9/5/2013. PHY 113 A General Physics I 11 AM-12:15 PM TR Olin 101. Plan for Lecture 4:

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1 9/5/3 PHY 3 A Genel Phscs I AM-:5 PM TR Oln Pln fo Lecue 4: Chpe 4 Moon n wo dmensons. Poson, eloc, nd cceleon n wo dmensons. Two dmensonl moon wh consn cceleon; pbolc ecoes 3. Ccul moon 9/5/3 PHY 3 A Fll 3 -- Lecue 4 Upded schedule 4.,4.,4.35,4.6 9/5/3 PHY 3 A Fll 3 -- Lecue 4 Tene em des:. Sepembe 6, 3 coeng Chp. -8. Ocobe 3, 3 coeng Chp. 9-3, Noembe 6, 3 coeng Chp. 4, 9- Fnl em: Decembe, 3 9 AM 9/5/3 PHY 3 A Fll 3 -- Lecue 4 3

2 9/5/3 Fom eml quesons on Webssgn #3 Poblem Noe: In hs cse he ngle f s cull mesued s noh of es. f d b q fbq 9/5/3 PHY 3 A Fll 3 -- Lecue 4 4 Fom eml quesons on Webssgn #3 -- connued Poblem 3. gphcll. d Fnd A B A q B mgnude decon m couneclockwse fom he s 9/5/3 PHY 3 A Fll 3 -- Lecue 4 5 Fom eml quesons on Webssgn #3 -- connued Poblem 3.9 F F 9/5/3 PHY 3 A Fll 3 -- Lecue 4 6

3 9/5/3 In he peous lecue, we noduced he bsc noon of eco. In hs lecue, we wll use h noon o descbe poson, eloc, nd cceleon ecos n wo dmensons. clcke eecse: Wh spend me sudng wo dmensons when he wold s we know s hee dmensons? A. Becuse s dffcul o dw 3 dmensons. B. Becuse n phscs clss, dmensons e hd enough o undesnd. C. Becuse f we undesnd dmensons, eenson of he des o 3 dmensons s l. D. On Thusds, s good o sck o plne. 9/5/3 PHY 3 A Fll 3 -- Lecue 4 7 ecl decon up hozonl decon 9/5/3 PHY 3 A Fll 3 -- Lecue 4 8 Vecos elen o moon n wo dmensons Dsplcemen: Veloc: d d d d Acceleon: d d d d 9/5/3 PHY 3 A Fll 3 -- Lecue 4 9 3

4 9/5/3 Vsulzon of he poson eco of pcle 9/5/3 PHY 3 A Fll 3 -- Lecue 4 Vsulzon of he eloc eco of pcle d d lm 9/5/3 PHY 3 A Fll 3 -- Lecue 4 Vsulzon of he cceleon eco of pcle d d lm 9/5/3 PHY 3 A Fll 3 -- Lecue 4 4

5 9/5/3 Fgue fom ou e: 9/5/3 PHY 3 A Fll 3 -- Lecue 4 3 Vsulzon of pbolc eco fom ebook 9/5/3 PHY 3 A Fll 3 -- Lecue 4 4 The eco gphs of he moon of n obec esus s funcon of me, look somewh lke pbol: A B C clcke eecse A. Ths s supsng B. Ths s epeced C. No opnon 9/5/3 PHY 3 A Fll 3 -- Lecue 4 5 5

6 9/5/3 6 9/5/3 PHY 3 A Fll 3 -- Lecue 4 6 Poecle moon ne eh s sufce ecl decon up hozonl decon g g 9.8 m/s 9/5/3 PHY 3 A Fll 3 -- Lecue 4 7 Poecle moon ne eh s sufce d d g g g d d noe h noe h 9/5/3 PHY 3 A Fll 3 -- Lecue 4 8 Poecle moon ne eh s sufce g d d d d g g d d noe h

7 9/5/3 Poecle moon ne eh s sufce g d g d cosq snq d g d 9/5/3 PHY 3 A Fll 3 -- Lecue 4 9 Poecle moon ne eh s sufce Teco equon n eco fom: g g Teco equon n componen fom: g g Asde: The equons fo poson nd eloc wen n hs w e cll pmec equons. The e eled o ech ohe hough he me pmee. 9/5/3 PHY 3 A Fll 3 -- Lecue 4 Poecle moon ne eh s sufce Teco equon n componen fom: cosq g sn q g cosq g snq g Teco ph ; elmnng fom he equons: cosq nq snq cosq g cos q PHY Fll 3 -- Lecue 4 9/5/3 3 A g cos q 7

