Physics 207, Lecture 3

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1 Physcs 7 Lecue 3 Physcs 7, Lecue 3 l Tody (Fnsh Ch. & s Ch. 3) Emne sysems wh non-zeo cceleon (ofen consn) Sole D poblems wh zeo nd consn cceleon (ncludng fee-fll nd moon on n nclne) Use Cesn nd pol coodne sysems Pefom eco lgeb Physcs 7: Lecue 3, Pg D Poson, Dsplcemen me (sec) y poson -, -,,,, 3, (,y mees) poson ecos ogn Physcs 7: Lecue 3, Pg Pge

2 Physcs 7 Lecue 3 D Poson, Dsplcemen me (sec) y poson -, -,,,, 3, (,y mees) poson ecos ogn dsplcemen ecos Physcs 7: Lecue 3, Pg 3 Poson, Dsplcemen, Velocy me (sec) y (g) f f dsplcemen ecos elocy ecos Velocy lwys hs sme mgnude & lengh CONSTANT ( ) fnl + nl / m/s Physcs 7: Lecue 3, Pg 4 Pge

3 Physcs 7 Lecue 3 Acceleon l The ege cceleon of pcle s moes s defned s he chnge n he nsnneous elocy eco dded by he me nel n whch h chnge occus. l Bold fons e ecos l The ege cceleon s eco quny deced long Physcs 7: Lecue 3, Pg 5 Acceleon l Pcle moon ofen noles non-zeo cceleon The mgnude of he elocy eco my chnge The decon of he elocy eco my chnge (ue een f he mgnude emns consn) Boh my chnge smulneously l E.g., pcle wh smoohly decesng speed g Physcs 7: Lecue 3, Pg 6 Pge 3

4 Physcs 7 Lecue 3 Aege Acceleon g ( f ) fnl f ( ) nl f l Queson: A spne s unnng ound ck. seconds fe he ss he s unnng noh m/s. A seconds he s unnng m/s eswds. l Wh ws hs ege cceleon n hs me ( o secs)? Physcs 7: Lecue 3, Pg 7 Aege Acceleon g ( f ) fnl f ( ) nl f l Queson: A spne s unnng ound ck. seconds fe he ss he s unnng noh m/s. A seconds he s unnng m/s eswds. l Wh ws hs ege cceleon n hs me ( o secs)? N f + 4 m/s / s.4 m/s o he SE Physcs 7: Lecue 3, Pg 8 Pge 4

5 Physcs 7 Lecue 3 l Aege cceleon Insnneous Acceleon g l The nsnneous cceleon s he lm of he ege cceleon s / ppoches zeo f Physcs 7: Lecue 3, Pg 9 Poson, elocy & cceleon fo moon long lne l If he poson s known s funcon of me, hen we cn fnd boh he nsnneous elocy nd nsnneous cceleon s funcon of me! ( ) [ s funcon of ] d d d d d d Physcs 7: Lecue 3, Pg Pge 5

6 Physcs 7 Lecue 3 Poson, elocy & cceleon fo moon long lne l If he poson s known s funcon of me, hen we cn fnd boh he nsnneous elocy nd nsnneous cceleon s funcon of me! ( ) [ s funcon of ] d d d d d d Physcs 7: Lecue 3, Pg Gong he ohe wy. l Pcle moon wh consn cceleon The mgnude of he elocy eco chnges d d d d f e unde cue - Physcs 7: Lecue 3, Pg Pge 6

7 Physcs 7 Lecue 3 Gong he ohe wy. l Pcle moon wh consn cceleon The mgnude of he elocy eco chnges l A pcle wh smoohly ncesng speed: e unde cue f f + + ( f - ) Physcs 7: Lecue 3, Pg 3 So f consn cceleon we cn nege wce cons Physcs 7: Lecue 3, Pg 4 Pge 7

8 Physcs 7 Lecue 3 Two ohe elonshps l If consn cceleon hen we lso ge: ( ) ( (g) + ) Physcs 7: Lecue 3, Pg 5 Emple poblem l A pcle moes o he gh fs fo seconds m/s nd hen 4 seconds m/s. l Wh ws he ege elocy? + l Two legs wh consn elocy bu. Ag Physcs 7: Lecue 3, Pg 6 Pge 8

