Science Advertisement Intergovernmental Panel on Climate Change: The Physical Science Basis 2/3/2007 Physics 253


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1 Science Adeisemen Inegoenmenl Pnel on Clime Chnge: The Phsicl Science Bsis hp:// /3/7 Phsics 53
2 hp:// /3/7 Phsics 53
3 3 Sus: Uni, Chpe 3 Vecos nd Scls Addiion of Vecos Gphicl Mehods Subcion of Vecos, nd Muliplicion b Scl Adding Vecos b Componens Uni Vecos Veco Kinemics Pojecile Moion Soling Poblems in Pojecile Moion Relie Veloci /3/7 Phsics 53
4 4 Secion Two Poblem Assignmen Q3.4, P3.6, P3.9, P3., P3.4, P3.73 Q3., P3.4, P3.3, P3.43, P3.65, P3.88 /3/7 Phsics 53
5 Veco Kinemics: Displcemen, Veloci, Acceleion 5 Now h we he ecos well descibed we cn focus on he genel descipion of moion in muliple dimensions. Ech of he quniies displcemen, eloci, nd cceleion, which we discussed in Chpe, he moe genel eco epesenion As shown in he figue he displcemen: Occus in he ime inel o i j z ( k nd so ) i ( i j z ) j ( z k z ) k /3/7 Phsics 53
6 Aege nd Insnneous Veloci Vecos 6 The ege eloci eco is he obious eension of ege D D eloci: Noe h he diecion of he ege eloci nd displcemen e idenicl As ppoches zeo we he he insnneous eloci eco: lim d d Tking he deiie of he eco equion we see d d d d dz i j k d d d i j k z /3/7 Phsics 53
7 Aege nd Insnneous Acceleion Vecos 7 The ege cc. eco is he eension of e.. D D cc: As ppoches zeo we he he insnneous cc. eco: d d Noice h ) cceleion m be in diffeen diecion hn el. cceleion m be due o chnge of eloci mgniude, diecion, o boh lim d d i d d j i z d d k j d d z k /3/7 Phsics 53
8 8 Summ of Genelizion d d d d d d d d /3/7 Phsics 53
9 /3/7 /3/7 Phsics 53 Phsics 53 9 Veco Genelizion of Veco Genelizion of Eq Eq. of Moion.. of Moion. If we he consn cceleion eco, hen he equions If we he consn cceleion eco, hen he equions deied fo deied fo D ppl sepel fo he pependicul diecions. D ppl sepel fo he pependicul diecions. Some of hese cn be ecs s eco equions, hough he Some of hese cn be ecs s eco equions, hough he componen fom is moe pcicl. componen fom is moe pcicl. consn, consn ( ) ( ) o o o
10 Emple: A D Spcecf The spcecf hs n iniil eloci of V o m/s nd V o 4 m/s nd n cceleion of 4m/s nd m/s. The diecions o he igh nd up he been chosen s posiie componens. Afe ime of 7. s find ) nd V, b) nd V, nd c) he finl eloci. /3/7 Phsics 53
11 Since he diecions e independen we simpl follow he D dill fom Chpe. Diecion: Known 7. s o m/s 4m/s Unknown?? The eqs.. we need: o Subsiuing m 9 74 / s m m m Diecion: / o / s s Known 4 7. s m / s 7. s o 4m/s m/s 7. s ( 4?? m / s Unknown )( 7. s ) 98 m / s nd 38 m /3/7 Phsics 53
12 The wo eloci componens cn be combined using he Phgoen Theoem o find he mgniude of he finl eloci: V V V (9 m/s) (98 m/s) o V m/s (We keep onl he posiie soluion s i s s he onl phsicl one.) The diecion is gien b θ n  (V/V)) n  (98 m/s / 9 m/s) ) 7 o Thus, fe 7. s he spcecf is moing wih speed of m/s boe he posiie is. Noe how we eed he wo diecions independenl. This is cucil poin. /3/7 Phsics 53
13 3 Though Epeimen One: Fom he op of cliff oelooking lke, peson hows wo sones. The sones he idenicl speeds V o, bu sone is hown downwd n ngle θ nd sone is hown upwd he sme ngle boe he hoizonl. Which sone, if eihe, sikes he we wih gee eloci? /3/7 Phsics 53
