TAM203_spring06_Prelim2_solutions

TAM203_spring06_Prelim2_solutions - Your Name: 5 T H F F /...

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Unformatted text preview: Your Name: 5 T H F F / H . [— u T [5 TA name and section time: — V’fl // T&AM 203 Prelim 2 Tuesday April 18, 2006, 2006 Draft April 18. 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, linear momentum, or angular mo— 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; :l: all signs and directions are well defined with sketches and/ or words; —>| reasonable justification, enough to distinguish an informed answer from a guess, is given; you clearly state any reasonable assumptions if a problem seems W W; a work is I. ) neat, II. ) clear, and III.) well organized; 0 your answers are TIDILY REDUCED (Don’t leave simplifiable algebraic expressions); El 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 “67 = 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: z 25 Problem 5: z 25 Problem 6: z 25 KB =XA+QX£B/A+—rel as :§A+9—X (ans/AHQXEB/AHQXXM +56; -=— 32mm or WM 1) (29 pt) A car with mass m1 moving at 01 crashes into the rear of a stationary car with mass m2 and sticks to it. The duration of the crash is At after which the cars move together. Give all answers in terms of m1, m2, 121 and At. [Later work may not be graded if it depends on incorrect earlier work] . a) (15 points) Please re-read the rules at the front of the exam. How fast are the cars moving after the crash? b) (5 points) What is F (the force of car 2 on car 1) during the crash, assuming F is constant in this time interval. c) (3 points) Given v1 and m1 consider a range of cars that might be hit by car 1. For what mass m2 car is its acceleration during the crash the biggest compared to all other possible cars? (Answers of the form 7712 —> 0 or 7112 —> 00 are acceptable.) (1) (3 points) Like part (c), for what mass m2 car is its final kinetic energy maximum (that is, more than the kinetic energy of any other car with a different m2)? e) (3 points) Like parts (0) and (d) for what mass m2 car is the total crash energy dissipation maximum (that is, more dissipation than for all other m2)? 0a) before “Cram [3,?“ Cliff: Taking m, , m; as systm. m m “We , u FM, 2 u, mommtwm beiom crash 2 'ma memifmh imm- 0, {:33 a 3‘ {it v crash durin crash . WW 7n ‘5'. 2) my, + o : («11¢ mZ ) u, z) u: mjwm r 1 ml: "’1..." it! b) F cur mm mg _ , _ . 2 m 71} V. w , a ,3 :3 rz 711 um mart — 771.0“. _ m c 2.». -— Minis-“M.” 1 '— ran: A ' mm ml+mz B ' thfl’lg, if: .. IF“, :lF"} ~-- F 3 m’ v’ this is Max a 1%“; mi am; fi?frl.« ' m rah www ‘ C?) Oficelexa’cion 06 11 du‘m‘l C a mi (mum )At— 2. ,1,” ‘9 K m —_- LL”: —— "1.1 w = MW { wmuwmm d.) Funai E o 2 I Z i M 2‘) 2 (L I“; for 'max KE dJJfE‘) :0 3‘) an“; Cmfimz )1“ ZCWI‘tmg) :0 => CmI+mL mgr-m,) 1' O aw». .wmm =) ’mzrmgl wnmnmmNo—mwmwar’ _ r 8) TotO-Q wash we??? d‘géipai‘inn = Wit-ks“ Fm“ m: “ 2 2. _ l '2. » 7770'}! -—'m0 -— fitmm-Wzl WW" 2 ’ ‘ 7m+m;) {,ox wax dissipabon 102 J— m ' 35 mm =) 70,-?th is m” 7‘ mr+m1 2) (27 pt) A particle with mass m slides with no friction in a parabolic trough that is described with the equation y 2: 6x2. Equivalently you could think of a head on a Wire. Gravity 9 points in the, negative y direction. The bead is released from rest at :c = x0. Find the force of the trough /Wire on the mass/ bead when it reaches ac = y = 0. Answer in terms of some or all of 3:0, 0, g, m, i and j. ‘\ we“ .2, kg m, Vl<a dnggKV/ITWN eNePé‘wV. T1+VIL = T14'V'2 ===> O+Mj(cxf>: (lip/V22. V20 (“View 33% w) ’l‘ T “VFODICXO’J (3:1)3COM) => 1V1 :: X ‘2 236 i Wham X50, ‘1 = O HAL {5, N 3) (27 pt) A motor drives link A at given constant wA. All three links are equal length (3. All questions concern the velocities and accelerations when the system is passing through the configuration shown. a) (9 points) What is the angular velocity of link 8. b) (8 points) On figure (b) draw in, as accurately as you can, the velocities of points B, C and D. The velocity of point B is drawn for you. This problem will be graded independently of problem (a) and your reasoning can be based on equations or any thing else. c) (8 points) Write out, but do not solve, one or more vector ——- equations from which you could find the angular acceleration of 15’. Clearly indicate which terms are known and which unknown in your equation(s) and explain how the number of equations match the number of unknowns. Egressions like _r_B/A should be evaluated in terms of Z, i and j. ...
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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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TAM203_spring06_Prelim2_solutions - Your Name: 5 T H F F /...

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