Physics 201 Lecture 3. dx v x. l What was the average velocity? l Two legs with constant velocity but. l Average velocity:
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1 Phscs Lecure 3 Lecure 3 l Moon n one-dmenson (k Knemcs Emne ssems wh non-zero cceleron (oen consn Sole D problems wh zero nd consn cceleron (ncludn ree-ll nd moon on n nclne Phscs : Lecure 3, P Poson, nsnneous eloc & cceleron ( uncon( ( d d d d ( d d Phscs : Lecure 3, P Oen so Emple problem l Veloc uncon cn be used o obn poson uncon ( l A cr moes o he rh rs or. sec. m/s nd hen 4. seconds. m/s. d d ( ( d ( l Are under he ( cure elds he dsplcemen l Specl cse: Veloc s consn ( l Wh ws he ere eloc? l Two les wh consn eloc bu. l Aere eloc:,, chnen poson chne n me Phscs : Lecure 3, P 3 Phscs : Lecure 3, P 4 Emple problem l A prcle moes o he rh rs or. seconds. m/s nd hen 4. seconds. m/s. l Wh ws he ere eloc? l Two les wh consn eloc l Fnd he ol dsplcemen ( l Consn eloc ( ( - ( - l - ( - ( ( - ( - l m/s ( s m/s (4 s m n 6. s or.7 m/s Phscs : Lecure 3, P 5 Anoher specl cse, consn cceleron l Prcle moon wh consn cceleron The eloc ecor chnes d consn d d d re under cure Phscs : Lecure 3, P 6 Pe
2 Phscs Lecure 3 Consn cceleron n D l Prcle moon wh consn cceleron l A cr, srn res, wh smoohl ncresn eloc (o he rh: ( I consn cceleron we cn nere wce cons ( Phscs : Lecure 3, P 7 Phscs : Lecure 3, P 8 I consn cceleron hen we lso e: (, ( (,, ( Phscs : Lecure 3, P 9 Phscs : Lecure 3, P Dsplcemen wh consn cceleron A prcle srn res & mon lon lne wh consn cceleron hs dsplcemen whose mnude s proporonl o (. Ths cn be esed. Ths s poenll useul resul Phscs : Lecure 3, P Free Fll l When n objec s le o lls owrd he round!! The orce h cuses he objecs o ll s clled r. l Ths cceleron on he Erh s surce, cused b r, s pcll wren s lle l An objec, be bsebll or n elephn, eperences he sme cceleron ( when s dropped, hrown, sp, or hurled,.e. s consn. - ( Phscs : Lecure 3, P Pe
3 Phscs Lecure 3 Gr cs: l does no depend on he nure o he merl! Glleo ( ured hs ou whou nc clocks & rulers! Eercse Moon n One Dmenson When hrown bll srh up, whch o he ollown s rue bou s eloc nd s cceleron he hhes pon n s ph? l Feher & penn behe jus he sme n cuum l Nomnll, 9.8 m/s A he equor 9.78 m/s A. Boh nd B., bu C., bu D. None o he boe A he Norh pole 9.83 m/s Phscs : Lecure 3, P 3 Phscs 7: Lecure 3, P 4 Thrown bll up l You hrow bll up 9.8 m/s, how hh does oes nd how lon does ke? l nl eloc 9.8 m/s nl eloc m/s ( m/s 9.8 m/s 9.8 m/s. s ( 4.9 m 9.8 m/s (s 4.9 m/s (s Phscs 7: Lecure 3, P 5 Thrown bll up l You hrow bll up 9.8 m/s, l Inorn r ressnce, how s s relln when lls ps ou? ( m 9.8 m/s ( 4.9 m/s (. s,. s ( 9.8 m/s 9.8 m/s 9.8 m/s (. s Phscs 7: Lecure 3, P 6 Home Eercse More comple Poson s. Tme Grphs In drn rom Mdson o Chco, nll m speed s consn 65 mph. Aer some me, I see n ccden hed o me on I-9 nd mus sop quckl so I decelere ncresnl s unl I sop. The mnude o m cceleron s me s en b, Queson: M eloc s me rph looks mos lke whch o he ollown? A. B. C. Phscs 7: Lecure 3, P 7 Eercse D Freell l Alce nd Bll re sndn he op o cl o heh H.. Boh hrow bll wh nl speed, Alce srh down nd Bll srh up.. The speed o he blls when he h he round re A nd B respecel. A. A < B B. A B C. A > B Alce Bll H A B Phscs 7: Lecure 3, P 8 Pe 3
