TAM203_fall06_Prelim1_solutions - f ,. Your Name: Mam/3‘4...

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Unformatted text preview: f ,. Your Name: Mam/3‘4 A .3er Section time: T&Al\/l 203 Prelim 1 Tuesday September 26, 2006 Draft September 25, 2006 3 problems, 25Jr points each, and 90+ minutes. Please follow these directions to ease grading and to maximize your score. a) No calculators, books or notes allowed. A blank page for tentative scrap work is provided at the back. Ask for extra scrap paper if you need it. If you want to hand in extra sheets, put your name on each sheet and refer to that sheet in the problem book for the relevant problems. b) Full credit if '\ / . . o —-+free body d1agrams<—- are drawn whenever force, moment, linear momentum, or angular mo— mentum balance are used; 0 correct vector notation is used, when appropriate; T any dimensions, coordinates, variables and base vectors that you add are clearly defined; all signs and directions are well defined with sketches and/ or words; .___) :t ——+| reasonable justification, enough to distinguish an informed answer from a guess, is given; a}; you clearly state any reasonable assumptions if a problem seems Willy Wail; . . work is I. )neat, II. ) clear, and III.) well organized; . your answers are TIDILY REDUCED (Don’t leave simplifiable algebraic expressions); E] your answers are boxed in; and >> Matlab code, if asked for, is clear and correct. To ease grading and save space, your Matlab code can use shortcut notation like “07 = 18” instead of, say, “thet a7dot = 18”. You will be penalized, but not heavily, for minor syntax errors. 0) Substantial partial credit if your answer is in terms of well defined variables and you have not substi— tuted in the numerical values. Substantial partial credit if you reduce the problem toga clearly defined set of equations to solve. Problem 1: z 25 Problem 2: [25 Problem 3: [25 CD 1) (25 pt) Pulleys. In the problems below you are asked “What is the relation” between this and that. This means you should write the simplest possible equation in which this and that are the only unknowns.) a) (1 point) Please read all the rules and hints at the front of the exam. Write here: “I read the cover page”: ' b) (3 points) The ideal pulley system (make the usual assumptions) in (b,c) below shown is part of a larger mechanism. What is the relation between TA and TB? Clearly justify your work from first principles. c) (10 points) For the same pulley system what is the relation between (1A and a3? Clearly justify your work from first principles. I [Part (d) will only be graded if (b) and (c) above are correct] cl) (11 points) The two pulley systems below (d) are treated as having all ideal components. What is the relation between ac and am? You may use the results from parts (b) and (0) above without re-deriving them again and again. When comparing the systems use m = m and T=T. Cop/‘fflflt _ y, ._ J ‘ ’ A;»,..-;na 7’74" ,1) f Hf"? '\ {I any “if.-.” q ~ ‘ \ ’ : (Maggi—1L (Xfi’fimxfij A v 1" n ' “ «‘1 7' —- ‘11))”; .1. 2‘ I «my, a i ; é w r‘t’ aims x A i {I g ‘ v - l c p'vp .2 t a ) X A "l’ X g " )Q a - L) C" fix-'efiii.az’tr"‘>'j "ii/“5" n - x3 =} 5’ gm : a3 ( “>1” ' - “my 'pmrtt b) ' Me abave FED; Can Ac? awn/Med NZL on m gym. ‘ 2.05m? [art I) 2715 aims F50: W56 esfaéiikéei O“. . 771 file». HST S u b S w t {n 5 '\. \A e . V AN 8 of Q q d va'dvnfi 6) C2) , :1 ' 8 WE . W S (32)” a c ® 2) (25 pt) MATLAB etc- The block of code shown calculates motions from a dynamics problem rel- evant to this course. It runs without error; (This code is no good outside a test, obviously, because the variable names are not suggestive, intermediate variables aren’t used, and there is no commenting.) a) (10 points) Write a mechanics question (with values, units, basic assumptions etc.) that the output of this code answers. Your question should make no reference to matlab or computers but should be in the language of mechanics. [Grading of parts (b) and (0) below depend on the answer to (a) above being correct. So be confident before moving on.] is added just below the b) (10 points) Assume that the command command plot(t,z(: ,2)) t(end). Draw, as accurately as you can, the resulting plot. Label (give numerical values) key points and asymptotes which you find using your own pencil—and- paper analysis. Label the axes (even though the code does not do this). 