9 Physcs 7 Lecue 3 Emple poblem l A pcle moes o he gh fs fo seconds m/s nd hen 4 seconds m/s. l Wh ws he ege elocy? l Two legs wh consn elocy bu. + Ag l We mus fnd he dsplcemen ( ) l And + ( - ) + ( - ) l Dsplcemen s ( - ) + ( ) ( - ) + ( - ) l m/s ( s) + m/s (4 s) m n 6 seconds o 5/3 m/s Physcs 7: Lecue 3, Pg 7 Dsplcemen wh consn cceleon + + A pcle sng es & mong long lne wh consn cceleon hs dsplcemen whose mgnude s popoonl o ( ) +. Ths cn be esed. Ths s poenlly useful esul Physcs 7: Lecue 3, Pg 8 Pge 9

10 Physcs 7 Lecue 3 Fee Fll l When ny objec s le go flls owd he gound!! The foce h cuses he objecs o fll s clled gy. l Ths cceleon on he Eh s sufce, cused by gy, s ypclly wen s lle g l Any objec, be bsebll o n elephn, epeences he sme cceleon (g) when s dopped, hown, sp, o huled,.e. g s consn. y -g y( ) y + y g Physcs 7: Lecue 3, Pg 9 Gy fcs: l g does no depend on he nue of he mel! Glleo (564-64) fgued hs ou whou fncy clocks & ules! l Fehe & penny behe jus he sme n cuum l Nomnlly, g 9.8 m/s A he equo g 9.78 m/s A he Noh pole g 9.83 m/s Physcs 7: Lecue 3, Pg Pge

11 Physcs 7 Lecue 3 Eecse Moon n One Dmenson When howng bll sgh up, whch of he followng s ue bou s elocy nd s cceleon he hghes pon n s ph? A. Boh nd B., bu C., bu D. None of he boe y Physcs 7: Lecue 3, Pg Eecse Moon n One Dmenson When howng bll sgh up, whch of he followng s ue bou s elocy nd s cceleon he hghes pon n s ph? A. Boh nd B., bu C., bu D. None of he boe y Physcs 7: Lecue 3, Pg Pge

12 Physcs 7 Lecue 3 Home Eecse Moe comple Poson s. Tme Gphs In dng fom Mdson o Chcgo, nlly my speed s consn 65 mph. Afe some me, I see n ccden hed of me on I-9 nd mus sop quckly so I decelee ncesngly fs unl I sop. The mgnude of my cceleon s me s gen by, Queson: My elocy s me gph looks lke whch of he followng? A. B. C. Physcs 7: Lecue 3, Pg 3 In dng fom Mdson o Chcgo, nlly my speed s consn 65 mph. Afe some me, I see n ccden hed of me on I-9 nd mus sop quckly so I decelee ncesngly fs unl I sop. The mgnude of my cceleon s me s gen by, Queson: My elocy s me gph looks mos lke whch of he followng? A. Home Eecse Moe comple Poson s. Tme Gphs B. C. Physcs 7: Lecue 3, Pg 4 Pge

13 Physcs 7 Lecue 3 Eecse D Feefll l Alce nd Bll e sndng he op of clff of hegh H. Boh how bll wh nl speed, Alce sgh down nd Bll sgh up. l The speed of he blls when hey h he gound e A nd B especely. (Neglec essnce.) A. A < B B. A B Alce Bll C. A > B H A B Physcs 7: Lecue 3, Pg 5 Eecse D Feefll l Alce nd Bll e sndng he op of clff of hegh H.. Boh how bll wh nl speed, Alce sgh down nd Bll sgh up.. The speed of he blls when hey h he gound e A nd B especely. A. A < B B. A B Alce Bll C. A > B H A B Physcs 7: Lecue 3, Pg 6 Pge 3