4 Phscs Lecure 3 Eercse D Freell : Grphcl soluon l Alce nd Bll re sndn he op o cl o heh H.. Boh hrow bll wh nl speed, Alce srh down nd Bll srh up. cl bck urnround - pon cl - dencl dsplcemens (one nd one - round round round Phscs 7: Lecure 3, P 9 The rph rh shows he eloc ersus me rph or bll. Gr s cn downwrd n he - drecon nd he -s s lon he horzonl. Whch eplnon bes s he moon o he bll s shown b he eloc-me me rph below? Eercse,D Freell A. The bll s lln srh down, s cuh, nd s hen hrown srh down wh reer eloc. B. The bll s rolln horzonll, sops, nd hen connues rolln. C. The bll s rsn srh up, hs he celn, bounces, nd hen lls srh down. D. The bll s lln srh down, hs he loor, nd hen bounces srh up. E. The bll s rsn srh up, s cuh nd held or whle, nd hen s hrown srh down. Phscs 7: Lecure 3, P Fe Seps: Problem Soluon Mehod: Focus he Problem - drw pcure wh re we skn or? Descrbe he phscs - wh phscs des re pplcble - wh re he relen rbles known nd unknown 3 Pln he soluon - wh re he relen phscs equons 4 Eecue he pln - sole n erms o rbles - sole n erms o numbers 5 Elue he nswer - re he dmensons nd uns correc? - do he numbers mke sense? A scence projec l You drop bus o he Wlls Tower (44 m boe he sde wlk. I so hppens h Supermn les b he sme nsn ou relese he bus. Supermn s ln down 35 m/s. l How s s he bus on when cches up o Supermn? Phscs 7: Lecure 3, P Phscs 7: Lecure 3, P A scence projec A scence projec l You drop bus o he Wlls Tower (44 m boe he sde wlk. I so hppens h Supermn les b he sme nsn ou relese he cr. Supermn s ln down 35 m/s. l How s s he bus on when cches up o Supermn? l Drw pcure Phscs 7: Lecure 3, P 3 l Drw pcure l Cures nersec wo pons Supermn Supermn bus Supermn Supermn Supermn Phscs 7: Lecure 3, P 4 Pe 4
5 Phscs Lecure 3 Home eercse o D moon problem l A cr s nll reln Es consn speed o m/s. When s hlw (n dsnce! o s desnon s speed suddenl ncreses nd hereer remns consn. All old he cr spends ol o s n rns wh n ere speed o 5 m/s. l Wh s he speed o he cr durn he nd hl o he rp? l Ths s ron on he n clss emple bu much more dcul. Home eercse o D moon problem l A cr s nll reln Es consn speed o m/s. When s hlw (n dsnce! o s desnon s speed suddenl ncreses nd hereer remns consn. All old he cr spends ol o s n rns wh n ere speed o 5 m/s. l Wh s he speed o he cr durn he nd hl o he rp? l Dnmcl relonshps (onl consn cceleron: cons ( ( ( Phscs 7: Lecure 3, P 5 And (dsplceme n ( ere eloc (ol me Phscs 7: Lecure 3, P 6 Drwn he pcure Usn ( > ( > m/s m/s m/s m/s l Plus he ere eloc l Knowns: m s m/s s 5 m/s relonshp beween nd l Four unknowns & nd mus nd n erms o knowns Phscs 7: Lecure 3, P 7 ( ( l Four unknowns l Four relonshps l Focus on ( Phscs 7: Lecure 3, P 8 Usn ( > Usn ( > m/s m/s m/s m/s ( / s 5 m 5 / s 5/4 s m 5 s 5 m s 5 m 5 m 5 m ( 5 / 4 s (5 / 4 s Phscs 7: Lecure 3, P 9 l Elmne unknowns rs ne ( hen 3 & ( ( 4 ( 4 Mul. b / Phscs 7: Lecure 3, P 3 ( Pe 5
