i-clicker!! x 2 lim Lecture 3 Motion in 2- and 3-Dimensions lim REVIEW OF 1-D MOTION
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1 Lecture 3 Mtin in - and 3-Dimensins REVIEW OF -D MOTION TODY: LSTCHNCETOMKEUPTHEPHYSICS PRETEST(u get pints fr cmpleting the pre and pst tests) Where: SERC 6 (SEC 6) When: Yucanarrieantime3:0pm 6:30 pm (theprctrwillwaitwithuuntilufinishif ucmeat6:30.) ; ; lim a t t0 t d Fr CONSTNT acceleratin in -D at t speed = (magnitude f ) a lim t t0 d ( ) a Free Fall: replace a with -g i-clicker!! iclicker student btains a graph f an bject s elcit ersus time and then draws the graph f the acceleratin ersus time fr the same time interal. a What, if anthing, is wrng with the graph f the acceleratin ersus time? ) The last acceleratin segment shuld nt be zer when the bject is ming. ) The psitie acceleratin segment shuld be further frm the time ais than the negatie acceleratin segment is. C) The sign f the first acceleratin segment is incrrect. D) The first acceleratin segment shuld steadil decrease in magnitude. E) The graph is crrect.
2 iclicker iclicker riel and rn are ming alng a straight hallwa. If the ertical ais is psitin, which f the fllwing statements is TRUE? riel rn, s riel and rn are ming alng a straight hallwa. If the ertical ais is elcit, which f the fllwing statements is TRUE? riel rn, s ) The tw children are neer at the same psitin at the same time. ) The tw children are at the same place at t = 0. C) The tw children neer he the same elcit simultaneusl. D) The tw children neer he the same acceleratin. E) Nne f the abe are TRUE. ) The tw children neer change directin. ) The tw children neer he the same elcit. C) The tw children are ming at the same speed at t = 0. D) The tw children neer he the same acceleratin. E) Nne f the abe. The graphs shw the elcit ersus time fr si bats treling alnganarrwchannel.ineachgraph,apintwhichisbeing discussedismarkedwithadt. Whichfthefllwingis INCORRECT(at the time indicated b the dts)? D Velcit Velcit Velcit )ThebatsinandChethesameelcit. E iclicker Velcit )ThebatsinandFareminginthesamedirectin. C)ThebatsinDandEaremingwithnegatieelcit. D)ThedtngraphEcrrespndstalargerspeehanthe dtngraph. E)ThedtngraphEcrrespndstalargerspeehanthe pintngraphd. C F Velcit Velcit MOTION IN ND 3 DIMENSIONS Recall: Displacement is a ectr! Has magnitude and directin S are elcit and acceleratin Represent ectr b arrw: Here: (Same magnitude and directin) D nt need t lie n tp f each ther Furthermre: (Same Magnitude, Oppsite Directin) Ntatin: = Magnitude f ectr Write: = NOTE: and C C Fr ectrs abe: = = C = C =! ( - sign indicates directin)
3 dding tw ectrs graphicall Subtracting ectrs Tw ectrs ma be added graphicall using either the parallelgram methd r the head-t-tail methd. animatin animatin Cpright 0 Pearsn Educatin Inc. Cpright 0 Pearsn Educatin Inc. Multipling a ectr b a scalar If c is a scalar, the prduct c has magnitude c. Cmpnents f a ectr dding ectrs graphicall prides limited accurac. Vectr cmpnents pride a general methd fr adding ectrs. n ectr can be represented b an -cmpnent and a -cmpnent. Use trignmetr t find the cmpnents f a ectr: = cs θ and = sin θ, where θ is measured frm the +-ais tward the +-ais. animatin Cpright 0 Pearsn Educatin Inc. Cpright 0 Pearsn Educatin Inc.
