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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 uniformdensity thick hollow spherical
shell 01' mass M and inner radius H1 and outer relline 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 tenthhie 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‘Lrj vs. a, where r iii the dietan ce between the email ammo and the center of the spinem, for CI ‘7. r i on. Problem 2: You have two spring", both with the same equﬂibI :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 waye. T1: the ﬁrst. you connect the aprinma W k k;
aide hireide. 01' in "parallei’, Ht aha«'5': hehrw. In the mud, 3am ' lWW
wunect the springs enritaend. 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‘lClCTlﬁ. Emu if ynu
hum. the answers. you tau5L 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 :rrdiwctiun. 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 munondinaie oi the center of 1111335 at" the plate. Problem 4: Van. am asked LU ﬁnal3.1L an “extreme“ influ
muster track. Amumo the roller «mater car with passLugms
SLM‘LE [mm Tﬁﬁt at the my 1.14;: marl Hiideﬁ without. IrisJinn
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‘icuml ”liig’H": while yO
at the top 0f the “amt" in the trackl the pusaimigem ﬁne to just comm1mm ‘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 hottorn of the
trough its aL y — i] and the top 01' Lbs crest ii: at y = 23g. Frat10m 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 pailct 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 iiinail 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'Jl {EH"'9“ {1] and m}. “1'3 IJ'JUBt lIHH the Bamr} velocity u; just helnre the. roliiﬁirm. u} Detnrmlne for both war: {i} and mm [Iii] the kinetic: unﬁtg}; imputed tn the can as a result
Hf HIP. collision. ' ﬂ 33] DOW“mil“! fﬁr I'Mt" £350 {1] and HawP. {ii} the linear munmlmm vatrmr imparted to the can
as n rEHtIit of the caLLisixm. C} Which pt'llL'i. hm; L1 hFHET chance Lil kmclcing the can'uﬂ [he fmcpcist? Problem 6: After cnmpching thin Exam, you go Lu u. IHu' Mid
Dl'dm' H martini 1'0 nucleimm yﬂur SUEEEEEBII. Before you know it. the
glass is BIILII'lI‘r' except 101' an uliwL. You twirl the uprhght empty
ELM! With an“: El! wmiunt angular wiocity u: Rbu ut 11}: symmntry
axiai and nuts LhnL we nlim: ailI93 up the inside ul‘ the.l class. '1'hc
himi of the ﬂitst. 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 gay11.; 5r
in lament.) ...
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 Spring '10
 Budinger

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