6 Phscs Lecure 3 m/s l Plus he ere eloc l Gen: m/s s 5 m/s Fn ( > m/s ( 5m/s m/s 5m/s m/s m/s 5m/s Phscs 7: Lecure 3, P 3 Tps: l Red! Beore ou sr work on problem, red he problem semen horouhl. Mke sure ou undersnd wh normon s en, wh s sked or, nd he menn o ll he erms used n sn he problem. l Wch our uns (dmensonl nlss! Alws check he uns o our nswer, nd crr he uns lon wh our numbers durn he clculon. l Ask quesons! Phscs 7: Lecure 3, P 3 Cone Rch Problem: For dscusson Problem: l On brh sunn d ou re wlkn round he cmpus wchn one o he mn consrucon ses. To l bunch o brcks rom cenrl re, he he brouh n helcoper. As he plo s hoern he/she ccdenll releses he brcks when he re m boe he round. A worker, drecl below, snds sll or seconds beore wlkn w. (Le m/s There s no wnd or oher eecs.. We need o nd he me kes or he brck o h he round.. I > sec. hen he worker s ssured surl. m Does he worker le? (Crer or ln..he worker moes beore he brcks srke he round Phscs 7: Lecure 3, P 33 Phscs 7: Lecure 3, P 34 Problem # (Group or home l You re wrn shor denure sor or our Enlsh clss. In our sor, wo submrnes on secre msson need o rre plce n he mddle o he Alnc ocen he sme me. The sr ou he sme me rom posons equll dsn rom he rendezous pon. The rel deren eloces bu boh o n srh lne. The rs submrne rels n ere eloc o km/hr or he rs 5 km, 4 km/hr or he ne 5 km, 3 km/hr or he ne 5 km nd 5 km/hr or he nl 5 km. In he plo, he second submrne s requred o rel consn eloc, whch ou wsh o eplcl menon n he sor. Wh s h eloc?. Drw drm h shows he ph o boh submrnes, nclude ll o he semens o he rp or boh bos. b. Wh ecl do ou need o clcule o be ble o wre he sor? c. Whch knemcs equons wll be useul? d. Sole he problem n erms o smbols. e. Does ou nswer he he correc dmensons (wh re he?. Sole he problem wh numbers. Problem # (A home l As ou re drn o school one d, ou pss consrucon se or new buldn nd sop o wch or ew mnues. A crne s ln bch o brcks on plle o n upper loor o he buldn. Suddenl brck lls o he rsn plle. You clock he me kes or he brck o h he round.5 seconds. The crne, orunel, hs heh mrkns nd ou see he brck ell o he plle heh o meers boe he round. A lln brck cn be dnerous, nd ou wonder how s he brck ws on when h he round. Snce ou re kn phscs, ou quckl clcule he nswer.. Drw pcure llusrn he ll o he brck, he lenh lls, nd he drecon o s cceleron. b. Wh s he problem skn ou o nd? c. Wh knemcs equons wll be useul? d. Sole he problem n erms o smbols. e. Does ou nswer he he correc dmensons?. Sole he problem wh numbers. Phscs 7: Lecure 3, P 35 Phscs 7: Lecure 3, P 36 Pe 6
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