Exam 1 222 Fall 2009 solutions

Exam 1 222 Fall 2009 solutions - t) The apparent weight...

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Unformatted text preview: t) The apparent weight ai'a steel sphere immersed in various liquids is measured using a spring seale. The greatest reading is ebtaiaed tier that liquid: V V {35 lat“: ' “"3 ‘ (“73’ string tlte smallest density Eel-'1 : having the largest density gr). C] subieet te the greatest atmesplterie pressure u 1]) having the greatest yelume U. E} in which the sphere was submerged the deepest __ ill-Ca LQJ‘ETZF Jeep:an 2) A certain blaelt af 1Liane-d has a yelume ul' ifiti eat3 and Heats urt water {density = lfltltl kgtma] with 25% of its 1relun'te submerged. The downward three that must be applied to held the bleek completely under water is abeut: rill-LEE if ,__ Mutt N ___‘| )flJTI'N (gilt? "a: Wild s a swift; E)1.-lxltl"hl =2 Patti: = {Pf-“(ma F+ fleesslhlfifl Wvfih = ‘3 3} A 31] kg selid sphere, made et'a metal with a density ef' 23GB kgtmi‘. hangs suspended by a eerd. 1When the sphere is immersed in a liquid ef‘ unknewa density, the tensieu in the card is reduced la 23 N. The density at the liquid is elesest te‘. Gill titltt lustre3L T patch; a} use them3 _ a: use t:me : m: “T. _. n) tsae ligme [3 up a) teen kgrmi '6 rs = _ _ ___ a {ennui { l We} 4] A U—tube is partially filled with water. One side ufthe tube is inside ul'a hex with still air and the ether side has a wind blewing aeress the apes end with a yeieeity at" St} ltnu’lt. What is the difference in the height e-l' water between the twe sides at the tube? a Note: ptair] = 1.2 kgfml. ptwster] = ltlt'ltl hgtm]. l . A) Ufllbem fistdé—Egaqu; —"- Yfi‘t guided: L 1.12 t . n} will: f’fit?“ ' if’mffi CD E] Ilfifil‘fl Ill) mafi‘ Eh:ch «is. Fe + Mr : fig flips ; [A ,__ Ee—EJ "IS-L {:'r:5t3%: la'fimfil\ 3"] aims {it 5} Bernoulli "s equation can be derived from the conservation of: @nrrsr B] mass C) angular momentum I D} volume Lt Ll—Uflt“ [to-b) CH E} pressure a} Kepler‘s second law, “A tine from the Sun to a given planet sweeps out equal areas in equal times.“ can be derived from conservation of: A} energy mmass gee Leflorr pars} or“ lsooL I'll Elli HT I'l'tfllf'l'l ent LITI'I volume E) pressure 7"} 'l‘wo uncharged metal spheres+ i. and M. are in contact. A negatively charged plastic rod is brought close to 1., but not touching it._ as shown below. The two spheres are then slightly separated an d, after this separation, the rod is removed. As a result of these steps: insulating support: A) both spheres are neutral l3) both spheres are positively charged C) hotlt spheres are negatively charged D l. is negatively and M is positively charged is positively and M is negatively charged The real Twenties “nut fifiw‘ @ nit/tan m Selma/a as: strpm’flngl! 11% m c: ens-3t. mm W {DA l-E rimmcl) M LW in MLL... afar fidiilfi‘tl-fifi'irei ’Tltffi'UGDtmfi' "lli, agave. 3} What equal. positive chargee maid have ta he placed an the Earth and the Sun ed as tfl balance their gravitational attraedcn‘? {Mass at" Sun ~ 2 a ifl‘w kg} at auxin-“’11:: Leir'a LEE-M fl}: LLWQE 9r a} same” t: L — .i r C)5.?aifl”C L i = (-3; »%b dig-95mm LEW} mfiL aanane figs: 5"“ m 5% mmb mt“ (fibula t: a J ‘ ie ii} ‘l‘we particles, X and "'1’, are 4.1] m apart. H has a charge of 20 and Y has a charge at" Q. The ratie cf the magnitude ai'the electrostatic faree an X to that en ‘t’ is: IQ} The diagram below ahewa the electric field iinea in a regian of space enniaining {Wu small charged apheres, Y and 2. We can deduce that: A} ‘i’ is positive and E’. is negative (at, H) the magnitude at‘the eleeLt‘it: field is the aarnc everywhere C the electric field is strangest midway between Y and Z. a email negative charge piaecd at point X wnuid experience a three to the leFt E] ‘t’ and Z must have the same Sign I". «ELM/ta exng at XI £0”: ll} In the figure below. a small EU g sphere is suspended from point P by an insulating thread that is fit) em long. The sphere bears an unknown ole-ego. Q. A positive point charge, q = +1.0 p0, is brought to a position direetliI below P and the sphere is repelled to a new position. 3:] em to the right ol'q. as shown. The eharge Q is elosest to: ’F— Tfii‘E}: Cr“ engr‘i'esafi :73 A) L3 til: 3} 2.13 ttC :EM pC 3.0 pC 3.5 ttC 12} The diagrams below show four possible orientations of an eleetrie dipole in a uniform eleetrie field [for 2 and 4 the angle with respeet lo the applied field is 45" and 135°). Rtuilt them ueeonling to the magnitude of the torque exerted on the dipole by the field. |e_ast to greatest. a is as T” a s a ———+—-} ——,4——> ——+—% ———k—+ 1 2 A 3 4 mulls it" " iWEi [$14.12.] - {311.143 131-. E ffi‘g D 3,2and4tie,llten1 ‘3 I: 1: EnttddtieJhenfl 1:2 1 “CL! : 13} A point eharge, Hg is plaeed 1t] em from an infinite sheet of eharge that has o = +ltl pC‘frnl. ll‘tlte magnitude oi" the eleetrie field is here hall" way along the line from the slteet to the point eharge, what is the size ol'Q'? Q1. Ell-m let" @aisae F r Leg; ’ 0 a; Lotti: mans: fir: —" 31.. ' L1} lent: :— ei iflflttC I Q i. H F Qua—ea. ' t} l l: -. — 14} A hollow eondueting sphere has an inner radius offlfit} m and an outer radius of LED m. The sphere eitrries u elmrge oi" Sflfl nC. A point charge of+ 30B of: is present at the eenter of the sphere. The surface charge rlensit}.r on the outer sur face is closest to: = WHL 4- Qtfiflfl '7 O CS}er : «Damn e. “TIC-tiff? : Twang fl Ii nCr’m" C} .to "Hot: D)-28nCJ'm _ _-.1(§/ “L £11-44 wormI 0" IS} The {'1 gore beiow shows l‘oor eggdshnped Gaussian surl'aees. labeled I, 2. 3. and 4. enclosing IL}. I. 2. 3 [mini charges. respectively. The point ehsrges are +0. +20 and —50. Rank the surfaces in terms of the magnitude of total flux. lfllmlj. through each. item lowest to highest. lfi] It snlid, insulating sphere of radius R contains a uniform volume distribution nf pnsitive eharge. Which [if the graphs helth etirteeti},r gives the magnitude, E, of the eieetrie field as at funetie-n of r‘? l s e E“ QJ‘ES‘eiL J 'E 3‘3 F, .l ( mast} 31119.9 1" r r fiw’fififl r Di R R -efivj. D E iqfiée 9-3 1?} A leng eyi indrieai insulatnr (r = [l3 In] has a cross section as sh ewn. A smaller, eylindrieel. heilew spaee (r = {12 In} is drilled parallel tti the axis at" the larger eylinder, hut centered en a paint half tire},r between the eenter and edge ef the larger cylinder. Ifthe volume charge density ed" the insulating material is p = id mCImJ. what it the magnitude ef the eleetrie field at the eenler til” the hollow space? .3 ii iii“ we [(77 i3] 4.5XIUHNEC 6 _ _\ C}e.flslu*t~tt{f - J 394m D} “singlets: r -- Var-1“ Nit? . . " _>-' : E} 181K“) 1 I d; I] r K 1; ff afh. ,r'" _ : t3?“J 0.01%‘fi3' “with %{Q;WWD%V fits-#59361 - E‘( W 1 ‘9" 5‘ l ' effixfitmwifi‘fnd 13} Two charges Q are fixed at the yertiees of an equilateral triangle with sides of length a. Using it = lt'fil'ecu, the work reguired to move a third charge, q, from the third vertex to the center ol'thc littcjoining the two lixed charges is: wmt': sweetie -. + SD I‘LH] Itthan s 9L SE; C qufal C» qua. E) (alsthan [9} It ring ol‘eharge has a radius of 1 m and a linear charge dettsity of 3 mem. If Wm] = it. what is the electric potential 2 m from the center of the ring along the axis of symmetry (along the line perpendicular to the ring, going through its center't‘:1 A}l.1xifl:V 1? El QM“ sf .2; m See-it'll one}: 0.9;“ Tia—r I. ' J ‘ j+l1 llfiujtrm (givinmiy .3.