14 Physcs 7 Lecue 3 Eecse D Feefll : Gphcl soluon l Alce nd Bll e sndng he op of clff of hegh H.. Boh how bll wh nl speed, Alce sgh down nd Bll sgh up. clff bck unound -g pon clff - dencl dsplcemens (one + nd one -) gound gound gound Physcs 7: Lecue 3, Pg 7 The gph gh shows he y elocy esus me gph fo bll. Gy s cng downwd n he -y decon nd he -s s long he hozonl. Whch eplnon bes fs he moon of he bll s shown by he elocy-me me gph below? Home Eecse,D Feefll A. The bll s fllng sgh down, s cugh, nd s hen hown sgh down wh gee elocy. B. The bll s ollng hozonlly, sops, nd hen connues ollng. C. The bll s sng sgh up, hs he celng, bounces, nd hen flls sgh down. D. The bll s fllng sgh down, hs he floo, nd hen bounces sgh up. E. The bll s sng sgh up, s cugh nd held fo whle, nd hen s hown sgh down. Physcs 7: Lecue 3, Pg 8 Pge 4

15 Physcs 7 Lecue 3 Fe Seps: ) Focus he Poblem Poblem Soluon Mehod: - dw pcue wh e we skng fo? ) Descbe he physcs - wh physcs des e pplcble - wh e he elen bles known nd unknown 3) Pln he soluon - wh e he elen physcs equons 4) Eecue he pln - sole n ems of bles - sole n ems of numbes 5) Elue he nswe - e he dmensons nd uns coec? - do he numbes mke sense? Physcs 7: Lecue 3, Pg 9 A scence pojec l You dop bus off he Wlls Towe (44 m boe he sde wlk). I so hppens h Supemn fles by he sme nsn you elese he c. Supemn s flyng down 35 m/s. l How fs s he bus gong when cches up o Supemn? Physcs 7: Lecue 3, Pg 3 Pge 5

16 Physcs 7 Lecue 3 A scence pojec l You dop bus off he Wlls Towe (44 m boe he sde wlk). I so hppens h Supemn fles by he sme nsn you elese he c. Supemn s flyng down 35 m/s. l How fs s he bus gong when cches up o Supemn? y l Dw pcue y Physcs 7: Lecue 3, Pg 3 A scence pojec l Dw pcue l Cues nesec wo pons y y g y Supemn g Supemn bus g g Supemn g g Supemn Supemn Physcs 7: Lecue 3, Pg 3 Pge 6

17 Physcs 7 Lecue 3 Home eecse of D moon poblem l A c s nlly elng Es consn speed of m/s. When s hlfwy (n dsnce!) o s desnon s speed suddenly nceses nd heefe emns consn. All old he c spends ol of s n ns wh n ege speed of 5 m/s. l Wh s he speed of he c dung he nd hlf of he p? l Ths s on on he n clss emple bu much moe dffcul. And Physcs 7: Lecue 3, Pg 33 Home eecse of D moon poblem l A c s nlly elng Es consn speed of m/s. When s hlfwy (n dsnce!) o s desnon s speed suddenly nceses nd heefe emns consn. All old he c spends ol of s n ns wh n ege speed of 5 m/s. l Wh s he speed of he c dung he nd hlf of he p? l Dynmcl elonshps (only f consn cceleon): + + cons + (g) ( ( + ) ) And ( ege elocy) (dsplcemen) (ol me) Physcs 7: Lecue 3, Pg 34 Pge 7

18 Physcs 7 Lecue 3 Dwng he pcue m/s ( > ) m/s l Plus he ege elocy l Knowns: m s + m/s s g 5 m/s elonshp beween nd l Fou unknowns & nd mus fnd n ems of knowns Physcs 7: Lecue 3, Pg 35 Usng + m/s ( > ) m/s + ( ) + ( ) l Fou unknowns l Fou elonshps l Focus on ( ) Physcs 7: Lecue 3, Pg 36 Pge 8

19 Physcs 7 Lecue 3 Usng + m/s ( > ) m/s ( / s ) 5 m 5 5 / s 5/4 s m s s 5 m 5 m 5 m 5 m ( 5 / 4) s (5 / 4) s Physcs 7: Lecue 3, Pg 37 m/s Usng ( > ) m/s l Elmne unknowns fs ne ( ) + hen 3 & + ( ) ( ) 4 ( ) 4 Mul. by / ( ) Physcs 7: Lecue 3, Pg 38 Pge 9

