59940-45_exam3_s07 - PHY 31?K 1 May Elli}? NAME: Exam 3 —...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PHY 31?K 1 May Elli}? NAME: Exam 3 — PHYEITK Instructions: . I , I Take alternate seats if possible. e No notes. textbooks1 calculators or similar aids are permitted. You may only use the sheet with formulas as provided. I Use the scantron answer sheet to provide the answers. Follow exactlyr the directions how to mark it. Write your name, course number, unique number. Sign and date it. Mark solutions for all problems. Mark your answer sheet using #2 pencil. Ir Any questions you may have about the test have to be directed to the instructor —- no conversations andfor collaborative work are permitted. i The next page contains some equations and other information that may be useful on this exam. You may not ask questions about this sheet, however. I A blank page is attached at the end for scratch paper. You may use both sides of all pages. Some Useful Equations 4 Newton‘s-Law of Universal Gravitation: F = HGE‘EEH where G = (id? x lil“”§i-1n"fl’kg”. Gravitational potential energy: U = 4:29:52“. 4! Kepler’s Law of Periods: T2 = %r3 I Pressure as a function of height in a fluid of densityr p: 'p = pm - pgh. I Archimedm‘ Principle: The buoyant force on an object equals the weight of fluid it displaces. I Equation of Continuity: pAu = constant. e Bernoulli’s Equation: 13 + in)? + pph = constant. I if F = flies. Utes} = film-2, and E = K + U = irkiefn, where mm is the amplitude. I For various aimple'hlarinonie osdillators. the period T is given by: Mass and spring : T = flex/"1:5 Simple pendulum : T = flux/E Toreionalpendulum'. T: EFfi Physical pendulum -. T = 211' all-fl Recall j' =1;'Tand w = 21rf= ‘2sz. I Sinusoidal traveling 1ivave: yfz. t} = ymsin [ks—wt—qb} = ymsin 27" [s-ei—e'r']. pm is amplitude1 A is wavelength, k is wave number [it = wal}, 1.I is phase velocity {tr = aika a! is angular frequency [to = 2T" = 2n)“ = 27's}, and at is the phase constant. {I is frequents.r and T is the period.) I Wave velocitv on a string: e = ar'Tfp {T is tensionI p: is the mass per unit length]. I Allowed wavelengths on a string clamped at both ends: Jr = ELfn {n = 1.2.3....1. Allowed wavelengths in a column of air with one end open. one closed: J. = 4Li’f2n — l]: e For sound: intensityr in decibels {dB}: 43 = Wing-i, where IO = 10—12 'me2. Relative intensities of f1 and I; in dB: 1D log-E. - Beat frequency: as = If: — er. I Doppler efieet: f’ = ffv :I: name 2121.5]. where e is the wave speed, vs the speed 0f the source, and 1),, the speed of the observer. Upper,“ lower signs refer to approachingfreseding. I Speed oflight {in vacuum}; 3 x 10“ mfe. I Tirne dilation: t = "ft; = err; length oontraction: L = Luff; 7 = 3,117 if! = ufe. I Relativistic transformation of veloeitim {for velocity u in the z-direetion in frame 5 and velocity u‘ in. frame 3', where 5" moves with speed it along the +e-direction with respect to 5'): a- i d .u _ E. u _l—1.I'u:fe2 an - 1+1.I"u,l"r:2 . ax“ = e, (a; + ear}; ear = 1; {eat +uffizjfc] II Total energy: E = vmoz = K + mcz, where K is kinetic ailing].