Today s opc: MPULSE ND MOMENTUM CONSERVTON Reew of Las Week s Lecure Elasc Poenal Energy: x: dsplaceen fro equlbru x = : equlbru poson Work-Energy Theore: W o W W W g noncons W non el W noncons K K K ( KU g U ) ( ) el K U g U el Le U U g U el = Poenal Energy E KU = Toal Mechancal Energy cons E E (frcon, drag, work done by uscles, ec.) W non cons E E Conseraon of echancal energy orce and Poenal Energy: x du dx du dx U(x) du dx x Slow oon deo of las week s sprng launch: Skae Park naon Wha does he sprng do, oher han shoong up (and fallng down)? Does braonal/roaonal oon sore energy? Wha knd of energy? Dd you accoun for hs energy n las weeks workshop? Only abou % of he oal energy n braon, uch less n roaon!
Sprng launch ay sere as odel for olecules desorbng (.e., deachng) fro a surface: sprng can brae n any noral odes : The hgher he nuber of nodes, he greaer he braonal frequency. True no only for sprngs, bu any sold! Do hese odes connue o nfny (nfne # of nodes)? Roaonal Sae Populaons No, waelengh s led by spacng beween aos: Lace Vbraons or Phonon Modes. M. Zerann and W. Ho, Surface Scence Repors, 7-47 (995). Use feosecond laser specroscopy o easure phonon braons n LuMnO3 crysal: MOMENTUM & MPULSE NEWTON S nd Law: a Wre dfferenly: Defne Moenu: d d ( ) p (Uns: kg /s = N s) Ne force = Rae of change of oenu Reflecy change x -5 Pup-Probe Delay (pcoseconds) S. Lou,. M. Zerann, R.. arynsk, N. Hur, and S. Cheong, Physcal Reew 79, 43 (). Consder hs relaonshp furher: ( ) p p Defne pulse: J p p ( ) p p Vecor ha equals change n oenu
Had: Work-Energy Theore, now hae: pulse Moenu Theore: Consder a arable force acng on an objec fro e o (e.g., baskeball drbble) negral of acual force fro o s equal o aerage force es neral p KE () COMPRSON: MOMENTUM s. KNETC ENERGY: p s a ecor ; KE s a scalar p relaed o e oer whch force acs! relaed o dsance oer whch force acs! J KE J p p ( ) J ( ) -kg box, nally a res, oes along a frconless horzonal surface. horzonal force o he rgh s appled o he box. The agnude of he force changes as a funcon of e as shown.. The pulse n he frs seconds s kg /s. The pulse fro 5 seconds o 8 seconds s -6 kg /s C. The pulse n he frs seconds s kg /s D. The pulse fro seconds o 5 seconds s kg /s E. The pulse canno be deernes wh he nforaon gen -kg objec acceleraes n response o an appled force. Durng he 5-second neral ha he force s appled, he objec s elocy changes fro 3 /s eas o 7 /s wes. Whch s rue abou he agnude of he pulse? E. wan pons subraced fro y grade J p p J p. equals kg /s. equals 8 kg /s C. equals 8/5 kg /s D. equals 4 kg /s E. canno be found wh he nforaon gen.
CONSERVTON O LNER MOMENTUM Consder wo solaed objecs ha nerac only by her uual force. (No ne exernal force) u on So: on on on on on (Newon s 3 rd Law) or solaed syse (no exernal forces) oal lnear oenu of he syse s consan: P p p consan CONSERVTON O LNER MOMENTUM d on ( p p ) on Conseraon of oenu s ald for any nuber of parcles neracng only wh each oher (No Exernal orces) P p Ranger and a Dels hockey player are fghng on he ce. The Dels player (M = kg) hrows a punch ha sends he Ranger ( = 8 kg) off a s a ecor quany ha s consered EXMPLE - physcs of hockey: R.5 /s. Wha s he speed of he Dels player, D? p R P ; p R f f P p R p D D P P f p R f P p D f R f p ( 8 kg)(.5 /s); p ( kg) Df ( 4 kg /s) ( kg) D f D f (4 kg /s).4 /s ( kg) Df D f Two boxes are ed ogeher by a srng and are sng a res n he ddle of a large frconless surface. eween he wo boxes s a assless copressed sprng. The srng yng he wo boxes ogeher s cu suddenly and he sprng expands, pushng he boxes apar. The box on he lef has four es he ass of he box on he rgh. n Case, a eal bulle peneraes a wooden block. n Case, a rubber bulle wh he sae nal speed and ass bounces off of an dencal wooden block. Wll he speed of he wooden block afer he collson be greaer n Case, greaer n Case, or he sae n boh cases? he nsan (afer he srng s cu) ha he boxes lose conac wh he sprng, he speed of he box on he lef wll be.).) C.) D.) Greaer han he rgh box Less han he rgh box Equal o he rgh box No enough nforaon proded. The speed wll be greaer n Case because he eal bulle exers a larger force on he block.. The speed wll be greaer n Case because he bulle changes drecon. C. The speed wll be he sae n boh cases because he bulles hae he sae ass and nal speed and ge he block he sae oenu. D. Canno be deerned.
MOMENTUM CONSERVTON ND COLLSONS Collson: ref, srong neracon beween objecs. f ex beween objecs, Neglec ex behaes as an solaed syse P p P p Toal oenu jus afer collson = Toal oenu jus before collson Classfy Collsons: Elasc Collson Toal oenu and Toal knec energy consered nelasc Collson Moenu consered KE s no (los o nernal energy) Copleely nelasc Collson Moenu consered (Objecs sck ogeher) KE no. (KE nernal) Moenu consered n any collson KE consered only n elasc collson EXMPLE: Copleely nelasc Collson The allsc Pendulu: bulle ( a, ) s fred no clp of pendulu whch swngs o hegh h. Wha s? TWO PRTS! Collson s copleely nelasc Use P P o fnd sae jus afer collson. P P ( Use conseraon of echancal energy: K U g K f U gf a a b) ( ) ( ) gh gh gh h llard all Collson -D Collson along x-axs (o subscrps) KE P 3 ELSTC COLLSON KE and P CONSERVED P KE efore fer PGE O LGER ( ) ( )? MGNTUDE O RELTVE VELOCTY UNCHNGED TER COLLSON EXMPLE: Pocke The Egh all 3 efore collson: ong a res 3 MPORTNT CSES ; ; ;
assue 3 Cars and are shown jus before hey collde. Whch (f any) of he followng saeens could possbly be correc? 9KE 3 KE. fer he collson, he cars wll sck ogeher and oe off o he lef due o Car hang ore speed.. They ll sck ogeher and oe off o he rgh because Car s heaer.. The speed and he ass copensae. or copleely nelasc collson, boh cars are gong o be a res afer he collson. V. or an elasc collson, hey wll change her drecons, so Car wll be ong o he lef a 3 /s and Car wll be ong o he rgh a 4 /s..).) C.) D.) V E.) & V Collson n wo densons (horzonal plane) efore: fer: Two dencal seel balls, S and T, are shown a he nsan ha hey collde. The pahs and eloces of he wo balls before and afer he collson are ndcaed by he dashed lnes and arrows. Wha s he drecon of he pulse on ball S? Wre separae oenu conseraon equaons for coponens: P P x : x x x x : y y y y y f collson s elasc: KE KE Three equaons, can sole for a axu of hree unknowns: Moenu and energy conseraon alone are no suffcen o deerne he fnal sae... Canno be deerned whou he e. C. C D. None of he oher answers. E. E p = Δp p f
Copleely nelasc Collson Moenu consered (Objecs sck ogeher) KE no. (KE nernal)