Physics 201 Lecture 15

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Octavia Kelley
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1 Phscs 0 Lecue 5 l Goals Lecue 5 v Elo consevaon of oenu n D & D v Inouce oenu an Iulse Coens on oenu Consevaon l oe geneal han consevaon of echancal eneg l oenu Consevaon occus n sses wh no ne eenal foces (as a veco quan) v Coae oce vs e o oce vs sance v Inouce Cene-of-ass oe: n Ea, ona, ach 9 h, 7:5 o 8:45 P Phscs 0: Lecue 5, Pg Phscs 0: Lecue 5, Pg Elosons: A collson n evese l A wo ece assebl s hangng vecall a es a he en of a 0 long assless sng. The ass of he wo eces ae 60 an 0 kg esecvel. Suenl ou obseve ha he 0 kg s ejece hozonall a 0 /s. The e of he eloson s sho coae o he swng of he sng. l Does he enson n he sng ncease o ecease afe he eloson? l If he e of he eloson s sho hen Befoe oenu s conseve n he -econ because hee s no ne foce. Ths s no ue of he -econ bu hs s wha we ae neese n. Afe Phscs 0: Lecue 5, Pg Elosons: A collson n evese l A wo ece assebl s hangng vecall a es a he en of a 0 long assless sng. The ass of he wo eces ae 60 an 0 kg esecvel. Suenl ou obseve ha he 0 kg ass s ejece hozonall a 0 /s. l Deche he hscs:. The geen ball ecols n he econ ( Law) an, because hee s no ne eenal foce n he -econ he -oenu s conseve.. The oon of he geen ball s Befoe consane o a ccula ah hee us be ceneal (.e., aal acceleaon) Afe Phscs 0: Lecue 5, Pg 4 Elosons: A collson n evese l A wo ece assebl s hangng vecall a es a he en of a 0 long assless sng. The ass of he wo eces ae 60 & 0 kg esecvel. Suenl ou obseve ha he 0 kg ass s suenl ejece hozonall a 0 /s. l Cons. of -oenu befoe afe 0 - V v V v / 0*0/ 60 0 /s T befoe Wegh (600) Befoe Σ a c V / T g T g V / (0) /0 900 Afe Eecse oenu s a Veco (!) quan l A block sles own a fconless a an hen falls an lans n a ca whch hen olls hozonall whou fcon l In egas o he block lanng n he ca s oenu conseve? A. Yes B. o C. Yes & o D. Too lle nfoaon gven Phscs 0: Lecue 5, Pg 5 Phscs 0: Lecue 5, Pg 6 Page

2 Phscs 0 Lecue 5 Eecse oenu s a Veco (!) quan l -econ: o ne foce so P s conseve. l -econ: e foce, neacon wh he goun so eenng on he sse (.e., o ou nclue he Eah?) s no conseve (sse s block an ca onl) 5.0 Le a kg block sa a es on a nclne an sle vecall a sance 5.0 an fall a sance 7.5 no he 0 kg ca Wha s he fnal veloc of he ca? kg kg Phscs 0: Lecue 5, Pg 7 Eecse oenu s a Veco (!) quan l -econ: o ne foce so P s conseve l -econ: v of he ca block wll be zeo an we can gnoe v of he block when lans n he ca. Inal nal P : V v () V 0 v () V V v / ( ) (8.7)/ /s V.4 /s j 5.0 g 7.5 ) a g sn 5 /s ) 5 / sn ½ a 0.5 /s s v a 0 /s v v cos 8.7 /s Phscs 0: Lecue 5, Pg 8 Iulse (A vaable eenal foce ale fo a gven e) l Collsons ofen nvolve a vang foce (): 0 au 0 l We can lo foce vs e fo a cal collson. The ulse, I, of he foce s a veco efne as he negal of he foce ung he e of he collson. l The ulse easues oenu ansfe oce an Iulse (A vaable foce ale fo a gven e) l J a veco ha eflecs oenu ansfe v I ( / ) Iulse I aea une hs cuve! (Tansfe of oenu!) Iulse has uns of ewon-secons f Phscs 0: Lecue 5, Pg 9 Phscs 0: Lecue 5, Pg 0 oce an Iulse l Two ffeen collsons can have he sae ulse snce I eens onl on he oenu ansfe, OT he naue of he collson. Aveage oce an Iulse sae aea av av bg, sall sall, bg bg, av sall sall, av bg Phscs 0: Lecue 5, Pg Phscs 0: Lecue 5, Pg Page

Phscs 0 Lecue 5 Eecse oce & Iulse l Two boes, one heave han he ohe, ae nall a es on a hozonal fconless suface. The sae consan foce acs on each one fo eacl secon.

c, wha s v a 4.0 s? l v Iulse l v I 0, I, I,4 lgh heav l v (-8) s ½ (-8) s ½ 6() s A. heave B. lghe C. sae v 4 s v /s v /s 4 /s D.

