Physics 231 Ch 9 Day

Transcription

1 Physs Ch 9 Day 0 0 Wed., /6 ab F, /8 n., / Tues. / 9. Rtatnal Enegy Quz 8 8 Enegy Quantzatn Reew Exam (Ch 5-8) Exam (Ch 5-8) RE 9.b bng laptp, smatphne, pad, Pate Exam (due begnnng lass) (.9) The Pnt Patle appxmatn RE 9. EP8, HW9: Ch 9 P s, 0, Equpment Wheel Clletn metal ng, wd ds, and plast ds Rd wth ball sewed t the end Battn Tw dss.py 09RtateVbateTanslate.py Fm last tme yu hae a mpund system, the mmentum s the same as the mass tmes the ente--mass elty s the net eet hang all the patle wth all the wn mmenta s that the ente--mass the system tanslates. p m p tans and espnds t extenal es just as a patle wth the whle system s mass wuld. p Fnet t m F t net F example, when we nsdeed pullng tw dss wth the same e the same tme, we saw the same tanslatn the ente mass. Hwee, the tw puks had ey deent ntenal mtns, n patula, ne ated the stng was wapped aund the umeene and the the ddn t the stng was attahed staght t the ente. Whle the tw systems had the same mmentum, they had ey deent eneges. Dem: 07_twdss.py ntenal Enegy When we lked at the knet enegy thugh, we saw a ey deent stuatn. We an easly sepaate the system s knet enegy nt tw tems, the enegy assated wth ts whle-sale mtn, the mtn ts ente mass, and the ntenal mtn. Essentally the ntenal knet enegy s just the sum eah patle s knet enegy, elate t the ente mass. nt tt Rtatn and Vbatn m all. el

2 Physs Ch 9 Day 0 We uld take t a step uthe and esle the elate eltes nt tw pependula mpnents tangental (n-and-ut) and al (aund.) nt m m tan el m m tan Vbatn: Radal mtn wuld be mng twad away m the ente mass. Take example a datm mleule, the tw atms an jggle bak and th, e. bate. nt. b m Rtatn: Tangental mtn wuld be mng aund the ente mass. Cnsde agan u datm mleule, t an ate. m nt. all. S, nt b O use many systems d bth at the same tme, but t ll be smplest us t nsde ne knd mtn at a tme. dn t eally hae muh me t say abut batnal, but atnal mtn an be ephased a bt t make me manageable. 09RtateVbateTanslate.py Rtatn. Nw, n the ase the puk, say, that ths wheel. Dem: Spn wheel. The nddual, ae spnnng aund and aund the ente mass. Futheme, the bjet sn t sgnantly demng, meanng that eah patle stays a xed dstane m the ente mass,, and that all ae gng aund and aund wth the same equeny. That s, ne pat ne spke takes 0.s t g all the way aund, then s des eey the pat the wheel. Angula Speed et s nsde the speed ne spt the wheel. That spt s a dstane ut m the axs abut whh ts spnnng and t s spnnng n a le, s we an say ts speed s umee ne ped T T The at, p/t s the ate wth whh the pnt sweeps aund and aund thugh angles ges aund p ans n ne ped. (say, n 0. s.) The ate wth whh t sweeps thugh angles s alled the angula speed T Wth that ntatn,

3 Physs Ch 9 Day 0 Nw, t s wth emphaszng that whle deent pees the wheel ae deent dstanes ut m the axs atn, they e all spnnng aund wth the same equeny / wth the same angula speed. S, hw an we ewte the suelate knet eneges n the ase atn? nt m el We e able t at ut the mmn at angula speed and what s let nsde the sum s mpletely ndependent the mtn t just depends n hw the mass s dstbuted thughut the bjet. n the ase a spnnng ds wheel, any bjet wth a ntnuus mass dstbutn, ths sum bemes an ntegal. n the smple ase dsete masses, as yu ll enunte n p.0, t s a smple sum. 9. Rtatnal net Enegy and ment neta Cnsde a gd bjet, say a blk, a d, a penl. What s speal abut suh bjets s that the nsttuent an t maspally hange the sepaatn m eah the, they an just tanslate and ate. Take example an ease. yu thw t, the ente mass tanslates and all the pats spn aund the ente mass. Take a d. The hnge s statnay, and agan all the pats ate aund the hnge. The pnt s that, ate whlesale tanslatn, atn s a mmn and mptant ategy mtn a gd bjet. We wll nw emulate u tls t me nenently dsuss atn. anly, ths means ephasng them n tems the angula untepats t suh thngs as lnea dsplaement and lnea elty. We wll est u speal way expessng knet enegy; we wll als lk at atnal wk, and atnal mmentum. Rtatnal net Enegy & ment neta Fst, we ll tanslate u desptn mtn nt angula aables. magne a ladybug standng n a ed as t ges aund and aund at a xed ate. The bug s knet enegy s use m. - But, unm ula mtn, suh as the bug s exeutng, we an ewte the speed, the dstane that the bug ges n ne ped, T s the umeene: C =, umee ne ped T T The at, p/t s the ate wth whh the pnt sweeps aund and aund thugh angles ges aund p ans n ne ped. (say, n 0. s.) The ate wth whh t sweeps thugh angles s alled the angula speed T

