiris Nikoletseas Associate Professor Computer Engineering and Informatics Department 2014-2015 Sotiris Nikoletseas,

Διαβάστε περισσότερα

MathCity.org Merging man and maths

MathCity.org Merging man and maths MathCity.org Merging man and maths Exercise 10. (s) Page Textbook of Algebra and Trigonometry for Class XI Available online @, Version:.0 Question # 1 Find the values of sin, and tan when: 1 π (i) (ii)

Διαβάστε περισσότερα

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΜΗΧΑΝΙΚΗΣ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ

ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΜΗΧΑΝΙΚΗΣ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΜΗΧΑΝΙΚΗΣ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ Πτυχιακή Διατριβή ΑΥΤΟΝΟΜΟ ΣΥΣΤΗΜΑ ΑΥΤΟΜΑΤΗΣ ΠΡΟΕΙΔΟΠΟΙΗΣΗΣ ΣΕ ΣΤΑΥΡΟΔΡΟΜΙ Αλαμπρίτης Μηνάς Χριστοφή Δημήτρης Λεμεσός 2016 1 ΤΕΧΝΟΛΟΓΙΚΟ

Διαβάστε περισσότερα

ΕΛΕΓΧΟΣ ΚΑΙ ΤΡΟΦΟΔΟΤΗΣΗ ΜΕΛΙΣΣΟΚΟΜΕΙΟΥ ΑΠΟ ΑΠΟΣΤΑΣΗ

ΕΛΕΓΧΟΣ ΚΑΙ ΤΡΟΦΟΔΟΤΗΣΗ ΜΕΛΙΣΣΟΚΟΜΕΙΟΥ ΑΠΟ ΑΠΟΣΤΑΣΗ ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΗΛΕΚΤΡΙΚΩΝ ΒΙΟΜΗΧΑΝΙΚΩΝ ΔΙΑΤΑΞΕΩΝ ΚΑΙ ΣΥΣΤΗΜΑΤΩΝ ΑΠΟΦΑΣΕΩΝ ΕΛΕΓΧΟΣ ΚΑΙ ΤΡΟΦΟΔΟΤΗΣΗ ΜΕΛΙΣΣΟΚΟΜΕΙΟΥ ΑΠΟ ΑΠΟΣΤΑΣΗ

Διαβάστε περισσότερα

AREAS AND LENGTHS IN POLAR COORDINATES. 25. Find the area inside the larger loop and outside the smaller loop

AREAS AND LENGTHS IN POLAR COORDINATES. 25. Find the area inside the larger loop and outside the smaller loop SECTIN 9. AREAS AND LENGTHS IN PLAR CRDINATES 9. AREAS AND LENGTHS IN PLAR CRDINATES A Click here for answers. S Click here for solutions. 8 Find the area of the region that is bounded by the given curve

Διαβάστε περισσότερα

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.

Απόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ. Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action

Διαβάστε περισσότερα

Στεγαστική δήλωση: Σχετικά με τις στεγαστικές υπηρεσίες που λαμβάνετε (Residential statement: About the residential services you get)

Στεγαστική δήλωση: Σχετικά με τις στεγαστικές υπηρεσίες που λαμβάνετε (Residential statement: About the residential services you get) Νόμος περί Αναπηριών 2006 (Disability Act 2006) Στεγαστική δήλωση: Σχετικά με τις στεγαστικές υπηρεσίες που λαμβάνετε (Residential statement: About the residential services you get) Greek Νόμος περί Αναπηριών

Διαβάστε περισσότερα

Αναερόβια Φυσική Κατάσταση

Αναερόβια Φυσική Κατάσταση Αναερόβια Φυσική Κατάσταση Γιάννης Κουτεντάκης, BSc, MA. PhD Αναπληρωτής Καθηγητής ΤΕΦΑΑ, Πανεπιστήµιο Θεσσαλίας Περιεχόµενο Μαθήµατος Ορισµός της αναερόβιας φυσικής κατάστασης Σχέσης µε µηχανισµούς παραγωγής