-r and me:E is the rest energy. Momentum: p = vfimc. E2 = lips)” + [turgid The invariant in all frames is mils“ = E2 — ripe]? Answer the following quefiiuns: 1. The mass of a hypothetical planet is 1f100 that of Earth and its radius is 1,34 that of Earth. If a person weighs 000 N on Earth, what would she weigh on this planet? {new a GMM {h} 48 N T; W“ . q 192M 12 Man- Th“ _.L_ l we: t“ ' II is) see N I em 2. An object released at rest infinitely far from the Earth falls in and crashes to the Earth at a speed of approximately 3 krnfsee. Using G e: i x 10‘11 ngg’kga, and using the fast that the Earth’s radius is approximately 'i'000 [on1 deduce the mass of the Earth. fluse conservation of energy1 and assume U = 0 infinitely far away}. .2x1024 kg = + {h} BAX-inset“ Ea ’ a M“ K. E5 = (flu-I I9 {e} 3.2x1013kg E]? :- ém‘ 3 5M“ {a} 0.21.):1015 kg ' R is] 22.4mm” kg .1174? .. Grit ‘2‘ Bus EMF. Cffilflbmygm “5&3: fishers»!h 2c} ‘ ' W's 3. A sphere of uniform density floats in 1water so that exactly 1 5' 10th of the spheres volume is above the surface. Assuming the dity of the water is 1000 kgfma. what is the density of the sphere? a sooaggmfl {puff} are uM-‘LIJ' «whiff-uni =we~3£+5£ kg} 1113 E'P'In u: u. KID e 1000 kglr’m3 (d) 110mgme G93 Waxy...» a ’ flimsy? {e} 1200 kgftna ' ’ fzfiun : (01%,; 4. An incompressible fluid is flowing through a. eiroulsr pipe of radius R st s velocity of U. Then the pipe widens to s rsdius 2R. If the pressure in the smaller section of the pipe is p, what is the pressure in the larger section? The pipe is horizontal. Take the fluid‘s 1':lensit;llr to be p. s 2 r ,1 {a}? 2r?“ :- T 4‘ If)“ Ehls+gsv2 i l __j_ 1 03' “rev” Jed-1:133 +— c” ma me: “P a? 1’ 21°C 3 (elsi'gsvfl “39R Pr}: 4dr r i I It _ .L. . H ' 'P*'F+ZPU("M Ado-Ad _U="""P' I? '1 . . . . . ~"-" "" PM! 32 5. A rock weighs 1400 N in air but has an apparent weight of Elflfl N when submerged in water (density,r lflEIfl kgfrnfl}. The volume of the rook is what? Use 9 = 10 m 3' s2. 4. F II (a) 0.14 m3 {b} 43.601113 mé‘ffflfis " w " (Ova- : LU (r: {191) m3 I .05 1113 (D = M ‘- ej 0.1111113 u. - u; gm “ \I = ——_fr. .1: " 0.515" p a. (I oouyte‘) _ E. A psrtiole moves in simple harmonic motion scording to :1: = 2 oos{5llltj, with s." in meters and t in seconds. Its maximum velocity is: (a) lflflsinfififlt} {b} lflfleosfiflr) fl“ d {sheet} .5 s - 2(fi)3;.(§of) (e) none of the shove = - [so stuGfi-t} 'F. A traveling were is described by y[:r,t} = 2.0 ElnEélJE — 101:), where m is in meters, 3: is in centimeters and t is in seconds. The wave number is: 3.