4 Physs Ch 9 Day 0 Wth that ntatn, S, we an ewte the bug s knet enegy as. Nw, magne thee s a send lady bug standng n the tuntable, at sme deent us ut. she s uthe ut m the pt pnt, she s taelng aste, she s lse n, she s taelng slwe, but egadless, t takes he the same amunt tme t g aund ne, T. S she has the same angula speed. m. Say the whle suae the tuntable s eed wth ladybugs. The knet enegy the atn ths lletn s, Sne all pats the system hae the same angula elty, e ated that ut the sum. What s let depends just n the masses the and the pstns, e., the system s mass dstbutn. We ddn t put a name n ths last tme we met t, but ths sum s alled the ment neta abut the ente. mptane the ment neta: What the ppety hae we assated wth neta? What des neta mean? Resstane t hange / tendeny t keep dng what smethng s dng. We last sad that mass epesented an bjet s neta, elutane t hange ts state mtn. As mass s t tanslatn, ths newly dened, ment neta s t atn. The bgge t s, the hade t s t hange an bjet s state atn. Cmpae example a bwlng ball and an equal szed ball styeam. Whh ne takes me et t get spnnng? The bwlng me mass n the. Ths makes sense beause yu e tyng t me me masse. Take example a lage ng wth all ts mass n the utsde and a small ds wth all ts mass nea the ente. Whh takes me et t spn up t speed? The ng geate dstane n the. Ths makes sense beause, ne atn say, yu e mng an equal amunt mass muh uthe n the ng than the ds..

5 Physs Ch 9 Day 0 5 et s nsde example: Example: Cnsde a CO mleule. Wth the nule (whee the ast majty the mass s) lned up as s: m m m - d d What s the mment neta abut the ente mass? Whee s the ente mass? The C atm s nuleus. m d m 0 m d m d Example: Cnsde a ng us, mass, what s the mment neta abut the ente mass? ng. m tunately, eah patle s the same dstane m the ng all. ente mass: s we an pull ths nstant ut the sum. m R R Then we e let wth smply ng. all. all. ng a sum mass all matte n the ng, e. the mass the ng. n Geneal. F a ntnuus bjet, the dsete sum bemes a ntnuus ntegal e the ull bjet. (Yu wn t be asked t set up and pem suh ntegals ths semeste). Example: Thn Rd length. ente d. d all. The dea the sum s that yu g t eah msel mass, ed hw a t s m the ente, squae that, and ed hw muh mass s thee, and multply that n. e magned ddng the d up nt umpteen msels, eah length. Hw muh mass s n ne msel? Well, we magne the d has unm mass densty, then the at ts mass t ts length shuld equal the at the msel s mass t the msel s length. m d. d all. d all.

6 Physs Ch 9 Day 0 6 Nw, magne athe than hang 50 small msels, thee wee 500 muh smalle msels, muh-muh smalle, n the lmt that the msels ae anshngly (deentally) small, d. lm 0 d / / d / / / / 8 The bk qutes esults the ne gemetes (yu ll get t d sme these n Phys, ate yu e had me expeene wth ntegals). ylnde. R ds. R sphee 5. R The pedue s the same tanslate a msel mass nt a msel lume, then tanslate the sum e mass nt a sum e lume - a lume ntegal. F nn-ntegable shapes, the dea emans the same, but yu d hae t nd the mment netal numeally athe than analytally. Example: Wk dne n hangng the angula speed sme bjet abut ts ente mass. Hw abut spn a quate n edge ( smplty, magne t desn t tael) System: quate Ate suundngs: yu 0 R ~0.0m ~0.00m ~ 0.0kg F y

7 Physs Ch 9 Day 0 7 Say yu stat wth the n just sttng n edge, nt spnnng, 0 then yu lk t and get t spnnng up t spn aund 0 tmes a send, s t sweeps thugh an angle 0 *p ans n a ped T = s, s 0 s 0 / s Hw muh wk dd yu d n ths n? W net. ext E quate W yu quate.. 0 Nw, spnnng abut ths axs, the mment neta s R kg 0.00m 0.0kg 0.0m 8. 0 kgm.5 0 kgm.5 0 kgm W yu kgm 0 / s.9 0 J Rtatn nt abut ente mass. What abut atng abut anthe pnt, all t pnt A, athe than the ente mass, C? magne a ball munted at the end a stk length then atng abut the a end the stk. Any msel the ball spns m ang ne way, all the way aund t ang that way agan n the tme t takes the ball t make ne ull bt, s the knet enegy assated wth atng abut the ente mass s stll just all. C Then the tanslatnal knet enegy, as we und last tme s smply tans But the ente--mass speed an be ephased as the umeene the le that t sweeps aund pe the ped, e., umeene ped T T S tans Puttng these tw tgethe, tans n sht, t s the knet enegy the system s atn abut ts ente plus the knet enegy ts ente mass s atn abut the the axs. Example: Wk t takes t swng smethng aund.