3 Phscs 0 Lecue 5 Eecse oce & Iulse l Two boes, one heave han he ohe, ae nall a es on a hozonal fconless suface. The sae consan foce acs on each one fo eacl secon. Whch bo has he os oenu afe he foce acs? Dscusson Eecse l The onl foce acng on a.0 kg objec ovng along he - as. oce ha he lo s foce vs e. l If he veloc v s.0 /s a 0 sec, wha s v a 4.0 s? l v Iulse l v I 0, I, I,4 lgh heav l v (-8) s ½ (-8) s ½ 6() s A. heave B. lghe C. sae v 4 s v /s v /s 4 /s D. can ell Phscs 0: Lecue 5, Pg Phscs 0: Lecue 5, Pg 4 A efecl nelasc collson n -D l Conse a collson n -D (cas cashng a a sle nesecon...no fcon). A efecl nelasc collson n -D l If no eenal foce oenu s conseve. l oenu s a veco so, an z ae conseve V v V v v v befoe afe l If no eenal foce oenu s conseve. l oenu s a veco so, an z Phscs 0: Lecue 5, Pg 5 befoe afe l - : v ( ) V cos l - : v ( ) V sn Phscs 0: Lecue 5, Pg 6 D Elasc Collsons Bllas l Pefecl elasc eans ha he objecs o no sck an, b sulaon, echancal eneg s consevse. l Thee ae an oe ossble oucoes bu, f no eenal foce, hen oenu wll alwas be conseve l Conse he case whee one ball s nall a es. afe befoe b a v c P a φ Befoe Afe The fnal econ of he e ball wll een on whee he balls h. Phscs 0: Lecue 5, Pg 7 Phscs 0: Lecue 5, Pg 8 Page

4 Phscs 0 Lecue 5 Bllas: Whou eenal foces, consevaon of boh oenu & ech. eneg l Consevaon of oenu l - P : v befoe v afe cos V afe cos φ l - P : 0 v afe sn V afe sn φ befoe b afe afe Cene of ass l os objecs ae no on-lke bu have a ass ens an ae ofen efoable. l So how oes one accoun fo hs cole n a saghfowa wa? Eale P afe φ If he asses of he wo balls ae equal hen hee wll alwas be a 90 angle beween he ahs of he ougong balls Phscs 0: Lecue 5, Pg 9 l In fooball coaches ofen ell laes aeng o ackle he ball cae o look a he navel. l So wh s hs so? Phscs 0: Lecue 5, Pg 0 Sse of Pacles: Cene of ass () l If an objec s no hel hen wll oae abou he cene of ass. l Cene of ass: Whee he sse s balance! v Bulng a oble s an eecse n fnng cenes of ass. oble Phscs 0: Lecue 5, Pg Sse of Pacles: Cene of ass l How o we escbe he oson of a sse ae u of an as? l Defne he Cene of ass (aveage oson): v o a collecon of nvual on-lke acles whose asses an osons we know: (In hs case, ) R L Phscs 0: Lecue 5, Pg oenu of he cene-of-ass s jus he oal oenu l oce ( ) ( v ) v v l Iulse an oenu consevaon ales o he cene-of-ass Phscs 0: Lecue 5, Pg... Sale calculaon: l Conse he followng ass sbuon: X X ( 0 4 )/4 ees R (,6) Y ( 0 0 )/4 ees (,) X ees Y 6 ees (0,0) (4,0) î Y ĵ Z kˆ Phscs 0: Lecue 5, Pg 4 Page 4

5 Phscs 0 Lecue 5 A classc eale l Thee s a sc of unfo ass an aus. Howeve hee s a hole of aus a a sance b (along he -as) awa fo he cene. l Whee s he cene of ass fo hs objec? 0 b ( σ ( σ geen sk (0,0) ( b,0) hole σ π 0 0 ( σ ( σ ba / a / 0 ba b a Phscs 0: Lecue 5, Pg 5 Sse of Pacles: Cene of ass l o a connuous sol, conve sus o an negal. whee s an nfnesal ass eleen (see e fo an eale). Phscs 0: Lecue 5, Pg 6 Reca l Thusa, Revew fo ea l o Tuesa, Rea Chae Phscs 0: Lecue 5, Pg 7 Page 5

5-1. We apply Newton s second law (specifically, Eq. 5-2). F = ma = ma sin 20.0 = 1.0 kg 2.00 m/s sin 20.0 = 0.684N. ( ) ( )

5-1. We apply Newton s second law (specifically, Eq. 5-2). F = ma = ma sin 20.0 = 1.0 kg 2.00 m/s sin 20.0 = 0.684N. ( ) ( ) 5-1. We apply Newon s second law (specfcally, Eq. 5-). (a) We fnd he componen of he foce s ( ) ( ) F = ma = ma cos 0.0 = 1.00kg.00m/s cos 0.0 = 1.88N. (b) The y componen of he foce s ( ) ( ) F = ma = ma