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pt1 - MEEN 221 —Fall 2006 Exam 1 Dr McVay Section Name...

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Unformatted text preview: MEEN 221 —Fall 2006 Exam 1 October 12, 2006 Dr. McVay Section: Name: Student Number: "Aggies do not lie, cheat, or steal, nor do they tolerate those who do. " — Aggie Code of Honor By my signature below I pledge that my conduct on this exam is consistent in every way with the Aggie Code of Honor: l l Signature: 1. This exam consists of Five (5) problems that are egually weighted Some problems have multiple parts. Be sure to carefully read and properly analyze each question that is asked. Do not jump to unfounded conclusions, but also do not overlook or oversimplify problems eithfir. 4. Be sure to show all work, including sketches, Free Body Diagrams , and calc lations, and organize your solution procedure as clearly and systematically as possible. 5. Work problems in the space provided on the exam' sheets. One extra space sheet is provided for each problem. Clearly indicate continuation of the problem. Do not write on the back of any sheet. 9N 6. Work efficiently, neatly, and use pencil. 7. Clearly indicate final answers by enclosing in a "box" or place answer in Ex if box is provided. Include any and all appropriate units. 8. No electronic device of any kind, except a hand calculator, is allowed. 9. Do not write your name on any other page of the exam. Problem 1: I20 Problem 2: / 20 Problem 3: / 20 Problem 4: /20 Problem 5: / 20 TOTAL: mm: wow zm£ om Emma», BEE? Some .3 $2525 95 05 :8qu m 088, we 2:5:me 2t 3 .wfimmsm SEER 835553 E on 8 $2525 5095 ES :85qu 95 2: How SEQ 5 303m on $58 0:22: 2: £033 S @ Ewan 05 Am oEEBHoQ €339 ch a 89—38% _: m m n m m n n T m n n_oocuw m “nan Ev ,-__---___--____-J. tutu: IA .8255 xon E .955 8.2a can :5 £995 9: can 8h .9? mac. 5 56:9 9:. ”mEEEuwo .55 Egg, m 3.033 ucm >w=aa 825:2... m .w>o 5:096 x w>Emoa 9: E was. 0 Eon 9 uwcomtm mac. 2:: mg... .5505 mm m Eon 2 8:0th 2 850 9: can < ESQ E :95 Em: m 9 8:0th m_ much 95 v6 95 $50 9:. .5505 E9w>m $65208 N->-x m5 *0 E95 9: A 0 E63 Hm um: mwao. $95 9 8:936 39 m >5 8.533 m_ EQQS n. ooom < Amp—:2. ch N # Emioi Problem 3 (20 points) Consider the force and the couple shown in figure. Point B lies on line L that passes through point G and is parallel to the unit vector e = 2i +9 j —~3—k. All coordinates are 7 7 7 in meters. (a) Replace the force and the couple with an equivalent system at O. (b) What is the moment about the line OB? Draw a sketch to indicate the sense of this moment. A (0, 4.5 ,0) " G(3,0,4) 5 kN-m Problem 4 (20 points) Determine the reactions at support A and the tensibn in the cable for the system shown below. Neglect the weight of the beam and assume the pulley at D is frictionless. Include a free body diagram of the system. Sketch the resultant force at A. (5) 20 Pts. The figure (a) below shows a plate like structure suspended by 2 hinges and a cable. The plate lies in the x-y plane, i.e. z = 0, as shown in figure (b). The plate is bounded by the straight sides x=0 and yI = 3x and the curved side y2 = 4—x2. (i) 4 pts. Determine the area A of the plate. (ii) 4 pts. Determine the x coordinate xc of the centroid. (iii) 5 pts. Determine the y coordinate yc of the centroid. (iv) 1 Pts What is the x and y positions for the point of applicatiOn of the weight vector W in the free body diagram for the plate? (v) 6 pts. Determine the x coordinate for the centroid of the composite area in figure (c). TABLE 5-1 CENTROID LOCATIONS FOR A FEW COMMON LINE SEG ENTS AND AREAS Circular arc L=2ra rsincr IC? 0 Ic—O 2 2r Y“="‘ ’TT 21 yC‘W L=7rr Ic=f , _& JL 7r Rectangular area A=l1l1 b IC:? II Ilc=§ Tria nguJar area 17}: “7 x .33 C‘ 3 _h I/C"§ Triangular area bh ”“7 “a Ac— 3 h yc=§ 212 v" ‘\ r/N / a CJ_I D Circular sector A=r2a t 21 sing 'C 3a Ila-=0 Quadrant of a circle 111'2 A=T ‘_4r lC—3—7T _4r 3/c-3; Semicircular areh ‘D m- A _ 2 Kc = T _ 1 VC 377 Quadrant of an fillipse )‘ A : 711117, ‘I‘ 4 4a AL I) IC = — 32- _ 371' T | ‘ I _ 4b . H 1 yc — 377 ' a - Parabolic spamdrel .” Quadrant of a parabola th A=T' _ _ 5!! 1.5-? _211 3/7—? ...
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