- Jrcm (it-s -wt) 7 4 8. A standing wave has developed on a. string which is fixed at its two ends! so that the ends of the string are not free to move. The length of the string is L. Which of the following sets of positions1 measured from one end of the string1 may be e list of all the onfinodes of the standing wave? U1 L 2, L ,- {all x r, \ {b} Lysssgs ml. L “4‘ 4, ELM ‘ -- r” {e} Lffi,Lf31Lf2,2Lf3,fiLjfi T (e) Lli'irl ELJHT _ m 9. The intensityr of is sound wave is ll] me2. What is the sound level of this wave in decibels {dB} '3' {e} is en * E\ = l” Eb} IEdB - l0 (It, la (JD-fl fines d} see 1 m lub( {012) [e] 3 dB '= in (133 -= i'So it). An organ pipe is 11.75 rn long. It is closed one end and open on the other. 1|flu-"hat is frequency of the 3"; harmonic? [Recall the 151 harmonic, or fundamental, is the lowest possible frequency, so it has the longest possible wavelength.) Use 1: = 35f} 1113's for the speed of sound. The answer is closest to one of the following: la} him H: A if: 4L 4 L = g— melt—7‘; dogma inn. " Zia—i - g c TDDHZ [djflflflHz rU—z Aha, .C: All“ 1—“: (e) 901] Hz 45." M Q S; {Om-)3: I": 5510551 11. As an airplane approaches and then recedes from a stationary source of sound, the pilot measures a frequency dr'fierence (i.e., between approaching and receding) of EDD Hz. If the speed of the airplane is If“) mfs and the speed of sound in the air is 300 mfs, what is the frequency of t e sou he‘ g rnad hy the stationary source? 43— (“M3 an (W {a} 225 Hz '— 0 T a”. {bjflflfl'Hz “w __U+U 2U _ . z {c}4f}UHs fll‘r1_-¥b(-—a——T-"— ‘4‘?) 1: 3 fig: EDoHe=%(% 12. Two protons of mass mp collide head-on to make a new particle1 called the 11", which has a mass M a: 3m,,. When we View this collision in the center-of—momcnturn frame, with what {equal} speed must the two colliding protons approach one another in order to have just enough energy to create the III? __ z, ETGT :— - 2 E11? Er! “P I'M—F- -+-—-—ue eh .a-Hx E, F:- s e3 A C!" U loltn Ena- who ' h 13. in stationary observer in frame 5' notices that e clock which is moving with respect to 3 runs slow by a factor cf exsetly 2;“ The speed of the clock in frame 3 is: tam-99c 'i’='~‘-ut/nr = ltd/Vs {1:} es c ' {dues . (ejcflfl __ _J_ ._.. a“...__ .E .. ._L #1” r / *r . 1 141. An unstable particle is created in my experith with speed 1.: = gc. It traveled mm in my laboratory befere decaying. What is the particles lifetime [according to the particle)? in lath :i' 'iH‘fl-fll-l' d: Uh“ = g8fi)’tm' ? x 10—11 5 bd John. . Vii Cele“: d:lfl'i§ll¢n‘) d1. Tfsfit’e—ai ¥M=¥¢tr _ i 3 . 4 in! l_ 1* 5 3*“ r in .3be H. :jbls 21' 1 a. may 9: '3' " 1175' 15. A particle of mass m has kinetic energy 4mg. It‘s speed is: {a} r- . use heme-0y”: M (c) %c 6:57-23:19 C" I 3" 4' (a) 3:35 Y: Q _____L_—#——- r— 6 I "' lye.