14 4 M nie guess is h he downwd hown sone will he he gee eloci, cull h's no ue. Conside he upwdl hown sone. Fis i ises o is mimum heigh nd hen flls bck o eh. When he sone euns o is iniil heigh i hs he sme speed hoizonl nd eicl speed s when hown. (We discussed he eicl speed smme in one dimensionl moion.) The ngle is lso θ below he hoizon. This is ecl he speed nd diecion he downwd hown sone hd when i lef he cliff. Fom his poin on, he wo sones he idenicl eloci. So boh sones sike he we wih he sme eloci. /3/7 Phsics 53
15 Pojecile Moion Genell: An objec moing feel hough i in wo dimensions ne he eh s s sufce Onl eicl cceleion inoled, g9.8 m/s downwd. Glileo ws he fis o nlze pojecile moion The wo dimensions independenl The hoizonl componen hs no cceleion The eicl subjec o he cceleion of gi. 5 /3/7 Phsics 53
16 6 hp://webphsics.didson.edu/couse_meil/ p3/demo/illusion_4.hml /3/7 Phsics 53
17 Moe Elemens of Pojecile Moion 7 The ke: The indiidul componens o dimensions cn be nlzed sepel. Conside bll moing in wo dimensions: The hoizonl componen of he moion, which is cceleion fee, is independen of he eicl componen of he moion which is subjec o cceleion! Veicl diecion: V is zeo bu inceses linel wih ime due o g. Hoizonl Diecion: no cceleion nd consn eloci Noe in his figue dopped bll nd hown bll fll he sme e nd ech he gound he sme ime. /3/7 Phsics 53
18 8 Though Epeimen Two: A child sis upigh in wgon which is moing o he igh consn speed. The child osses up n pple while he wgon coninues o moe fowd. Ignoing i esisnce will he pple lnd behind, in o in fon of he wgon? /3/7 Phsics 53
19 Well we could do full blown nlsis clculing how much ime he bll is in fligh nd how f i would c nd how f he wgon would moe. Bu h s s unnecess once we elized boh he bll nd he wgon he he sme, unchnging hoizonl eloci. No me how long he bll is in fligh boh el he sme disnce duing h ime. The bll will lnd in he wgon. B he w his is wh ossed bll in ou c lws lnds in ou lp! Thee s s no i esisnce inoled inside he c nd ou nd he bll he he sme consn eloci. 9 /3/7 Phsics 53
20 Kinemic Equions fo Pojecile Moion ( up,, g 9.8m/s g o o g g /3/7 Phsics 53
21 /3/7 Phsics 53
22 Finding Finl Vibles Gien Iniil Vibles: A kicked foobll A foobll is kicked n ngle θ37. o wih n iniil eloci of.m/s. Wh will be Mimum heigh? Time of el? Finl displcemen? Veloci pe? Acceleion pe? Fom jus he iniil condiions he pojecile equions poide e ll subsequen hiso of he jeco /3/7 Phsics 53
23 3 Well wh do we know? he iniil eloci nd iniil posiion nd cceleion. o o o o cosθ ο (.m/s)cos37. o 6.m/s o o sinθ ο (.m/s)sin37. o.m/s 9.8m/s The fis unknown quni is he mimum heigh. Well, we ge his b consideing he dimension. You e done his befoe! Filling ou he ble: Known o o m/s 9.8m/s Unknown? The hid equion does he ick! (.m / s) 9.8m / s 7.35m /3/7 Phsics 53 g g
24 Ne comes he ime of el. If we jus conside he dimension we see e fmili poblem: Known o o m/s 9.8m/s Unknown?? And we use he nd equion which s shown on he igh hs wo oos coesponding o he iniil kick nd o he eun o eh. nd  o g (m / s) (9.8m / s ) (9.8m / s ) (m / s) (9.8m / s ) (m / s) ( (9.8m / s ) (m / s)) ((4.9m / s ) (m / s)) nd.45s 4 /3/7 Phsics 53
25 5 Now h we he he ime of el we simpl un o he dimension equions o ge he finl displcemen o 6. m / s.45s 39.m A he pe so hee is onl hoizonl moion so o 6.m/s The quesion he cceleion he pe is ick quesion. Acceleion is lws 9.8m/s down! /3/7 Phsics 53
26 6 Schedule Pojecile moion is quie ich, we ll coninue o eploe he consequences. Reiew Feb 7 No clss Feb 9 Tes Feb Fis wo poblem ses due Feb If ou need help see me soon! /3/7 Phsics 53
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