Revised 11/08. Projectile Motion
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1 LPC Phsics Prjecile Min Prjecile Min eised 11/08 Purpse: T mesure he dependence f he rne f prjecile n iniil elci heih nd firin nle. Als, erif predicins mde he b equins ernin prjecile min wihin he eperimenl nd hereicl uncerinies inheren in his eperimen. Equipmen: Bllisic Gun Apprus Prjeciles Shelf Brds, Clmps -meer Sick Crbn Pper, Scrch Pper, Mskin Tpe Grphicl Anlsis Sfwre Ther: A prjecile fired frm heih h wih iniil elci n nle θ ο be he hriznl will rel disnce ien b he fllwin equin: (,, h) sin sinθ h θ csθ θ Eq. 1 1 f 7
2 LPC Phsics Prjecile Min eised 11/08 Ne h if h 0 in Eq. 1 hen sin θ Eq. nd if θ ο 0 in Eq. 1 hen h Eq. 3 s h he iniil elci,, cn be deermined frm he relin: h Eq. 4 if bh nd h re knwn. Eperimen: Pr A: Deerminin he Iniil Velci 1. Clmp he prjecile un securel n he ble s h prjecile m be fired wihu bsrucin.. Selec lch sein n he un h will llw is rne be ner he mimum ilble disnce. Se he nle ner 30 derees nd fire he prjecile. If i rels fr r n fr enuh, hen djus he sein. Als, se he prjecile 90 nd be sure h he prjecile desn srike he ceilin (herwise, u ll need cnduc he eperimen uside, r use shrer rne sein). Chse ne rne sein (shr, medium, r ln) nd use his sein fr he enire eperimen. D n chne his sein. f 7
3 LPC Phsics Prjecile Min eised 11/08 3. Se he elein nle zer nd mesure he heih f he prjecile (bm flr). 4. Cck nd fire he prjecile few imes nd bsere where i lnds. Tpe piece f pper (cenered n he ere psiin) n he flr his pin nd cer i wih piece f crbn pper. 5. Fire he prjecile 5 imes (i.e. i mus srike he pper 5 imes). If ne piece f pper desn cer he rne f impcs, pe ddiinl ppers dwn. Sr prjeciles cn be inred. 6. eme he pper nd mesure he disnce h ech prjecile lnds frm he bse f he un. ecrd hese disnces n pper nd, ler, in Grphicl Anlsis spredshee. 7. epe Seps 5 nd 6 seen mre imes unil u he l f 00 prjecile impcs. 8. Befre u hme, lbel ur rup's prjecile luncher -- ls remember which rne sein u used -- u'e wrked hrd find he elci fr priculr sein --- u wuldn' wn his sein disurbed befre u cn pu i use ne week! 9. Be sure d he Anlsis fr Pr A befre cmin clss ne week. Pr B: Deerminin ne s Funcin f Firin Anle 1. ise he un n nle f 15, 30, 40, 45, 60, 75 nd 90 nd fire he prjecile see where i lnds fr ech nle. Plce shee f pper nd crbn pper in he re re, nd fire en imes frm ech sein. ecrd he lues f n pper, nd ler, in ur spredshee. Ne: Be creful plce ur un s h i fires ur rih while fcin i. Anlsis: Pr A: 1. Usin Grphicl Anlsis, pen up spredshee nd ener he 00 lues f.. Usin he 00 lues f, deermine nd σ, where σ is he sndrd deiin in. Of curse, u shuld cull clcule hese usin GA s sisicl nlsis funcin ( d his: Yu mus cree pl f ur d. I des n need be sred r in n priculr rder. In he X clumn, ener numbers 1-> 00 (r hweer mn d pins u end up wih). In he Y clumn, ener ur lues. GA will umicll cree rph f Y s. X. Chse Anlze > Sisics, nd windw 3 f 7
4 LPC Phsics Prjecile Min eised 11/08 will pper n he rph iin u he ere, m, nd min lues, nd he sndrd deiin in.). 