Physics 231 Ch 10 Day

Transcription

1 Physcs 3 Ch Day 3 r., / Scaerng R.b Mn., /8 Tues. /9 Wed.,/ Lab r., /.9-. Cllsn Clcans: Inelasc, Relasc, & Quanzed.5,. Deren Reerence raes L Cllsns (ballsc endulu?). Translanal Angular Menu Quz R.c P9 (Re Washnn s 3/ ss Thurs ngh 7) R.a; HW: Ch Pr s 3*,, 3, 39, quen Lab cars and rack (n ar rack) & car weghs (black bars) Her ucks (aybe) Cllsn 8_Ruherrd_ds.y, and Scaerng.exe r Las Te S, bere he es, we d sared hnkng abu cllsns Cllsn shr, srng neracns; can neglec all her neracns durng cllsn. We d sared by lkng a jus -D cllsns. Reew wh s quesns Ch. 9 Cllsns: xlrng he Nucleus Cllsn: A relaely bre and srng neracn. Syse = cars. Le s ake ur syse be he w cars n he ar rack, and ur e neral be jus bere jus aer hey cllde. Syse = cars. Le s ake ur syse be he w cars n he ar rack, and ur e neral be jus bere jus aer hey cllde. Then.b.b a.a syse syse ne. ex ( ar able. rcn s s sall enugh. able. nral arh. gral ar...) De: Maxally (Perecly) Inelasc. bg bg. sallsall. bg bg bg. sallsall. bg sall bg. sall. sall.

2 Physcs 3 Ch Day 3 De: Perecly lasc. (cllde cars and bunce agnecally). Nw, n hs case,, we sll need a secnd equan we wan bg. sall. sle r w unknwns. Wha her relan hlds hrugh hs cllsn? Cnseran nergy.. a. b. a. b. b b. a. a Pung hese geher when bg was nally a res, we g. b. a. a Prjecle & Targe Scaerng Las e, we lked a head-n cllsns. We elyed cnseran energy and cnseran enu redc he aer-ah he cllsns, and we g alar wh he range ssble u ces (deendng un he relae asses he cllders and her relae elces.) Nw we re gng cnsder he re general case an -axs cllsn. O curse he resul s he cllders bunce a deren angles requrng -D descrn. Such cllsns lay a ajr rle n arcle hyscs where he behars arcles when hey cllde ges us ran nran abu her reres such as charge, ass, and een nernal srucure. Tday, we re gng walk he lne beween really geng n he ah and sayng qualae. De: her ucks cllde -axs. De: Alha_n_alha.y P.. cs,... Inal,, nal cs sn. Ne: easures dwn r he hrznal, and s s negae, sn,,

3 Physcs 3 Ch Day 3 3 Cnseran Menu:.. xˆ : cs yˆ : sn sn cs Cnseran nergy: nergy s a ecr quany, s we ge he exac sae, sngle, equan we dd r a -D cllsn. r dr syse. c. c r ne. ex.n.n. c. c.n.n Le s say we chse ur bere and aer a ns he sae enal; s lkely enal, r he bjecs are n lnger neracng. lasc Cllsn. I he cllsn s elasc, we can say ha he nernal energes he w bjecs are he sae bere and aer he cllsn (hey ghn be durng he cllsn, bu we re n cncerned wh hen.) Three quans / ur Unknwns. Three quans. Wren hs way, we hae hree equans (enu x, enu y, and energy) ur unknwns. ur unknwns (agnude nal enu, agnude nal enu, drecn nal enu, and drecn nal enu ). urh ece n. We re gng cus a b day n ha 4 h ece nran. Cllsn geery. I yu re gng redc all he nal araeers, yu re gng need ne re ece nran, seccally, he drecn he rce cllsn ha ges he drecn he change n enu r each bjec. Generally, yu need knw sehng abu he cllsn sel. r ur w ucks, ha s a aer geery: wha are he rad he w ucks and hw d hey care wh he nal uck s ah hs deernes exacly where he w ucks cllde. r a cllsn w charged arcles, yu need cnsder he rce law he neracn. U, sn sn

4 Physcs 3 Ch Day 3 4 Only 3 unknwns (knw / easure ne nal) Then agan, n any suans, yu are able easure he nal and nal enu ecrs (agnude and drecn) ne he arcles, and hus yu can deduce he recl he her. r exale: yu re alha arcles a gld nucle, yu can see he gld nucle, bu yu can dcae he alha arcle s nal enu and easure s nal enu, and s deduce he gld nucleus recl. qual Masses. Our w ucks are rey uch equal asses. We ge an neresng resul n hs secal case = =. r cnseran energy: r cnseran enu: Then, squarng ges r Carng hs wh he equan r he cnseran energy, clearly he las er us be. The d rduc s cs. Q: There are hree acrs here, s here are hree ways her rduc can be zer. Wha s ne? rjecle neer h arge, s = rjecle h arge head n, s rjecle sed and arge carred, s = he angel beween he w nal ena s 9 De: Try cllde ucks n he hree ways (ay need sene hel cach ucks) Nce ha I was able redc he angle beween he w arcles ha cllded, bu I culdn redc he drecn hey d g relae he nal drecn. Wha was abu he cllsn ha deerned ha? 8.3. Iac Paraeer Whch case we hae (and exacly hw he 9 s rened) deends n he cllsn sel. r ur ucks, s sle geery: he ra he rjeced cener--cener dsance wh he ucks rad. Ths dsance s reerred as he ac araeer, b. he ac araeer s larger han he su he w ucks rad, hen here s a ss: Mss Bg b b

