Final Exam Fall 2007 Solutions

Final Exam Fall 2007 Solutions - PHYSICS 221 Fall 20D?...

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Unformatted text preview: PHYSICS 221 Fall 20D? FINAL EXAM: December 10. 200? 7:00-9:er pm Name (printed): Recitation Instructor: Section # INSTRUCTIONS: This exam contains 25 rnultlpl-e-cholcl questions plus 2 some credit questions. each worth it points. Choose one answer only for each question. Choose the best answer to each question. Answer ail questions. Allowed material: Before turning over this page. put away all materials except for pens. pencils. erasers. rulers and your calculator. There is a torrnule sheet attached at the end of the exam. Either capital; of the formula sheet are not allowed. Calculator: In general. any calculator. including calculators that perton-n graphing. is permitted. _ Electronic devices that can store large amounts of text. ldata orequations {like laptops. palmtope. pocket computers. PDA or e-bcoit readers} are NOT permitted. If you are unsure whether or not your calculator is allowed for the exam. est-c your TA. How to fill In the bubble sheet: Use a number 2 pencil. Do NOT use tl1lt. If you did not bring a pencil. ask for one. Write and tilt in the bubbles corresponding to: Your last name. middle Initial. and first name. ** -. -. .=Z:H-'rr-. Special carries it to L are your recitati section. {Hone two digits leg. (11.1219. 11. 13} u -. . e e rs section. please enter 24}. Air-trays use Please turn over your bubble sheet when you are not 1rrr-ritlng on it. If you need to change any entry. you must completeiy erase your previous entry. else. circle your mowers on this exam. Before handing in your exam. be sure that your answers on your bubble sheet are what you intend them to be. You may also copy down your answers on a piece of paper to tat-re with you and compare with the posted answers. You may use the table at the end of the exam for this. When you are finished with the exam. place aii exam materials. including the bubble sheet. and the exam itself. In your folder and return the folder to your recitation instructor. Ho cell phone calls allowed. Either turn off your cell phone or leave It at home- enyone answering a cell phone must hand in their work; their errem Is dyer. Best or took. Perri Genfleid and Paula Herrera SS. "flu-cc capacitors and a hatter}.r are connected as shown below. The capacitors are fully charged. The charge in capacitor #3 is El] nC. What is the emf of the battery? CI Ct ('31 CI=LflIlF C1 '= 11'] BF (:3: 3.1] HP a.) 1thF r 13v @2131; Codi = r = ‘5“:- D) ZTV J— L Enos ‘33 Cl’rC'L I L. UD -. in“ -. iaev i531? 56. A parallel plate capacitor with charge Q is filled and surrounded by vacuum. Let E and Vhe the magnitude of the electric field and the magnitude of the potential difference beheeen the plates, respecfively. if the space between the plates is filled with a dielectric with If} i, which of the following comparisons to the unfilled capacitor is true? E increases, Vrernains the same E decreases, Vdecreases )5 remains the same, Vremaics the same DJ E increases, Vdccreases E) Edecreases. Vremains the same 5?. The circuit below cunsists of three resistors and thrss hiss] hatterics. Find the current though the 21] £1 msistamc. ‘ 1AA "TL: mif’r badly) L1 S-flfl @mw {19m bum L. ‘ L?- H.335. miss ‘5’" fimnflh'a L" 2.09 E} ma . 2m? mv % L1 = sun 20.s‘2silw‘3c.l——tu=0 j; .r‘li'L ‘ ’20“21175§‘10'D H“! 