“ ‘ 16. A. [1.21] kg object atttaohed to a spring with l: = 500 N! m executes simple harmonic motion with amplitude 13.14] m. Its maximum speed is 51115 = _ a fi?« 6 f.- F 1" 0,”,1‘3 " 12.549 )4; {d} 15.8 mfs = 5-bit]! [s] 13.2 mfs 11'. The sketch helou'r shows the potential and kinetic energy of a pendulum as a function ' of time. I start the pendulum in motion at t = {1. Which statement best describes situation? (a) I draw the pendulum to the side and release it1 initially at rest. and it goes into simple harmonic motion. {h} Starting with the pendulum hanging down at its lowest point, I whack the pen— dulum so it starts moving to the side, and “it thereafter executes simple harmonic motion. in) I draw the pendulum to the side, and at t = [l I ping it. downward {back toward the hanging down position), and it thereafter goes into simple harmonic motion. draw pendulum to the side, and at t = [1 I give it a ping upward, away from the . equilibrium point. {e} None of these descriptions is consistent with the sketch time I) gin-£- gacksamt. idea-lit... 4; Sam- > pun-Mm gun-'11 Lnrl' lasflli’fifin'é, hm. manta}, Z) Huts; altar-fl dtmc aim: 3 3) Peta/Hm W tomcat-t- 18. The low edge of your hearing is about 2U Ha. What is the wavelength of such a wave? The speed of sound is about 340 rn ,3 s We“! Zflflaqefifi'}; geese”? my (a) BEEN] In is] 1.? m {d} 1.? on: to] none of these 5 III?!" 19. The largest number of beats per second will be heard from which pairs of tuning' forks? (a) 2m) and rolls: {sf-g; -_-. I (b) are and see Hz '- I = q. {o} 534 and 540 He 3 {9 (e) 3420 and 3422 Hz :- a 2D. III- am about 1 year older than my spouse. I would like to blast ofi in a space ship for what I judge to he 1 year {13.5 years away from earth, [11.5 years haech1 and have her be 1 year older than me upon my return. How fast must my ship be moving? (note: these things matter when you‘re pushing alfll}. lair: x {EEC yarns-45%;? Xt-l C EC “is: For an (rel-«Hg fl {el 4 c éim e“- fret-:31- (kt—r.) soc—t) = 3 me. Hue :5!qu e=re’ 9 Ysg: diia rigor-me. rs x—l firm: I!- LXH)+-I " x+z ME) "ME-- HIE III-Cu? EI-{ifi Chili“? fill?) Elsi?- ufii? ENE) CHE) HE.) Unfit ICE life"! HE INE- ‘tlit'j 1Q (Ct-Tl (E 1:}. .- ‘--‘ HI 5 l 3 i E; 5 3 1! "ICE?! “@NEJHI’E' _ EIL-g'} flfiji can any HE] era: Hit—'9 NICE EEIIIHE' .- 1E3 my) 163 15:; date-.1 :- 5 E E 3 R E H E E 3 MIC-jug) u@u@m@ turf; Elli] 55.} at?) fitfl UEGIE} HIE Liar—u} ESEIHE “E 1:15“: «Ha-Hr) - «IE-«IE, E e E K E iE E E "(El “I! “IE Uh?) -' DE) GIG-J a! DIE ul- GIE DEE) at"? In?) Uzi" rurin Iii) mtg-“I nfyi) 1E) 1E: «IF-J nits-j u- [H l- N M E 1'- 1- 'l- 'l- I- 'l- 'I- 'l-' I- N '43 “ICE! HE) may uni-j) NE} :36: era are; c631 fl. til-HIEUEE‘FDIHEJ life) are“) III. WE ENE «Sulfide-(@1553 . . a II- N H 1- In H r- u d: :1 III 'E} “.31.? In (E: In ui‘. Lu fin“: ,- fl EU u iii} n gt; a if. UNIQUE # DATE m3) my) :3 aw. Unl'nj mien nee {Jig—I} M's“) --a at; u it) o (if. EWRSE U! 2 E .