TAM203_fall06_Prelim2_solutions - l Your Name: 14 5%] é...

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Unformatted text preview: l Your Name: 14 5%] é flwédL Section time: T&AM 203 Prelim 2 Tuesday October 24, 2006 Draft October 24. 2006 3 problems, 25+ 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, llnear momentum, or angular m0— mentum balance are used; 3 correct vector notation is used, when appropriate; T—) any dimensions, coordinates, variables and base vectors that you add are clearly defined; :1: all signs and directions are well defined with sketches and / or words; «4 reasonable justification, enough to distinguish an informed answer from a guess, is given; 3; you clearly state any reasonable assumptions if a problem seems warmly Wed; 0 work is I. ) neat, II. ) clear, and III.) well organized; . your answers are TIDILY REDUCED (Don’t leave simplifiable algebraic expressions); D 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 “(97 = 18” instead of, say, “theta7dot = 18”. You will be penalized, but not heavily, for minor syntax errors. 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 4: ' [25 Problem 5: z 25 Problem 6: z 25 4) (25 pt) Particle sliding in circles in a parabolic bowl. As if in a James Bond adventure (in a big slippery Cornell—managed radio- telescope bowl in Puerto Rico), a particle—like human with mass m is sliding with negligible friction around in level circles at speed 1). The equation describing the bowl is z = CR2 2 C(zv2 + 312) a) (20 points) Find 1) in terms of any or all of R, g, and C. b) (5 points) Now say you are given w, 0 and 9. Find 1: and R if you can. Explain any oddities. /\ ll? Sb, 1.2 z=CY2 FBD E WM ' O ‘ \l/E' GXPMAL (ml ..... .sr N circa/m mghbflflhflut ecm‘u. 0. (:9 . mi, tdmfl: .3. * 3C? —d G at? FER A A ' l‘ ._.__ 2 also I W’s/M M’L A _ I 2 T90”. . ma’ // A )R A I I —”m3+N/2\ :mwflzh‘la" ? q ' 0 mafia” W I 4‘) _ 7}}? :7 any?” Noam—5m” “'“R @ : 77” Z " W7+N6M0: O 7’) Nwe % a ’ k :7 " - . hmvt . z 9429"“. "-9 24.7 2) wmav'fi"? ” N R O© w,C,c}9i-wm; w— ’2 — R Wmmdj‘fiad@) :7 vam M WW WNW, @ Zé=42cg=w T T 5) (25 pt) Collision. Two Velocifi equal mass m spherical particles have a frictionless collision with coefficient of restitution 6. Before the collision their two velocities are The normal to their common tangent plane at contact is 11 = egg i + sin 0 j. In terms of some or all of v, m, e, 0, i and j, find the velocity of particle 2 after the‘ collision. h ’7 r ' Cowl +SW06. B‘E FORE m = COLMSION ‘ .7“ {’1‘ : nonma/ Noam/M 3‘ I,‘ l f‘} .- A .t— Miami I: £:si}n0i—m6 J W621 542 Smce Aired? ) MK; 3) v,—_v; ' " f regfi‘r‘afl'an bid def/M14707! of caeffiC/owt a e , 7/6/0071/ 0/ Jefieaafim 'Ve’lac/Iy «final 6 3 V, + V2. __ (0'2 L 14:71,? ' sz9+vwa wow => 7/1 : evmg . /\ ' A _ -yémg ,9 + (fl/(34692, =_rysy'm9 (swaf—mai )H’Vme '— (waif-S503) 6) (25 pt) A person mass mp walks up and back, all the way to the bow and to the stern, in a boat mass mb. The person walks continuously and repeatedly, over and over and over again, moving relative to the boat sinusoidally in'time, with period T. The length of the boat is L and the drag force on the boat from the water is F 2 cm. After a while the boat just moves back and forth also. How far does the boat go back and forth? (That is, the bow of the boat goes back and forth between two points, what is the distance between those two points?) Answer in terms of some or all of mp, mb, L and T. 777079027 of péo’SOW and“ wax? X fl}, "5 a2 o FED _ - -L_ => Up/ = Material PEOPGYJC'Q, I) b a : v C vs ® . :> (1,7,, A :5 LMB ZF 3 L a .a a "7 —- a 4‘ b 5 F0 - 77740 P a a L - a’v ll” => —C\/b=(m+m)v,, + mic.) 606L015 [b b L 7. 1}f'c Vb .2 _777P'7: C' A (5) CO: can/T => l'ob‘rclv": Away” “(D C»: C/(mwm) L 7— WWbSo/Mml/bMo’MXé :,mp w Vb' él’) ((96001 + Dsénwt Wag/f w'z Q ,1; W ~Bw5m‘awi + Doom/mat + Bowman} v DC; sm'oa/f = flaw/2‘ ewe/W9 gmy My cot/Mat Wm «BOO +DC; ‘3 O DU) +BC' : A 80’”? "i W 9% 1D: Aw &. Ac. oOl+ B: wL+C.L => v _ A . b " . 601+(4) (magawi—i— Lea/neat) 11> X5 = A f; Smart— th> + Comim/ 05 f’nfrfu/SM (431+Cl" (’0 90.3 7—) W%/I"7’Ww(£ :- A 1+, : A ’ who} and cflw?’ x50) 00.5fm“ M W banal? Mc/ Joz/fiw‘; éx/flrnfi/xw/ ._—————-'-’ ‘ 29 ’60 c.5001 ...
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This note was uploaded on 07/09/2009 for the course ENGRD 2030 taught by Professor Ruina during the Spring '08 term at Cornell University (Engineering School).

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