3. Nw u will see if he lues f re rul rndml disribued bu he men lue. T d his, u will cree hisrm f ur d. A hisrm crees bins f d, nd cuns hw mn d pins fi in ech bin (his number is clled cuns r frequenc ). The rph hen displs frequenc s. bin. T cree hisrm f ur d, chse Inser > Addiinl Grphs > Hisrm frm he p br menu. Yu wn cree 10 d bins, s u need ell he prrm hw wide mke he bins. Yur bins re f disnce reled b he prjecile, s he bin widh wuld be (d m d min )/ In hese sr f sisicl eperimens, d m be fuded b creie cnsrucin f binnin. Yu knw u he fund d bin size if chnin he sizin up r dwn des n chne he shpe f he hisrm. T check ur binnin, quickl cree w mre hisrms, ne wih 11 bins, he her wih 9. Is eiher cure drsicll lpsided? If n, d! If s, u need find beer bin size wrk wih...see ur insrucr fr help. Once u he deermined d bin size fr ur d, keep h hisrm nd delee he res. 5. Is ur rph Gussin in shpe? If s, u shuld be ble find he sndrd deiin b nin h he equin fr Gussin cure is: N ( sm ) σ N e Eq. 5 m Since his equin describes he cure, h mens h when m σ, hen: Emple: 1 me. 606 N N 0 N m Eq. 6 The rph belw is Gussin cure cenered n he lue m 15. The mimum lue f his cure is N m 1. A ne sndrd deiin frm he mimum,.606* A his pin 10.5, nd 19.5 (pprimel). Thus ne sndrd deiin cn be fund b: σ , r σ f 7
5 LPC Phsics Prjecile Min eised 11/08 6. Usin his relinship described be, deermine he lue f σ Ρ frm ur rph. Des ur lue f σ Ρ frm he rphicl mehd mch he sisicl mehd? If n, wh n? 7. Deermine he eperimenl lue f nd is uncerin δ usin he relins: h Eq. 7 δ δ Eq. 8 In his cse, δ is he sndrd deiin in, (σ Ρ ). Unless ur rphs indice resul he cnrr (i.e. nn-gussin cure), use nd σ Ρ. 8. Derie Eq. 1, srin frm he equins f min in w dimensins (belw). Include he deriin in ur lb repr. ) ( ), (,, 1 1 Hin: Since he hriznl cmpnen f he elci is cnsn, () where up dwn. Ne, cnsider h when he prjecile reches i mimum heih, 5 f 7
6 LPC Phsics Prjecile Min eised 11/08 hen 0. Als, dwn is simpl he ime i kes fr he prjecile free fll frm is mimum heih. Pr B: 1. Usin he lue f u deermined in Pr A, clcule he hereicl lue f s ien b Eq. 1, fr ech nle θ nd crrespndin heih h. Use ur spredshee perfrm his clculin. T es ur equin, perfrm he clculin fr θ 0, nd θ 90. The resuls shuld be (frm Pr A) nd 0 respeciel. Ne: A cmmn miske in his clculin is use rdins rher hn derees.. T displ ur resuls, pl br rph f m, min,, nd her s. firin nle. Yu m need rerrne ur spredshee d clumns mke his wrk. 3. There is ne ls lse hred befre u ie ll he d up in ne pcke. The uncerin in elci (clculed b he sndrd deiin in ) cuses sinificn uncerin in he hereicl lue. This cn be fund b he prpin f errr echnique: d δ her δ d In prcice his cn be dunin sk, especill ien he cmplei f equin. Hweer, i cn be simplified b nin h he firs w erms in equin (1) depend n nd re hus mre effeced b uncerin hn he erm inside he squre r (which depends nl n he firs pwer f ). This is equilen cnsiderin he rne f prjecile fired frm heih h 0. Thus, sin(θ ). The deriie wih respec is simpl d/d sin(θ)/. Clcule δ her fr ech lue f θ. Cree w mre clumns n ur spredshee. One will be he mimum hereicl rne lue ( her δ her ), nd he her will be he minimum hereicl rne lue ( her - δ her ). Cree br rph s befre, displin he m nd min lues f her ln wih he mimum nd minimum lues f ep. 4. Inerpre he resuls f he rph in Sep 3 nd discuss n nmlies h m be presen in he d. 5. A wh lunch nle did he prjecile rel is mimum disnce? Wh ws his nle n equl 45? A wh nle d u epec he mimum disnce (hin: his mih require sme clculus)? Include ur nswers in ur lb repr. esuls: Wrie les ne prrph describin he fllwin: 1. wh u epeced lern bu he lb (i.e. wh ws he resn fr cnducin he eperimen?). ur resuls, nd wh u lerned frm hem 6 f 7
7 LPC Phsics Prjecile Min eised 11/08 3. Think f les ne her eperimen mih u perfrm erif hese resuls 4. Think f les ne new quesin r prblem h culd be nswered wih he phsics u he lerned in his lbrr, r be erpled frm he ides in his lbrr. 7 f 7
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