53. A brick~shapfid objsct with dimensiuns LB :11] x (1.1 cm x (1] cm is made of some ohmic material with resistivity ].G x it)” Q [11. What is the resistance 10 an elem-is ' current flowing slung the long side? L:I.DUH 1 .lfl';fl ,1 fig—52 L r” A s(fllsmj =(ID-‘3mj [1min ' EH} I: u out: w L .1 “Irina —3; R‘- (3 115' * ‘0 421m 5 ED L 59. A positive point charge is placed near a solid conducting Sphere. Consider points X, Y on the smfaoe of the sphere. and point 0, the center of the sphere- Rank the electric potential at these points: .VK'CFD'QV'V VXZVoZ V‘r -’x}Vo3’ Vt D. Vx=VY3’ Va E-Vx=V~r{Vo (9 wwwmgomt’wdw ‘mflwEWTt-Lai’afll with : so. Two point charges are fixed as shown. Find the eieotric potential at point P, assuming the potential is zero at infinity. X y A. 4.5 xlfigV 13.. —2.3 X to? v -1.9>< In”? El- D1] lfliflv .HHJ Q]: ' ' °‘ : Qz=—2.flt'.‘. o=2.flm :—— LQ‘MD‘HV til. Four identical bulbs are connected to an ideal battersr as shown below. Raul: the brightness of the bulbs, fi-om brightest to dimmt. tl “i1 4- 'Lq- Win-use... TM lei} Wei... Lino-a Mfg regulatth ’Tlcm “us. (105%.? Lam , ‘wa'a Badge 2:12.:- 63 W W "List—l M Sim cowl I52. A parallel plate capacitor, filled with air, is charged by e batter through copper wires with length L and cross~seetioual area A. For some applications, the charging of 1he capacitor [c.g., to reach 95% of the applied potential difference) needs to be done as fast as possible. 1Which of the following is the most efficient wag,I to speed up such a charging process? A. Double the emf of the batter},r 3. Double the resistance of the wire, it. (I. insert a dielecuic with a: = 2 between the plates. D. Double the length of the wires (keeping. the cross-sectional area the same)- {@Douhle the cross-sectional area of the wires {keeping ll'Ieir length Lhe same). Nezlficiitv cite-rat. .9.th M'WJO Em Thu—UM: {WM 1:12:22. ogum A W M were. warts EJC oval D MUM “*9 -E hm deutm'nb l1} {huh I, 63. A non-ideal battery with emf 12 “if is connected to points A and E in the circuit below. An ideal voltmeter connected to poinm A and E reads EH] V. What is the internal resistance of the battery? first} 33:. M can (3.2.351 6%“ o 4.2:: .. E son " "75% E -' If :: - a- "I2. r' E“ -M=r*£%:11i ail-lg 54. Widch of the following diagrams shows the egnigotemioi surfaces produced by two infinite sheets with identical, uniform charge density]r or? E] None of the above. 65. A heel; is at rest en a desk tep. Whieh ef the fellewhtg threes forms a Nemen’s third law pair with the book’s weight? A] The normal fence ef the table en the beak B} The fetee of the heel»: en the table C} The gravitational three of the earth en the heel: D The gravitational three at the heel: en the table None of the above shmwwlomhmtwk wheelers 65. The sketeh below shows the .r-dependenee of a three. Which point (er points) is a stable equilibrium pointis}? Fix”! ALIA BIB C D E} both A and C are stable equilibrium points. ET. The graph below Show the potential energyF of a Feree as e finnetien of x. Patentia] energy lsquare=llxlm Rank the 1: component of the force {including signs!) associated with this potential at pointsx=—2m,x=—1mandx=5 rn A] F,{—2 m] e lat—1 m} e F15 m) B) fit—1 m] c m4 m} «c at: m) C] F,{-l 1T1)": F45 In) ‘1' FIG-2 In) } Fifi m) if. Elf—2 r11) 6. Fxtj—l n1} @ 51:5 111) *1 FA—l m) -=: Fir-2 m} ‘12! =- —- M 21*— film) "@513 X:—'lffll Rt=o )ke-an"; 58. Two blocks of masses in and 3e: are connected through a messlcss. ideci suing that runs over no idea], mafiiess pulleyr in the arrangement shown below. There is no friction between the blocks anti the stn'feoes. Determine the magnitude ofthe acceleration of the upper block. f3 g : ng 1:) 3m g o] 1:2 3 EJE 7%931'1‘30". 1 -= '"j'" :: “Erna. W _ sh mfi’fiin '31) 2 :39. A iflfl g mess is attached to a spring [it = 3!} Nina} that is compressed Ifl cm from its eqniiihtium position. If the coefficient of friction between the mass and the table is fig =fl.Sfi, what is the 'tI'elovz'thIr ofthernesswheo the spring has 52:13dede 5.!) cm [i.e. when the spring is only compressed by 5.fl cm)? 