0) (5 points) Get as far as you can towards finding a numerical value for 1: (end) without using the computer. Ultimately you Will be stuck without a calculator. But get to a point where the job of the calculator is clear. “a”. - a ,v—sm. rams—INF [t,z,tev, zev, i] = this a mi °Pti°ns t“ I‘M“? , tCend) PM )7 7‘5 . E end so at; ‘medva/hl'cé queshzyn ’ should} i—émz . “J zdot = dwamol ..,.. ». ~ vv— .; Ma»; ,3. , function [value,done,dir] = fSally(t,z) function prelim1q2 =odeset ’ events ’ , @fSally); 'Jhis Dj- m farm function zdot = fgeorge(t,z); [2(2) -2*z(2)-10] ’; --'-) Epetnembe'r } I, *Arwml'a‘m _- ammwwl r . ode45(@fgeorge, [0 1000] , [0 10] ,options); suggests i il=xz .‘dexc;m:§¥..u , .zmfli'law-ZV‘S’A’: man «w‘m rm‘n‘u‘wm s 5' 2}. ~22} -I0 value = 2(1) ; done = 1; dir= -1; end L requires to dated: am cm Covrcsbonfimfi to 1C.=o 04m X, crosswime HM b-we , a) refillfilh% I.“ : 7C (Position) 752: 72" (Uelodtg) 1"" 36$ #9 d/b‘f eqa” M 0’7: 72° = w??? —:0 770%? M £15 a I [25 00/51 if: stamdarwl equ” or}. mac/vasz m 7°C + C72 + Ax = F 00 O F M 76 4' .9. 76 +5 )5 =,— m )7) 777- 0' - -£ 0 _£ + i 01 7C — mx m x m M See 19—: 2 _ liz=o T no sh'jfnm Hm mxwmu measurmmuwmmx m-Mm/bmal mMéw W WM? H12 meohmiw quesh'orL Cam,—WML£, be @ \\ , , x A PYOJCL‘h‘e 06mm 1K3 M perm'acjtedI/cvh'oalllgT :40 MHz, )0 m/s . 7711 m a W .0054? [WM/47W to, w my)? (my mxmt 2 N/(m/s) ). Fmd m 6W projech'le twice Jco hit EM gaowmi 450.01.” b) Plot (13226392) )4 W a plot 05 1} vs 1: “W 1} :- :22} '10 v t u ' d” jolt I I = " = —- 7.9+! = ' 't ‘ , jaw/0 > 11mg 0) ,9 Imb'aue -—> '0 '0 . Land/Mm _ -) m = _9.b 80- ' —21 v. —) Qu-Ho = 308 => 19 : 5 38‘“- 1) 11= o ( 2) é“ = '/s szt=£m3 t=§ma tLewd) ., “Mm-fifl- ~-- - a “a, t t C) 5/062 —I) a” o 3 r-Qt 3 z) > 7c= ‘36 -t 1‘ 75 770w fiend) occwu at £20 as to be salmfwt fiend) 770w M5 6 five ® 3) (25 pt) A car drags a cart. A car with known acceleration a accelerates up a hill dragging a cart. a) (15 points) Assume no friction. Find the force of the ground on the cart. Answer in terms of some or all of m, g, a,6,a and LAB. [Your score is the better of the two scores from part (a) and part (b).] b) (25 points) Assume there is friction between the cart and the ground. Find the tension in the cable AB. Answer in terms of some or all of m, 9, (1,0, (1, L A B and the friction coefficient [1 (or the friction angle ¢, defined as tangb = ,u). dire (J) b n. mam "1 fill/66 z} m (at? + at J ) I advent/d Krvoarrna/ acct/Curl)” acne/um?“ = o ‘> T(?"T)—mtgtjl.7)+IN(f.7) 1 mac (49d. 17'.-. mm 2 a) atww ‘ = a 37nd: big 2? Twéd - mg Sme m t Sim, are ‘5 __ (D t/g/UC . “'39 Tgii)_~m¢c3’.3)+wc3.3)= o W M @5051) M9 1 Tammi —mya940+N =0 .— ® 6W @ . N: mama—Taunoc —(3) 6m” (D T = mgsma +ma Md Subsh'Wg An (.9 N: Mgwfi- 3m“ (724959219 +7774) 6044 ' [N1 my} (mo—tamdébne)— (Lia/n4] I b) AN extm San'oh‘onm o‘nvce «wear ‘m Uu‘s bnk J »_~ Ii" e— direobbn of tens/m N 2 ,1 [.«l \ l 163' \fi ’7’? ‘_ all-Veda a/ong Hwy/M12141) l I/ . ._\'.,."\,/ . , -L‘§J‘,£«./.-.)9.—— >1” é— horizontal d/I’Crflm oxpr NZL on. Maw: m git/“ed, -—+ —» Fext : ma 4‘! 4‘ l" ‘ = Til—mgj/4-N3—acl: Mal "Omyffl/V I‘ n. N" 4"“ _. k-A = “m Lfi'i) 11: T(7”-:)‘W}(J-I)+NU"‘) FNL‘TL) “v: aux 60605-0) ° 2) Tmo<—7mysm6~,ur\l=”m0t (D 4‘ A f.‘ 0 . . . M” “X” -—flNC'-d) = WELL) H-a T(T"~3)-‘7’7”’)U'J)+Ncw—=J “ w a L’y—l I 0 Wald) “‘0 ” Tst—n’lgwd19+N=o ~® W (9 ® subsfi/mfim‘w [1v Wag]! in @ Twad— 724952149 - J‘U’WWM 473mg) = ma. >) TCw/sok +Msmo<>= ma+mg5r§z¢9+flmgwwi T: m (6H 3 {5m8+/‘w40§)! cm o( + M 503% o( my “.a‘imlflK-a-rw—n w Note :— from Q.) a/m/ WW aboue N: 720ng —~ TSMM : 7r;ng _. m smdéa-rj‘isma-fflmw’) codd+flSM0< PM fl=o to jam Wm haw/2‘ a) N(fl—'0): myma; mmmaqsmw ngCaM0~ tamdsma) ~atmo<J Mzfi/s W41 M fowl M a) ...
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TAM203_fall06_Prelim1_solutions - f ,. Your Name: Mam/3‘4...

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