Phsics 1 Lecue 5 Tod s Topics n Moion in D (Chp 4.1-4.3): n D Kinemicl Quniies (sec. 4.1) n D Kinemics wih Consn Acceleion (sec. 4.) n D Pojecile (Sec 4.3) n Epeced fom Peiew: n Displcemen eloci cceleion in eco fom n Kinemics equions in D fom n Pojecile moion in D.
Reiew: Kinemicl Quniies in 1D q Displcemen: chnge of posiion fom ( 1 1 ) ( ) Δ 1 q Veloci: e of posiion chnge. Δ g Δ q Acceleion: e of eloci chnge. Δ g Δ d d d d
Kinemicl Quniies in Veco Fom q Displcemen: Δ f i q Veloci (ege nd insnneous): g Δ Δ Δ d lim Δ Δ d q Acceleion (ege nd insnneous): g Δ Δ Δ lim Δ Δ d d
Kinemics fom 1-D o /3-D q Consn Posiion: q Consn Veloci: q Consn Acceleion: 1 1 No chnge in phsics onl new mhemicl emen!
Kinemicl Quniies in (z) q Like ll ecos kinemicl quniies cn be decomposed ino hei z componens: k j i k j i k j i ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ z z z
Kinemics in (z) Coodinion q Kineics wih consn cceleion: Oiginl Veco Fom In (z) ssem: (Afe clss eecise: wie down equion fo z componen) q Impon Noe: Fo consn kinemics fo z e independen of ech ohe. The onl common pmee is ime. 1 1 1
Pcicl Technique: Decompose Kinemic Pmees q Decomposiion j () j () j () θ i j i () θ i j i () θ i j i () cosθ sinθ cosθ sinθ cosθ sinθ q Inesel: nθ nθ nθ
Two Dimensionl Fee Fll q Fee fll: Moion unde sole influence of gi q Two dimensionl fee fll (pojecile moion): i hs hoizonl componen q Quiz:Duing he fligh of pojecile is cceleion: lws -g g/ -g/ g/sq() -g/sq() depends on he pojecion ngle (neglec i ficion)
Pojecile hoizonl: consn i i eicl: consn -g i - g i - ½ g
Demo: Bllisic c The bll comes bck down ino whee i ws lunched!
Demo: Hoizonl nd Veicl Componens of Pojecile Tjeco Also demo: Jumping up in c
Eecise: Pojecile Moion q A pojecile is sho n iniil speed i n ngle θ. Afe which i is in moion onl unde giionl foce. Find posiion n ime i ime he nge mimum heigh. Sep 1: decompose i i ( i i ) ( i cosθ i i sinθ i ) - g Posiion n (Te nd sepel ) : () i i cosθ i () i ½ i sinθ i - ½ g i ime (hink eicll Δ) : B Δ B i sinθ i /g T i Rnge (Think hoizonll) R i cosθ i T i i sinθ i cosθ i /g Mimum heigh ( hink eicll _A ): A: A i sinθ i /g ( ½ B!) h A i A ½ g A ½ i sin θ i /g (o use i hg)
Quiz: Which Ship Ges Hi Fis q A ble ship simulneousl fies wo ge ships diffeen disnce wih idenicl cnons. Which ship ges hi fis? (ignoe ship heigh). A B sme i sinθ i /g
Quiz : Which Ship Ges Hi Fis q A ble ship simulneousl fies wo ge ships diffeen disnce (noe: he wo cnons m no be idenicl) Which ship ges hi fis? (ignoe ship heigh). A B sme no enough infomion hin: Think eicll! A B
Eecise: Jumping Oe Sem q A bidge h ws 5.9 m long hs been wshed ou b he in seel ds go. How fs mus c be going o successfull jump he sem? Alhough he od is leel on boh sides of he bidge he od on he f side is 3 m lowe hn he od on his side. q Soluion: 3m Ø Se up es s shown 5.9m Ø Think eicll: Δ -3m -g i use Δ i ½ sq(*δ/ ).78s Ø Now hink hoizonll: Δ/ 5.9/.78 7.54m/s
Sme Eecise Diffeen Aes q A bidge h ws 5.9 m long hs been wshed ou b he in seel ds go. How fs mus c be going o successfull jump he sem? Alhough he od is leel on boh sides of he bidge he od on he f side is 3 m lowe hn he od on his side. q Soluion : Ø Choose nohe oienion Ø Think eicll: Δ 3m g i use Δ i ½ sq(*δ/ ).78s Ø Now hink hoizonll: Δ/ 5.9/.78 7.54m/s 5.9m 3m
Demo: Pojecile s Mimum Rnge q A wh shooing ngle he cnon cn chiee mimum nge? R i sinθ i cosθ i /g i sinθ i /g RR m when θ i 45 o (R m i /g) 75 o nd 15 o he sme nge 6 o nd 3 o he sme nge In genel: θ nd 9 o θ he sme nge See demo
Non-Smmeicl Pojecile Moion q A sone is hown fom he op of building s shown. Wh is he hoizonl disnce fom he building o he lnding posiion? q Pocedues: Sep 1: i cos3 o i sin3 o Sep : hink eicll. Δ i ½ g o ge fligh ime. (need o sole qudic eq.) Sep 3: hink hoizonll. i using fom sep.
End-of-Lecue Quizzes q Conside wo fee fll pocesses A nd B s shown. V i m/s θ i 3 o q If hown he sme ime which hi he gound fis? (hin: sin3 o.5) A B sme ime q Which one his he gound highe speed? A B sme