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C -3 -3 -t::t.}te.s- / lIot:~J,s ., I) "~'fC ","'~'-' ~{~ , ~Ls ~. ,rr- ~( 1 Yl ii ""- 'It f} 2' 1't- to ~Introduction to Vectors11A Hands-on Introduction to Displacement/Velocity Vectors andFrame of Reference through the Use of an InexpensiveWindIIFToyQPa\f@RiB8:1ttH9WQrizgptalGriVGwen Saylor, Department of Physics, State University of New York - Buffalo State College,1300 Elmwood Ave, Buffalo, NY [email protected]~Acknowledgements: This paper is submitted in partial fulfillment of the requirements necessaryfor PHY690: Masters Project at SUNY - Buffalo State College wlder the guidance of Dr. DanMaclsaac.Introduction to VectorsI2I.)-4b)l1rd'~"..jf/,..~;:;.L.._,Ih;~f ..~'1b~d"" ~ .Abstract: T'Y paper presents a set0hands-on actIVltIe;t(J e lise as an mtrodllctIOn to vectorterminology common in the New York State Regents Ph~>ics curriculwn through a focus ondisplacement and velocity vectors:\Vith inexpensive equipment student are able to visualize thetip to tail method of vector addition, deter line the horizontal and vertical components of vectorsand observe the combination of twoCOllIrrent parallel or perpendicular vectors. Studentsobserve the motion of a toyalla mov' g grid to establish the concept of frame of reference forrelative motion. The terminology d level of difficulty are geared toward a Iligh school Regentsclass. Through guided activity IVO sheets, student groups explore scenarios that frequently ,.Lappear on the New York State Regen~Pi4 IVam related to vectors. ~/5'~ "'i.I -'"If}f1A / ~"'~/7; () - ~ ~ ~ ~ ..~~ a~ ( {11)i.Jro ~;.D0Jtr1~r~~::':;L;fjj~~~~{ I'~ f(0.$.~\''/'''''')~'-~.",.~,v-rl1~' ~t~~','\0.; (h-e". ~--:(_\>QJ """~C ~l~~,."L ~~~IIntroduction to VectorsI31C; '"tSe~nt~4r{n4k,.i ~L,-I7) /t;Dc:()'I.Introduction:_.JIT"'"£ICeo.,Ier ( c,tIf . Throughout the yearr~dents a.!!,..confromed with problems that require combiningI'--t.ct ....,~e.. ., \parallel or perpen ICU ors quantities and resolving vectors into horizontal and vertical. Vectors areaHPl'w§"1sktlW8(fillttN~; sf ~hlilCS Students I,ave greater dIfficultyIe.~components. Students are also tasked to graphically solve for the resultant oftlVo vectors usingwIth vectors than IS reflected mmany lugh school cumculums. ~ure to address the central.C { • ~lIther head-to-tail or parallelogram methods for scaled vectors that are not necessanly alIgned torole of vectors in problem solving early on in the curriculum lea s sludellt diilictUty wIthCCo,...Itethe honzontal 01 the vertIcal axesproblem solving throughout the entire year. This paper summarizes a method for i ~~Ivectors early m the Regents PhYSICScumculum a - ce erated motIon The _ \ While questIonsmthe student worksheet are occasIOnally above the dIfficulty of theltles mtroduce the vector SkIlls and vector tenmnology that are appropnate to the ~YorkCo ~t.k -Regents cUfflculwn they are deSIgned to confront common mlsconceptlOns that lead tots PhYSICSCore CUfflculum The mtroductlon of vector quantitIes and vect~r ~ challenges as students develop a greater understandmg of vectors m over the course of the year.oper00 IPacement and velOCIty scenanos wbile~romotIng skills that appl \ ,. , If vector presentations are linlited solely to those presented on past Regents Physics exams,proJecttl erposltIon off<tces, momentum and fO~ft~i\ ~ students may develop misconceptions. In order for a student to transition from the basic level of\ 0\~orlI.')t ~1/Itrt :\,'fS,Jfunctionality listed in Key Ideas 5.1a-c in~Table ~o mastery of skills and concepts in the\; \' ~tt.(The two tIv S p~ this docwnf~t, "ACtIVIty One Ladybug TranSIt" andc: ~.'J.orIs .remainder of the curriculmn, learners mustbeable t~ aemonstrate the following skills and4)""r ,~~"AchvltyTwo:Lad aConveyorBelt"p~mstructIonaltools~~~makevector '"rf?¥ctI wlderstanding:~C<~characteristics both expl it an ighly vis or learners. Each activity~mducted in tbetI " -'pat ~.'I'.,space of a student desktop, ~ing ~aCh group member. Students observe the'1 ~""at .Define terms such as dIsplacement, velOCIty, resultant, equilibrallt and componenJ,.s\-;--1' •motion of the toys and apply Prio\~~ge from the kinematics unit, geometry and algebra.f~71 .Establish the relatIonship between compone,£ctood the resultant vectors Itfi:dmgr;..e.J. ~Activity One "Ladybug Transit" a1YSwsstudents to resolve vectors into horizontal and vertical ~ -#7'J7the concept of addItIve lllverse (Arons, 1995, g 107----f ~e«r-eo. ~ \components by graphical meth,ods and introduces the equations necessary for the analytical \ ~ ~rlJ'Jlf>t , .• .Define the meanmg ofa negatIve vectors m re aMn to the honzontal and vertIcal axescommlltation of vectors. During activity two, "Ladybug on a conveyor belt", students observe ~M •Understand that vector quantItIes are not fixed to a locatIOn (Brown, 1993)~ \JY\.the combination of concurrent parallel or perpendicular vectors using a moving toy and a moving ~ . <.\kI:\ .. ~~. grid to model two dimensional motions. By observingthetoy relative to the grid and relative to /' ~.Rrylew:J:>4r~(O>l"1&-A "'~\ ~the fixed frame students WIll learn that both path and velOCIty are dependent on the frame of In the same way that physics education has focused on modifying instruction to explicitly'v"C"..::r \reference. GUIded quesl10ns are used throughout the actIVitIes to support concept development, address student misconceptions related to forces through the Force
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