Διαβάστε περισσότερα

ΟΔΗΓΙΕΣ ΣΥΝΑΡΜΟΛΟΓΗΣΗΣ/ ASSEMBLY INSTRUCTION ΤΟΜΜΥ ΚΡΕΒΑΤΙ/BED

ΟΔΗΓΙΕΣ ΣΥΝΑΡΜΟΛΟΓΗΣΗΣ/ ASSEMBLY INSTRUCTION ΤΟΜΜΥ ΚΡΕΒΑΤΙ/BED ΟΔΗΓΙΕΣ ΣΥΝΑΡΜΟΛΟΓΗΣΗΣ/ ASSEMBLY INSTRUCTION ΤΟΜΜΥ ΚΡΕΒΑΤΙ/BED 1. Παρακαλώ πολύ διαβάστε προσεκτικά τις οδηγίες πριν την συναρμολόγηση/ Please read the instructions carefully. 2. Παρακαλώ πολύ όπως ελέγξτε

Διαβάστε περισσότερα

PhysicsAndMathsTutor.com 1

PhysicsAndMathsTutor.com 1 PhysicsAndMathsTutor.com 1 Q1. The magnetic flux through a coil of N turns is increased uniformly from zero to a maximum value in a time t. An emf, E, is induced across the coil. What is the maximum value

Διαβάστε περισσότερα

2. Μηχανικό Μαύρο Κουτί: κύλινδρος με μια μπάλα μέσα σε αυτόν.

2. Μηχανικό Μαύρο Κουτί: κύλινδρος με μια μπάλα μέσα σε αυτόν. Experiental Copetition: 14 July 011 Proble Page 1 of. Μηχανικό Μαύρο Κουτί: κύλινδρος με μια μπάλα μέσα σε αυτόν. Ένα μικρό σωματίδιο μάζας (μπάλα) βρίσκεται σε σταθερή απόσταση z από το πάνω μέρος ενός

Διαβάστε περισσότερα

Math 6 SL Probability Distributions Practice Test Mark Scheme

Math 6 SL Probability Distributions Practice Test Mark Scheme Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry

Διαβάστε περισσότερα

ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ

ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Ψηφιακή Οικονομία Άσκηση αυτοαξιολόγησης 4 Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών CS-593 Game Theory 1. For the game depicted below, find the mixed strategy

Διαβάστε περισσότερα

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ

ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ΠΑΝΕΠΙΣΤΗΜΙΟ ΠΑΤΡΩΝ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΤΕΧΝΟΛΟΓΙΑΣ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΣΥΣΤΗΜΑΤΩΝ ΗΛΕΚΤΡΙΚΗΣ ΕΝΕΡΓΕΙΑΣ ιπλωµατική Εργασία του φοιτητή του τµήµατος Ηλεκτρολόγων Μηχανικών και Τεχνολογίας Ηλεκτρονικών

Διαβάστε περισσότερα

5.4 The Poisson Distribution.

5.4 The Poisson Distribution. The worst thing you can do about a situation is nothing. Sr. O Shea Jackson 5.4 The Poisson Distribution. Description of the Poisson Distribution Discrete probability distribution. The random variable

Διαβάστε περισσότερα

Instruction Execution Times

Instruction Execution Times 1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables

Διαβάστε περισσότερα

2 Composition. Invertible Mappings

2 Composition. Invertible Mappings Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,

Διαβάστε περισσότερα

Sampling Basics (1B) Young Won Lim 9/21/13

Sampling Basics (1B) Young Won Lim 9/21/13 Sampling Basics (1B) Copyright (c) 2009-2013 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any

Διαβάστε περισσότερα

Local Approximation with Kernels

Local Approximation with Kernels Local Approximation with Kernels Thomas Hangelbroek University of Hawaii at Manoa 5th International Conference Approximation Theory, 26 work supported by: NSF DMS-43726 A cubic spline example Consider

Διαβάστε περισσότερα

CYTA Cloud Server Set Up Instructions

CYTA Cloud Server Set Up Instructions CYTA Cloud Server Set Up Instructions ΕΛΛΗΝΙΚΑ ENGLISH Initial Set-up Cloud Server To proceed with the initial setup of your Cloud Server first login to the Cyta CloudMarketPlace on https://cloudmarketplace.cyta.com.cy

Διαβάστε περισσότερα

HOMEWORK#1. t E(x) = 1 λ = (b) Find the median lifetime of a randomly selected light bulb. Answer:

HOMEWORK#1. t E(x) = 1 λ = (b) Find the median lifetime of a randomly selected light bulb. Answer: HOMEWORK# 52258 李亞晟 Eercise 2. The lifetime of light bulbs follows an eponential distribution with a hazard rate of. failures per hour of use (a) Find the mean lifetime of a randomly selected light bulb.

Διαβάστε περισσότερα