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bioePhysics 7a-fall07-mt2-Zettl-exam

bioePhysics 7a-fall07-mt2-Zettl-exam - (Zet‘rl...

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Unformatted text preview: (Zet‘rl Phqé‘ics 7e Mflitrm a} Problm] ]: This is a gravitational attraction pmltlem. The volume of a fiphcl'l: is %7rra'. Cmekle: a uniform-density thick hollow spherical shell 01' mass M and inner radius H1 and outer rel-line R2. The shell has a small tunnel er hale drilled through it alim'lng email particles to pass thmugh. Yen {neglect your must] the at the center at the sphere mid threw a Brandi atone nf nmte m directly at the hole. With what minimum 5|}qu mufit :mu throw the stone to that it will: a} just reach the inner part of the sphere. at R1? hi go through. the tunnel andjhtt mach the enter part al the sphere, at Hg? c} go through the tunnel and tenth-hie all" into free apnea, never LU return? d) Defining U _ Ell at 1' = 3:, detm'rnint explicitly and phi: the. gravitational pntanLia] energ- m‘ the system: L‘Lr-j vs. a, where r iii the dietan ce between the email ammo and the center of the spin-em, for CI ‘7. r i on. Problem 2: You have two spring", both with the same equflib-I :ium length Ln, but with different respective apting tanntmte 1:1 FHWLIEI Series anrl kg. The apriuga obey ileuke‘s law. Yuu decide to connect the. k1 springs in twu d'rfiereut way-e. T1: the first. you connect the aprinma W k k; aide hir-eide. 01' in "parallei’, Ht- aha-«'5': hehrw. In the mud, 3am ' lWW wunect the springs enri-taend. n: in “series". also as shown below. it: a} 'I'lmt the mmhiued timings. an nuns: ell‘ective epn'hg. Determine. in terms of in and k2. the EHHULit-‘IZ‘ spring constant it” for the ”parallel" and [or the “writs” muncL‘lClC-Tlfi. Emu if ynu hum.- the answers. you tau-5L shew the det'itretinne fur kn”. b} You take the spring. mmhinathm and eximnd it by an mount 3‘. Delmrnine how much work a he} pet-[arm thia extension tin terms at I. in. anrl kg), and haw much imtuutial 3'01: must d einn 2:. Do this calculaticm for bath the energy ends up in each al‘ the we springa at chIZ‘J'I namJJel and eeriee mmhinexicrna Prnhlem 3: it thin aluminum plate is cut uuL with a jig- saw into the “curved wedge“ shape bhmt'n helrm. The math- ematical curve vi the rul. 1:: given by: «y = TIRE. with H a constant. Along the :rr-diwctiun. the plate extends them 2- flmr=1. a) Determine 1he gr cwdinate at the center nf mate of the plate [il' ynu can figure this out without doing u calculation. juet state the usult and explain your reasoning}. h] Determine the m-unondinaie oi the center of 1111335 at" the plate. Problem 4: Van. am asked LU final-3.1L an “extreme“ influ- muster track. Amumo the roller «mater car with passL-ugms SLM‘LE [mm Tfifit at the my 1.14;: marl Hiidefi without. Iris-Jinn dawn tinn thick, pulled dtmrnwan‘] only by gravity 9. You want the ride to ha a thrill”: mi. the bottom DI the “laugh” in the finds. the: pimngeTi-‘u am to Qtpfll‘icum-l ”liig’H": while y-O at the top 0f the “amt" in the trackl the pusaimigem fine to just comm-1mm ‘Hieightleasncsé’, Le. thwy up. to just 1th off of their win. Untmnine the radii of curvatmc fur the trnugh and the 31951.: R; and R2: respectively. Nuts; that the hot-torn of the trough its a-L y — i] and the top 01' Lbs crest ii: at y = 23g. Frat-10m 51 T1155 is & mm—dinwns'mnul culiifiinn problem. "Tim ME trying in iniock a. su'fl can of 11mm J'If OFF n‘F a fnnocpoist by ahnnLing atpcllct. at it with a blingbimt. You have. two choices: {i} Yfiu can use a mull I'llhheT pail-ct of mam mo in your s]i_ugshot. “Finch such a ruliber [belief hits the. can right in the center, it. 00111ch fully aluzaticaliy and the pellet bounces straight back. (ii) Yum can use a iii-nail clay planet. of tlm Hanna mass. inn 'Whul: this clay pfillfit hit-.5 the can right in [11¢ martin“. 11'- eaticica in the can. in a. in 1.1:; inniastit‘ milis'lun. '11 l'JU'J-l {EH-"'9“ {1] and m}. “1'3 IJ'JU-Bt l-IHH the Bamr} velocity u; just helnre the. roliifiirm. u} Detnrmlne for both war: {i} and mm [Iii] the kinetic: unfit-g}; imputed tn the can as a result Hf HIP. collision. ' fl 33] DOW-“mil“! ffir I'M-t" £350 {1] and Haw-P. {ii} the linear munmlmm vatrmr imparted to the can as n rEHtIit of the caLLisixm. C} Which pt'llL'i. hm; L1 hFH-ET chance Lil kmclcing the can'ufl [he fm-cpcist? Problem 6: After cnmpching thin Exam, you go Lu u. IHu' Mid Dl'dm' H- martini 1'0 nuclei-mm- yflur SUEEEEEBII. Before you know it. the glass is BIILII'l-I‘r' except 101' an uliw-L. You twirl the uprhght empty ELM! With an“: El!- wmiunt angular wiocity u: Rbu ut 11}: symmntry axiai and nuts LhnL we nli-m: ail-I93 up the inside ul‘ the.l class. '1'hc him-i of the flit-st. mm I'H=. described by the mathematical] fm'muia y = 113:"? wimc :1 ii:- u knawn mstahL and u: is the radial distance {mm the mum maze nl Manon. L'mtcnntu: h, the hcight of the alive nbwc the human: ml the 31353. [You miuld assume gay-11.; 5r in lament.) ...
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