2/.— Fr: x=—]flcrn x=—5.{}cm x=t} A}fi.olrofs aims is i u wuss 1.21m“; (Ebjmfs Emih'd? : /A-'- [Do-r = 0414.71» EhM-D =. (xi: 0.03m J m- L%D¢fi *- _fikmod(ln*x\ Jihad é-tndh— «Lino-IL: _. (fit-x Ji- m.“ 1' _ {A'K o": m (A 3 ’erug ) TD. An insulating rod is balanced at its center of mass and is allowed to rotate about the origin of the horizontal Jig}- plane. The rod has a positive charge on one end of the rod and an equally sized, negative charge on the other end of the rod. Li" an electric field, E. = Iii-[III] MIC j, is applied, how should the rod be oriented so as to have the lower: potential energy?I A} Along the x axis, with the positive charge on the positive I side E Along the :1: axis, with the positive charge en the negative at side @ Along the y axis, with the positive charge on the positive 1; side Along the y axis, with the positive charge on the negative y side E} None of the above Lem 2F 9w! E Fan-l “"M m d‘r‘ia‘e‘e, “M 1m '31. A W rod ofntass Lilli kg and length 2.00 m can rotate freely.r about an axis through a point P that is 1.2L"! [it away from the center of mass of the rod. The rod is released from the horizontal position. When the rod is vertical, the angular speed of the rod is 4.30 rants. What is the moment of inertia of the rod about point P? A 1.12 kg m1 @12‘; kg m1 C} 1.33 irng D] 1.44 kg at1 E} 1.15? kg m1 “L! mac]. 1. -___-' T146. playground merry-gmde has a radius of 2.93 m and a mass of 150 kg and can be treated as a uniform disk. It is spirming with an angular velocity, m0 = GAS s". If a 50 kg child, with a velocity of {ll-ll} 1an runs onto the merry go round as shown (tangentially, a distance of lflfl to bore the center), what is the new angular velocity of the combined child I teeny go round system? a; 1mm: Egydrflto more; Ej4tuu Ia: + WK =- D = C). E“ :1: t- men” T3- Treat: the orbits of Earth and Mars as essentially eireular. A spaoecrafi is in an orbit about the Sun with the perihelion point at the orbit of Earth and the aphelion point at the orbit of Mars. Calculate the flight time for the spacecraft to travel from Earth orbit to Mars. {The radius ot'Mars‘s orbit is 2.3 x it)” fit and the radius ofEarth’s orbit is 1.5 a: ID” tn. The masses ofMaIs. Earth and the Sun are 15.42 x Illfl kg, 5.91 x 10" kg, and 1.99 x in“ kg reflective-1y}. A] 522 days Eel days 1'39 days D} 194 days E) 33.0 days T4. A pmten with speed ct" it'll] a It)13 ends enters an electric field at magnitude Hit} x] t}T NFC. traveling aleng the field lines. as cheap below. It" the regicn with the electric field is l .513 cm long, what is the preten‘s speed when it emerges fipm this regjcn? .4», an..- A] 1.93 a: 1133ch B} 4.44 x 1aE emits C) 5-01] x in“ cmi’s D]5.3fii<lflacrnf U "r—‘i‘ @raaxtciemt: .._._a, —" p #—e ——e firE’cl claim in '2. *“ y “N/ (rata‘hfl Dal) 2(1,Ea10 C_ it) __c-__,)I_._'L__# . tea I t . . _ l plastic “F5. An uncharged meta] red is resting en a small stand rod that is free to rotate. When a negatively charged ugfilrrg:§ W plastic red is brought close to one end (A) cf the meta] red, the metal red is attracted tcward the plastic red. \ Assume new that the negative red is retrieved, and that instead a peaitively charged plastic red is brought in a A turn clcse to each cf the ends cf the meta] red. $33331“ the fellcwmg heat dcscnhm the hBhflVIDl' of rotating stand A} There will be neither attractien ner repulsien cf the metal red [it is uncharged). ' E) The metal red will he repelled when the plastic red is near end A... and attracted when thc plastic red is near end B. C} The metal red will be attracted when the plastic red is near end A, and repelled when the plastic red is near end B. D) The metal red will he repelled, whichever end is clcse tn the plastic rcd. @ The metal