5 Physcs 3 Ch Day 3 5 asyerc large b I he ac araeer s jus saller han he cbned rad, hen he arge uck barely es and he rjecle uck s barely deleced. I he ac araeer near ½ he cbned rad, bh ucks dear arly syercally. syerc edu b As he ac araeer araches, he arge recees re he enu, unl b = and he rjecle ss un cllsn. Head-n b Generally. Say ur cllders aren equal ass; he cure s qualaely ery slar: he angle beween he w u cng ena deends un he ac araeer. 8.4 Dscerng he nucleus nsde as Turnng hs reasnng arund, say yu dn knw hw bg yur arge bjec s, say an ac nucleus, hen bserng hw rjecle bjecs, say alha arcles, scaer ells yu abu he ac araeer and he sze he arge. I was acually hrugh scaerng exerens, and ac araeer cnsderans, ha he nucleus was dscered and s srucure s rbed The Ruherrd exeren Alha arcles (He nucle) ake cnenen, arly asse, and + charged rjecles. Ruherrd s asssans acceleraed hese a a arge hn gld l and hen bsered where hey h a hshrescen screen n eher sde he l. The neracn an alha arcle wh he nucleus s gerned by q q nuc 4. In lab yu ll hae he runy del hs exeren. r nuc

6 Physcs 3 Ch Day 3 6 De: 8_Ruherrd_ds.y r a aeral unr ass and + charge dsrbun, ne wuld exec lle sgncan scaerng. Ne he lack sall-angle scaers and he ccasnal backscaer Cuer delng he Ruherrd xeren Dsrbun scaerng angles Lkng a he sulan, yu can see ha, gen he range ssble ac araeers, here s a crresndng range scaerng angles. r hard bjecs, lke l balls, here s a rey sle geerc relan beween arge & rjecle sze, ac araeer, and resulng scaerng angle. In Ruherrd s exeren, and hers lke, he arge can acually be seen, ndeed, he scaerng s used deduce he arge s sze. In hs cnex, ne res a barrage rjecles n he general drecn he arge & he racn ha scaer a deren angles ells yu wha racn yur bea s aken u by he arge Crss secn In a hard cllsn, lke ha l balls, he rjecle us be aed whn he geerc radus he arge n rder r here be any neracn / any scaerng. Thus, by lkng a he dsrbun scaered rjecles, s que easy gure u he sze, r re seccally, he crss-secnal area he arge. Crss-secn, Dars, and Prbably. Le s say I gd enugh a dars be guaranee ha I ll h he bard sewhere bu s cleely rand as where. Take he bull s-eye be he arge. Then he rbably ha I ge a bulls-eye s sly he ra he bull s-eye crsssecnal area ha he whle bard: bull P bull. Abard Slarly: P s s Abard Crss-secns, alha-arcles, and scaerng angles. Hweer, when we e g re lng-range neracns, such as ha an alha-arcle wh a gld nucleus, he alha-arcle needn acually h whn he geerc radus he nucleus ge deleced. We sll use he language crss-secn. I we say he bull s-eye s lke acually hng he arcle head-n, akng he alha-arcle bunce back, hen he nex rng u s lke cng que clse he nucleus and delecng sharly; he nex rng u s cng n s clse, and delecng a lle less sharly Agan, he rbably each ye delecn s rrnal he crresndng rng s crss-secn. De: 8_Ruherrd_ds.y rae lk head n and see bulls eye Cnseran Laws Vs. Deals he neracn

7 # scaers # scaers Physcs 3 Ch Day 3 7 Crss-secn / Scaerng Angle & rce law. Nw agne we had w arges, ne s a gld nucleus, wh s 79 rns, and ne s a nucleus wh wce as any rns. Yu sh randly a bh wh alha-arcles he sae energes. Le s say ha yu h whn hese ranges he cener a gld nucleus, yu wll be deleced by hese angles: De: 8_Ruherrd_gld.y rae lk head n and see bulls eye, see l Prbably scaer s. angle angle Iac araeer Snce each rng u has a bgger area, he nuber alha-arcles scaered a hese deren angles s greaer r he bgger rng / saller scaerng angle. The dsrbun scaers lks sehng lke he l besde. Nw agne he nucleus wh wce as any rns, a any gen dsance r hs nucleus, he rce s wce as srng as r he gld nucleus. Qualaley, hw shuld ur rng arges lk? angle xerence he sae delecn a a greaer dsance / ac araeer De: 8_Ruherrd_zercnu.y rae lk head n and see bulls eye, see l Prbably scaer s. angle. Deren rce law r ha aer, say we e g a deren rce law, say he rce des exnenally nsead lke /r. Hw wuld he arge lk derenly? Rngs wuld be narrw near he cener and que brad usde. Hw wuld he cun scaers s. angle lk? The sall angle scaers wuld be uch re ular. Mral: Scaerng exerens can be used dscer he naure he arge and he rce law by whch neracs wh he rjecle.