— G [Ll E r: E E § E Answer Sheet FOFt MARKING ANSWERS oornpletely ' Erase oleanty any answer you wish to change I Make no slray marks on the answer sheet ' Use black lead pencil only (No. 21k or softer} I Make heavy black marks that fill the circle ' Do NOT use ink or ballpoint pens Em- 1}: The University of Texas at Austin - EIMIIPLES individual opportunity, and responsibility. Each member of lhe University is expected to uphold these The oore values of The Uni-Persin ofTexas el Austln are leamlng. discovery. freedom. leadership. Values Through “959W. honesty. inlst. falmese. and respect towards peers and oommmity. The University of Thu“ at Austin Honor Code SIGNATURE INSTRUCTOR -_‘-[iii-E@afiHEED-EJCEEQEJEJEQWQEEIQ@E@@®®@@©@®@®®E®Efiiflfifl ' .J-':ii'?"1i=i-IE'fiiTil-CHIHEHEIt?)fifi'iifliéfliflEJEQ‘HE)@@(E€E§@®{E'fiE‘JE-EiEiE-E'QEE LEE-@011 ;_'2-I.'!i;-‘i_fl:I't-t';TEE)Lining)E)EILJE‘IEWE'@{E‘HE@EE‘EE@®@®@]Cfl@®&}@i@@t'§i-'§t -."J Lil-Jib “9‘: =25) v11) TILT-iii (E) E) 51" E'E‘III IE" @ERELEJ @E‘HEHE' til-{EILEE (.5) BE!) {{1} Ci} Gil) I51“?! 53-1!“- '3'!) Gil-(ElfEJTEEJ'E'CEEE‘JQIEHEQIIEIGMEQ}®@@®®E@E®@E@@{Efifiifil 'L"(~.'i‘-5_I" III-i1 ii:Eli-.HE‘IEJEJGJ’IT-Cétfi @ifiitifiifi @{EGJQJiEEfiCfljfz—Z‘EEEJEE~EEE‘I-Ekfii Vi" Ii'jftiiwfii£y*@:eife}@@3@®@(EEG)@fififiiflififiififlfififilfiflflfifiififflfil 1.? {ti-ii. Ul‘ 5.5.3 3-1- “i-I-‘ L53 Lil c—J-anmc93®@@@ @EE-EEEiEEPE‘EEIEEIE‘EiE-EJ LE ill-EM?) Li! 'Jar-Q}[E[Ei@®@IE)EJENEQmw®®©®®®®®m®®®®a®®®®®®®® ' I": Lester-n} “I;fit-3&1:rill-f"ii'E'3m@'@@l§i@i§}®i§i@@®®flfljkéfi9fi {elf-(5?»(FEE-ETFE'CEP'E'IILML' .l E @EEEtEfE-EFE-fe; in E- tan LE) re; cm:- :-er.- nu:- {u- -+~;- u: 'eir -. 29:" Tu} Lit-(£5? fit-ZEJG‘HFIJLEJ(JilmcflfiJEfiJCéZt-mfij FEJEHEJECE‘JCSE <.'}Ei1rm@@f§}';-EJ@@¢E@@m'fififlfilfififififiiwflfifi} “T-i:tdlffliédmit-Ie‘limLeia-tilt!){DiEEEE‘iEJnEEJLEJEIEELEJe-‘Jfl? :'_'.: :§:[i3-C@c.§}@iE-J@EGJE}G¥JE)@®@@@@@E‘IEEEEE -aw@fl@@@@a@®@m@@w@@@m@@@®ef "‘-@Lfiiflfi-fiififlfi-flfiltyfififilWIEfiEwCEEEEJEEEEE} I 221:: ti'i-@ e". -:E CE: fill if!) f.-_.‘- 153 I32.) Edi-mtg] (QB (II-HEW!) GE! ti-j {SEE LEI ENE nmmw@@@@@3@@@m@@@©@@®@@m®®® "'I'§£i:-:.E.‘-ffit Le:riocanerr-Hen@:e@@@@®@®®@@@®®® 2Q®®E®@@@Q@®®®@@®@®®E@E®®®E 3" -'II'II- ~l.-L I'Ft', Flt-I '11-?! '-_:.; ‘5'; Li) (-1- CE (ii if!) 1"?) {533' (51:3 (3.5) 'E: '1?“ (5:3 '35." 5'11?) Chi} .2 a... II a E 'II: D i5 E m Cl C} C3 (—3 {—31 {—3 ("1". '2' if L' a 'l- '2' ' ' 54”" 3% LAST NfiHE ...
View Full Document

This note was uploaded on 03/20/2008 for the course PHY 317k taught by Professor Kopp during the Spring '07 term at University of Texas at Austin.

Page1 / 10

59940-45_exam3_s07 - PHY 31?K 1 May Elli}? NAME: Exam 3 —...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online