red will he attracted, whichever end is close tn the plastic red mam (Q Theses m W Lem mtlfl 03.; cm; W may {-Lhul'l') cl... a. net” refit} aims .I' $15. A mt} g mass, shaped like a cube, is attached to a string that is wrapped around a pulley. The punfi}? is a uniferm disk with a mass ef 100 g and a radius of 2C- em and the string iniwinds them the pulley without slipping. What is the aceeieratien ef the cubic mass as the string unwinds? A} 5.6Tmfsz E) 135 me1 figsimfi Aims: E}*§t.31un’s2 :. l'la- 'F' WED: I Tziémfl. {:1 = it? 91 f : at J) Ma -* £mfl. '1 M-fl a : M 3 M+i1 '2.- Ti’. The graph heiew shnws the time dependent force that a 3.1.2141] kg mass. with an initial [1 = t} s) velueity of 2.011} nits in the positive .1: ItlirestitmI experiences. if the three is in the nusifive x direction. what is the mass's velocity at t= LEE) 3? @333 mt's B} 19.3 use 13.3 IILI'S mg D} 13.? me F (N) E] Nene at" the above the meet emits 11%. Hi) T9. Pt=1s= P3 Laboratory Final Consider a cart whose position is measured with an ultrasonic transducer (a “motion detector’ 'J, as you did in lab. {Assume the sensor gives positions relative to the X axis illuslrated in the £1 glare). Q Ji—b 3: T8. From the graphs heIow, pick one graph that definitely indicates that the can has reversed direction. Note the labels on the graph axes! D B x A x to © v, d; timid snags finish E] None of the above graphs. As in the Collision in Two Dimensions lab. consider two air pocks sliding with little friotion on a smooth. level surfaoe. Assume they each are moving with some velocity, collide. and men one subsequently rebounds from the edge of the tahte. Consider the total vector momentum. P. of the two pucks [only]. Let Pthe its value before the collision of the poets, P2 its vaioe after collision. and P3 its valocafter one of the [Jocks hits the edge of the table. Which of the following most accurately describes the relationship between these quantities? [Jone ( ioti Feribfififl P1=PE¢P3 C] Pl a! P1 = P3 D) F] at P2 # P3 E) Without knowing whether the collisions are eiastic, one cannot say. BID. In the experiment in which the free oscillation ofa plate hung from a spring was studied. the position of the plate was measured repeatedly h}! an ultrasonic "motion" detector. Using position data from this system, the computer calculaled the velocity of the plate. Such velocity data is represented in the graph below. Assuming that the coordinate system shown in the figure was used [increasing x representing an increasing distance between the force probe and the plate}, what point on the graph corresponds to the plate heing nearest to the floor? V1 tine E] For an object executing simple harmonic motion, it is not possible to sayr where the object is fi'cm such velocity information. (@313 (new. downotmcg (E>D\ Cling ill—a WW3 ($4.05 31. In the rotational motion experiment, the following graph was obtained when the wheel of the apparatus which you used was rotated by hand. Provide the most likely explanation for this partieula: graph. on it a as E '2 3- o: E '5 o.t it on o 2 4 e a to 12 14 ta is to rise {seconds} A) The wheel was rotated rapidly then stopped for a second or tttro1 then rotated rapidly, then stopped again, and so on. E} The wheel was rotated at different velocities, increasing in steps as time went on. C) The wheel was rotated slowly, and the angular encoder on the wheel axis has a solution of ll’Zfl of a revolution. The wheel was rotated slowly, and the angular encoder on the wheel axis has a lution of lflflfl of a revolution. E} The apparatus likely was malfunctioning. ...
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Final Exam Fall 2007 Solutions - PHYSICS 221 Fall 20D?...

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