8 9/5/3 Poecle moon ne eh s sufce Summ of esuls cosq cosq nq clcke eecse: snq g snq g cos q These equons e so beuful h A. The should be fmed nd pu on he wll. B. The should be used o pefec m enns/golf/bskebll/socce echnque. C. The e no h beuful. g 9/5/3 PHY 3 A Fll 3 -- Lecue 4 Dgm of ous ecoes echng he sme hegh h m: clcke eecse: Whch eco kes he longes me? A. Bown B. Geen C. Sme me fo ll. 9/5/3 PHY 3 A Fll 3 -- Lecue 4 3 h7.m q 53 o d4m.s 9/5/3 PHY 3 A Fll 3 -- Lecue 4 4 8

9 9/5/3 Poblem solng seps. Vsulze poblem lbelng bles. Deemne whch bsc phscl pncples ppl 3. We down he ppope equons usng he bles defned n sep. 4. Check whehe ou he he coec moun of nfomon o sole he poblem sme numbe of known elonshps nd unknowns. 5. Sole he equons. 6. Check whehe ou nswe mkes sense uns, ode of mgnude, ec.. h7.m q 53 o d4m.s 9/5/3 PHY 3 A Fll 3 -- Lecue 4 5 h7.m q 53 o d4m.s cosq d. cos53 4m 8.698m / s o cos53.s o. 4 9/5/3 PHY 3 A Fll 3 -- Lecue 4 6 Reew Poson, Veloc, Acceleon n one dmenson: d ' d' d d d ' d' Specl cse of consn cceleon : d Suppose : nd, d Then : 9/5/3 PHY 3 A Fll 3 -- Lecue 4 7 9

10 9/5/3 9/5/3 PHY 3 A Fll 3 -- Lecue 4 8 Reew connued: Specl cse of consn cceleon : Then :, nd Suppose : d d nl eloc nl poson Resul deed usng lgeb : nd cceleon : eloc, Relonshp beween poson, 9/5/3 PHY 3 A Fll 3 -- Lecue 4 9 Summ of equons one-dmensonl moon wh consn cceleon clcke queson: Wh dd I show ou p of he deon of he ls equon? A. Becuse pofessos lke o oue phscs sudens B. Becuse ou wll need o be ble o poe he equon ouself C. Becuse he poof helps ou o undesnd he menng of he equon D. All of he boe E. None of he boe 9/5/3 PHY 3 A Fll 3 -- Lecue 4 3 ecl decon up hozonl decon Reew: Moon n wo dmensons:

11 9/5/3 Vecos elen o moon n wo dmensons Dsplcemen: Veloc: d d d d Acceleon: d d d d 9/5/3 PHY 3 A Fll 3 -- Lecue 4 3 Poecle moon consn cceleon esonble ppomon ne Eh s sufce ecl decon up g hozonl decon 9/5/3 PHY 3 A Fll 3 -- Lecue 4 3 Poecle moon ne eh s sufce g d g d cosq snq d g d 9/5/3 PHY 3 A Fll 3 -- Lecue 4 33

12 9/5/3 Poecle moon ne eh s sufce Summ of componen funcons cosq cosq nq snq g snq g cos q g 9/5/3 PHY 3 A Fll 3 -- Lecue 4 34 Unfom ccul moon nohe emple of moon n wo-dmensons nmon fom hp://mhwold.wolfm.com/unfomcculmoon.hml 9/5/3 PHY 3 A Fll 3 -- Lecue 4 35 clcke queson: Assumng h he blue pcle s mong consn speed ound he ccle wh cn ou s bou s cceleon? A. Thee s no cceleon B. Thee s cceleon ngen o he ccle C. Thee s cceleon n he dl decon of he ccle D. Thee s no enough nfomon o conclude h hee s cceleon o no 9/5/3 PHY 3 A Fll 3 -- Lecue 4 36

13 9/5/3 Unfom ccul moon connued If n he dl decon nd he cenpel cceleon s : c, hen he cceleon 9/5/3 PHY 3 A Fll 3 -- Lecue 4 37 f Unfom ccul moon connued c c T c f In ems of me peod T fo one ccle: T In ems of he fequenc f of complee ccles: f ; πf T 9/5/3 PHY 3 A Fll 3 -- Lecue 4 38 c T T 4 h 6 mn/h 6 s/mn 864 s m/s c m/s 9/5/3 PHY 3 A Fll 3 -- Lecue

14 9/5/3 clcke eecse: Dung ccul moon, wh hppens when he speed of he obec chnges? A. Thee s onl ngenl cceleon B. Thee s onl dl cceleon C. Thee e boh dl nd ngenl cceleon D. I don need o know hs becuse nee hppens. 9/5/3 PHY 3 A Fll 3 -- Lecue 4 4 Ccul moon θ Assume : c d θ d θ c θ c 9/5/3 PHY 3 A Fll 3 -- Lecue 4 4 4