“ ME} W "J 'd’iie-“LL U 31 ‘3 tssx m‘v 4m The Paar {moms (P‘): x 1 .I' P d ‘1 U“ a”? on 1d] ‘l'wo itlet-ttieaL small, int-tulatiagH at = H] g, spheres each have + ] rat: oi'eharge uttifitrtuly distributed throughout their 1walttmes. They are initiain at rest with their centers separated by l tn. After they are released they are both free to move. Assuming that the only force acting on the spheres is the electrostatic one, what is the magnitude of their linal velocities? A} 3t] mtg den-imi mum 1?. {mum-d L B 94.? mt‘s L LN 94? mars L 43:”- -'.lt' C3 2 c} *1(3 \ D} fiflflfl rat’s " E} EQUUU 11135 b 'L 15—: \J i 2]} Suppose one has available: C 1 {£0 .3“— T'we sheets efcapper L m A at: m “1-; a sheet afmica {thickness = 0.1 m, K = is) UL Pr A sheet of glass {thickness = 1i} mm. K = 'i'] ii eat all; Wag, emu: A slab of paraffin {thickness = | cm, K = 2} cl Ta ehtain the largest capacitance. place the tth clapper sheets en either side cf: A a M15 mm air gap he mica ‘ _ C} the glass (Zeus Patti; —a “Him a} the paraffin mesaflwe I Y1 E.) the mica, glass, and paraffin {a campasite slab of thickness = [.21 em] J (.1. #1:": L c.— email emf first“) mice. sale-r“ puma—He C ' (“’5‘ EU as 5"?" Kid I‘m") go {3.0 '35.“: 5.1 :- ofi Galas. 22} The diagram shows six, 6 pl" capaciters. The capacitance between paints a and b is: 23} A battery is used ta charge a parallelrplfltc capacitor, after which it is Then the plates are pulled apart to twice their arigiaal separation. This p ccss will dauhlc the: A} capacitance W (JP-hi B. surface charge density (In each pittle C3 E" [cred energy I If C D} magnitude of the electric field between the two plates (J .: 2;; “I? C:- 1 a E.) charge an each plate 1 - Eda—d match =25ch d3 is car-aw which of the following equivalem oapacitancos is not possible? F 1. Aj4p]: —H—1 C=L+ '- EpF [1 [L H, @2pl: 7% ‘— 3} i3 pF - EJJfipF it C“1*Lfl+m‘%?F 25} Three capacitors an: arrangod as ShUWI'l in the sketch bolow. What is tho ratio of [he chargo on the plates ol'Ct ~= 2 pF, C2 = 4 #13 and C3 = o 14!“? J'- ‘2: L4|.) LT; {Elk/Fl“ [— r——4 kin-J —-—i i ‘1 E k. i. I ! I i a 5—- - h V —_—> ,5, (31:02:03 = A} I 4:9 1 '. I : | 1*" Q m. E; 3 : 2: I F.) 9 ‘ 4: I all 5L3} £3: (gli- ®,,::9_+s@ EXTRA CREDIT 6’???) mini" is: we 396W 5mm all ~me uni t1 feeuismii 25] Twer charges Q; = Li} C and Q: = 2.13 C are Ieeated cm the; axis at I] = i] and x1 = 2J2} em. A I]1ird charge Q3 is in he placed between them a: position x; such that Ihe whole system is in equilibrium. Find Q; and .13. G Q3 a G: I If - NsiVmi-nfil- ice—fl—Ic xg a? G.EEem,-D.34C u U U c521. lc. flu? * [Q _s_1 1.: } essum,+n_12c '9‘: r’figv‘h‘sfi l D] fl.52em,+fl.34C a; 5:1 _ is; E} ltisnetperssihlete achieve :hisequilihrium. { “ii-L : Tc? 2) ‘ 1 2 g *- (313 1.. I a F— (E—XB.‘ m": ' (Er-*5} [ 3 “i- Vx =V~r=Vz I. Vx=FY}Va (3} V5... supra; 'I D} Vs =l”r<1"z E} V); { Vv‘iijz Wall! ...
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This note was uploaded on 02/11/2012 for the course PHYSICS 222 taught by Professor Ogilvie during the Fall '05 term at Iowa State.

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Exam 1 222 Fall 2009 solutions - t) The apparent weight...

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