4 COMPONENTS ND COMPONENT VECTORS Clearl: i-clicker!!,, are cmpnent ectrs f are cmpnents f Ntice: sin sin cs cs sin and tan ; cs EXMPLE: Yu are driing east n Canal Street. The Empire State building is 5km at 53 N f E. Hw man km E and then N must u drie? E R E = cs(53 ) = (5km)(0.6) = 3 km N = sin(53 ) = (5 km)(0.8) = 4 km N N 5 E Cnsider ectrs f unit length in - and -directins iˆ ; iˆ ; iˆ ; UNIT VECTORS iˆ Unit ectrs make ectr additin er eas! C C C C C iˆ C C C iˆ C C ( C )ˆ i ( )
5 DISPLCEMENT r r r r r r r r iˆ zkˆ is displacement Suppse this displacement ccurred in interal (t t ) r r r t t t INSTNTNEOUS VELOCITY In analg with -D case: r dr lim t 0 t d iˆ erage elcit d is tangent t particle path ˆ dz j kˆ iˆ Particle path kˆ z 8 EXMPLE: In ne pla during the RU ftball game last Saturda, theballwassnappethequarterbackwhdrppedbackd in0.5s,hethenran5dsparalleltthelinefscrimmageins, thenhethrewtheball5dsatananglef37 frmthefrward directin in 0.5 s. What was the erage elcit,, f the ball during this pla? r r t t r 0 r ( d)ˆ i ( 5 d) C r i ˆ ( d)ˆ ( 5 d) j (4 d)ˆ i (3 d) r (3 d)ˆ i ( r r? d) C 37 C C C =Ccs(37 ) = (5 ds)(0.8) = 4 ds C =Csin(37 ) = (5 ds)(0.6) = 3 ds t = s (3 d)ˆ i ( d) d d (.5 )ˆ i ( ) s s s EXMPLE: Suppse u drie n a cured rad. Yur psitin is gien b: t ct ; kt 3 What is? What is? r 3 ( t ct )ˆ i ( kt ) ( ct )ˆ i (3kt ) ( t 0) ˆ i ( t 3) ( 6c)ˆ i (7k) (Nte: car at rigin when t = 0) What is fr the interal 0 3s? ( t 0) ( t 3s) rr t ; r ( t0) 0 r ( t3) (3 ( 3c)ˆ i (9k) 9c)ˆ i(7k) tacertaininstantintime,thelcatinairplaneisgienb: r 0 kmˆ i0 km 0 km kˆ Onehurlater,theplaneislcatedat: Theerageelcitftheplaneduringthathuris: : : C: Cannt tell. Need t knw psitin during that hur. D: E: r 0 kmˆ i 0 km i-clicker!! ( 0ˆ i 30 0 kˆ) ( 0ˆ i30 0 kˆ) 0 km kˆ ( 0ˆ i0 0 kˆ) ( 0ˆ i0 0 kˆ) r r t t
6 dditin f elcit ectrs: airplane in crsswind wind CCELERTION VECTOR Cnsider preius eample: changes directin changes magnitude erage acceleratin: a t t ( ) a t a 3 Instantaneus acceleratin a 0 a 0 a d lim t t fr an cured path if changes: magnitude r directin r bth EXMPLE: Cnsider car again: r iˆ j ˆ 3 ( t ct )ˆ i ( kt ) ( ct )ˆ i (3kt ) ˆ j a ( c)ˆ i (6kt) Parallel and perpendicular cmpnents f a : a : r iˆ j ˆ zkˆ d d dz iˆ ˆ j kˆ d d d z a i ˆ kˆ changes magnitude, changes directin f a Shw Phet Maze Game! TODY: LSTCHNCETOMKEUPTHEPHYSICS PRETEST(u get pints fr cmpleting the pre and pst tests) Where: SERC 6 (SEC 6) When: Yucanarrieantime3:0pm 6:30 pm (theprctrwillwaitwithuuntilufinishif ucmeat6:30.) If: a a same directin as a 0 nl changes directin ppsite (anti parallel) t increases decreases 6
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