20 Physcs 7 Lecue 3 m/s Fn ( > ) m/s l Plus he ege elocy l Gen: m/s s g 5 m/s ( 5m/s m/s ) 5m/s m/s m/s 5m/s Physcs 7: Lecue 3, Pg 39 l Red! Tps: Befoe you s wok on poblem, ed he poblem semen hooughly. Mke sue you undesnd wh nfomon s gen, wh s sked fo, nd he menng of ll he ems used n sng he poblem. l Wch you uns (dmensonl nlyss)! Alwys check he uns of you nswe, nd cy he uns long wh you numbes dung he clculon. l Ask quesons! Physcs 7: Lecue 3, Pg 4 Pge

21 Physcs 7 Lecue 3 Cone Rch Poblem: Fo dscusson l On bgh sunny dy you e wlkng ound he cmpus wchng one of he mny consucon ses. To lf bunch of bcks fom cenl e, hey he bough n helcope. As he plo s hoeng he/she ccdenlly eleses he bcks when hey e m boe he gound. A woke, decly below, snds sll fo seconds befoe wlkng wy. (Le g m/s ) Thee s no wnd o ohe effecs. Does he woke le? (Ce fo lng..he woke moes befoe he bcks ske he gound) Physcs 7: Lecue 3, Pg 4 Poblem:. We need o fnd he me kes fo he bck o h he gound.. If > sec. hen he woke s ssued sul. m Physcs 7: Lecue 3, Pg 4 Pge

22 Physcs 7 Lecue 3 Poblem # (A home) l You e wng sho denue soy fo you Englsh clss. In you soy, wo submnes on sece msson need o e plce n he mddle of he Alnc ocen he sme me. They s ou he sme me fom posons eqully dsn fom he endezous pon. They el dffeen eloces bu boh go n sgh lne. The fs submne els n ege elocy of km/h fo he fs 5 km, 4 km/h fo he ne 5 km, 3 km/h fo he ne 5 km nd 5 km/h fo he fnl 5 km. In he plo, he second submne s equed o el consn elocy, whch you wsh o eplcly menon n he soy. Wh s h elocy?. Dw dgm h shows he ph of boh submnes, nclude ll of he segmens of he p fo boh bos. b. Wh ecly do you need o clcule o be ble o we he soy? c. Whch knemcs equons wll be useful? d. Sole he poblem n ems of symbols. e. Does you nswe he he coec dmensons (wh e hey)? f. Sole he poblem wh numbes. Physcs 7: Lecue 3, Pg 43 Poblem # (A home) l As you e dng o school one dy, you pss consucon se fo new buldng nd sop o wch fo few mnues. A cne s lfng bch of bcks on plle o n uppe floo of he buldng. Suddenly bck flls off he sng plle. You clock he me kes fo he bck o h he gound.5 seconds. The cne, founely, hs hegh mkngs nd you see he bck fell off he plle hegh of mees boe he gound. A fllng bck cn be dngeous, nd you wonde how fs he bck ws gong when h he gound. Snce you e kng physcs, you quckly clcule he nswe.. Dw pcue llusng he fll of he bck, he lengh flls, nd he decon of s cceleon. b. Wh s he poblem skng you o fnd? c. Wh knemcs equons wll be useful? d. Sole he poblem n ems of symbols. e. Does you nswe he he coec dmensons? f. Sole he poblem wh numbes. Physcs 7: Lecue 3, Pg 44 Pge

23 Physcs 7 Lecue 3 See you Wednesdy Assgnmen: l Fo Wednesdy, Red hough Chpe 4.4 Physcs 7: Lecue 3, Pg 45 Pge 3

Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration

Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration Mh Csquee Go oe eco nd eco lgeb Dsplcemen nd poson n -D Aege nd nsnneous eloc n -D Aege nd nsnneous cceleon n -D Poecle moon Unfom ccle moon Rele eloc* The componens e he legs of he gh ngle whose hpoenuse