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TAM203_spring00_Prelim2_solutions

TAM203_spring00_Prelim2_solutions - Your Name M Your TA l l...

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Unformatted text preview: Your Name: M Your TA: _ l l ’SoLumNS " T&AM 203 Prelim 2 Tuesday March 28, 2000 7:30 — 9:00+ PM Drnfi Mnmln 25, 2mm 3 problems, 100 points, and 90+ minutes. Please follow these directions to ease grading and to maximize your score. a) No calculators, books or notes allowed. Six pages of formulas from the front and back of the text are provided. The back of the test can be used for tentative scrap work. Ask for extra. scrap paper if you need it. 'b) Full credit if K / —->free body diagrams+~ are drawn whenever linear or angular momentum balance is used; correct vector notation is used, when appropriate; 0 9.. T—> any dimensions, coordinates, variables and base vectors that you add are clearly defined; i all signs and directions are well defined with sketches and/ or words; _,I 5‘ U reasonable justification, enough to distinguish an informed answer from a guess, is given; you clearly state any reasonable assumptions if a problem seems warty defined; work iS I. )neat, II. ) clear, and III.) well organized; . your answers are TIDILY REDUCED (Don’t leave simplifiable algebraic expressions); Ci your answers are boxed in; and >> unless otherwise stated, you will get. full credit for, instead of doing a calculation, presenting Matlab code that would generate the desired answer. To ease grading and save space, your Matlab code can use shortcut notation like. “9-; = 18” instead of, say, “theta'ldot = 18". c) 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 to a clearly defined set of equations to solve. Problem 1: 3 0 [3O "7 Problem 2.: 2 [35 I - M Problem 3: 3) [35 TOTAL: ’00 [100 1)(30 pts) 3-wheeled robot. A 3-wheeled robot with mass m is being transported on a level flatbed trailer also with mass m. The trailer is being pushed with a. force F j. The ideal massiess trailer wheels roll without slip. The ideal massless robot wheels also roll without slip. The robot steering mechanism has turned the wheels so that wheels at A and C are free to roll in the 3 direction and the wheel at. B is free to roll in the i direction. The center of mass of the robot at G is b above the trailer bed and symmetrically above the axle connecting Wheels A and B. The wheels A and B are a distance b apart. The length of the robot is f. Find the force vector EA of the trailer on the robot at A in terms of some or all of m,g,E,F,b,h, i, j, and k . [Hints: Use a free bod)r diagram of the cart with robot to find thetr acceleration. With reference to a free body diagram of the robot, use angular momentum balance about axis BC to find PAP] ME: Fran-x ‘fi'fifi qhhouflce meh+; 2:6 = gov-421' : 9.2 The mbo+ docs 00+ move NH!“ FESPCC" to HA: cards. (13ch you "0““: r '2 -Hni$ Pow-d" ' mRoeoT * mad“ I 7. 2m L—MB : Zf: “11'th E LMB-j‘ => F=2may (n rmal flice 0:? N4“ m3 ,- Jr’ne «Oren—t let-bullied 1‘ mt Hoe cart) FESD Crbbcri) (Continue work for problem 1 here] ' _____........ A gig/041‘s BC : {ZM/c : E/c} 'ABC 1 rflj WWE 35C. = £3: ifacl ’\ b4 k z") >~Bc : “fl/‘40. The orn‘ly {Torres (:quan n+5 about? Cam‘s "BC mm: are £353ij 3 {EM/CY? gar—=55 chzi,‘ « fife/C x "W311; E ‘Agc u ee‘ " J« —m ‘27} 35¢ mtfi5 Free, y ziégt+JIK>xAgk+ ij+$1k)x 3 1h j—A'H' LN 32“ _ L A k . 2b+ ! ‘ +qkin AME .1: = (2} (A2 'mj) + 3 A2) (%)‘+l‘ ——#— 3 #1 ,\ ' /\ k {Eb—A—B/Q :Ei—M—IQ: E/Q‘} h. {Hi/C3 . ABC 5 {-3ch x mEL— 3)" ABC The 01’157 ‘For‘ce Crcafimj I I 3 E CflJu—lnlt) x m(2£mj)§ - ABC CL momen’r abou‘f Q. _ E” F A 3' £t+fi§ MW: ’E-&"m¢+1‘on :3 2 L thy‘dz W M l A « F1311 { :> Zfl/Q°k=i£A/QXA*LE I: T ‘MW‘ 4(4): +£35xAxtE-k =E— Axfi HI: = am A : ZMC=H 3 ABC _ A ,4 w: >5 —/ Mic bi w-EJE‘.‘ E/a'k:iEG/&A mf‘ixmfl-Fgfi“)—Si EMAZ'WVEM 4 :fl‘i- ”3f :1 « ZJ ..'“LR_FHD : g 4;: —|nt .5; blAi‘ ”3—: 7 _‘ _ if: ' .4 mg E11 . A A2: ”2"— +1 Z>ZZMJQ=HM§ 1: ,_.fi,__ 2){35 pts) Slippery money. A round uniform flat horizontal platform with radius R and mass m is mounted on frictionless bearings with a. vertical axis at 0. At the moment of interest it is rotating counter clockwise (looking down) with angular velocity 11:— Tfiorce in the my plane with magnitude F 15 applied at the perimeter at an angle of 30° from the radial direction. The force is applied at a. location that is qi from the fixed positive .1: axis. At the moment of interest a small coin sits on a. radial line that is an angle 6 from the fixed positive :1: axis (with _ ass much much smaller than an). Gravity presses it down, the platform holds it up, and friction coe‘ men =11 eep51 om511 g. Find the biggest value of d for which the coin does not slide in terms of _some or all of Famagaflawafiaqfisand fl. Lg'f “‘7' (0“! was; Support Bearing Coin (at: aura/FM 'u Wfid Ii-i flPL‘“) [Voila W 7"”‘(1510 rial/fiver, and ac! m at cfl/recflon art/Quota W ML "Wmafihw 30 (at (1/) ftgf M 0-21 MLCWW” {:72 {LEE 1’. rim n 7' “-3: -'> 5M0 ” Ho .4 ”3) n :5 Mo ’ g .g w; W {We " Mil (””03”“) 0 +9 -Hne com -—.‘> ”3 NW9 We, "ma/um mifldfi a TX = anad Omd Sim rm.<<rm 2 p<1 (Continue work for problem 2 here) 3) 35 pts) Cone on Disk. A disk rotatm with constant ratew about an fixed axis in the j direction. A right cone held in a fixed bearing at B rolls at. constant rate so that the point on the corner of the edge of the cone has the same velocity as the point it touches on the disk, EC = 1.0- Axis AB is in the my plane. Find the velocity and acceleration‘of point C on the cone in terms of some or all of w,r,,8, 1, j, and k. fl= £1.11 flo= 0031 ("-10% = no K 12c: bl}; (-OUS-Pé'l‘ 9m 6 J x rSMPC'W‘ij = WWMRM‘PEHMfi) : whampfi ' 6mm MPH» '3'? Ha: m=rwae~r= wa=zng=W. a: ' >r+ mxcwxn : number) ac: WWW») = W» (—MEvE-IF 9413) 40),. C-ml’g'l W31” Y4“? WP‘E‘MH’] = m(—MP$+%P§)X raw? = NORM? Cmfij+5“[3%) : r-fiwkfmfj-fgwffi) ...
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