Exam 3 2005 - ES 223 — Rigid Body Dynamics Exam DI March...

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Unformatted text preview: ES 223 — Rigid Body Dynamics Exam DI March 30, 2005 NAME/SECTIONS. HQ 2 L; / Closed book and closed notes. Show all work and enclose your final answer with a box. Problems will be graded for partial credit only if the work is neat and all intermediate steps are clearly shown and presented in an easy to follow format. Equations: Uniformly accelerated rectilinear motion: Acceleration due to gravity: _ 2 v=v0+m g—9.81mls 2 1 g = 32.2 fi/sec s = so + v01 + Earl v2 = v02 + 2a(s —- so) Normal/tangential (path) coordinates: 2=vé 2 A _ A (for circular motion) ('1 r —en + vet . .0 v = r9 ' 2 v - - 2 . . an=w=pfi2=vfi an=i=r62=v6 p r (11:13:54 a,=f::r§ a = an2 + at2 Polar coordinates: Quadratic equation: E:fér+r9'éa arz+bx+c=0 g = ('r‘— r92)ér +(ré'+ 2fé)é3 —bi«!b2 «4a.: 20 (for circular motion) V, = Power: V9 :7"; __ '2 a, — r0 8 _PWW Megan Coefficient of restitution: Tl + U1—y2 = T2 T, + Vgl + V91 + 07:42 = 1'"2 + V31 + 132 e 2 (V2). -(V1).. 1 (1,1)]: _ (1,2)» U=I£-d5 T=—mv2 2 __ ____ l ' 2 _ 2 ' UH: — 2 W2 x1 ) (39mg) Selected integgals: 1 V = m h V = —kx"" g g e 2 I ah: :lln(a+bx) a+bx b —P—-——-—Im “leOmenmmi j sin(a + bx)dx = —%cos(a + bx) g + 213d: = Q2 Ioos(a+bx)dx=%sin(a+bx) 'I G = mv in : ix "’1’. Relative motion — translatin axes: Rotation aboutafixed p_oint: VA 3133 +vV _ _ ""' 3 V2”) a =a a _A _..B+_% 2 2 v anzrw =—=va) r alzra . . . Relative motion — rotating axes: 14:23 +QXI+ENI 12:er . ‘ — “ QA=£B+2x£+2><®><fl+22xxm+gm 2H=Q><(Q><£) 25-02: E =_><£ m lawofcosines: C a a _ b _ c sinA sinB sinC c22a2+b2—2abcosC b 1. (25) Rod BDE is attached to crank BA and is guided by the slider at D that moves horizontally. At the instant shown, the angular velocity of crank AB is 4.5 radlsec clockwise. Determine the magnitude of the velocity of ' point E. Use the method of instantaneous center of zero velocity. Find: vE by the IC method Pram 1c. a? 5D: .. "Hg:- U330 (31'33'19 V380 : 3%— ‘3>‘UJE§ '1?fo 2‘ See 'o-E : 933,9 (Ia—E) From stmdar +rmn6l€$J Lt _ Ll. The“ IC'E: 357155.173- E a = 74? m 0124230019) =9 ‘ “lie: l5 b m \ 52¢ _ g ES; 4,127. 2. (30) At the instant shown, bar AB has a constant angular velocity of 3 rad/s counterclockwise. Determine the angular velocity of bar DE. Express your answer in vector form. Use the relative motion solution method. 93% :3}: ma /; «403335.32:- YJD 3 1/6" 1373/3 CD Find: QDE - /\ 20 - PDEXACDIE " 0305,}; x (— 0.27.5 Non) Subsvlfi‘ufe bad: mfo @ - 0.125 mg; 0.45;- (3.15%8’6 —o-3woe§3 2'. O :- —D'3LL)DB —‘> é": “ DDE 1‘ Dill-5. U005“ “’3- N (floét‘lfi‘ ‘19? S 3. (35) Two rotating rods are connected by slider block E. The velocity of the - slider E relative to the rod AD is constant and is 9 in/sec directed outward toward D. Determine the angular acceleration of rod EB. Express your answer in vector form. 4 Additional information for the instant shown: com = 2.52 rad/sec CW z - a .52 2k [3’ z. ‘ 3?:3225937rgd/sec CW 1: u/JQ? g ’\ Q (at = 0 BE= 10.7784 in F' d: 33 7 ’ m g Reiai'we. Mo'i‘tm't- whng axes 011“ H Comclaies UJI'H\ E and IS Q'Haohecl in DA 55/3: "0773?? #03 + [fig-in?!L 605%? 1 - 693;, t— 8.16% \2- '. 9m: 0 ggigfi +91F+UDXWKT+333X1JFG\*ST&1 areJ:o 1. h. M. M 'U 4.. 95E: “was E15+35J£EIB A A = —(|.aqq)‘f¢.q33+g.2e’3‘] +§Eshx[-tmqs1‘+8.'lba] ‘ 2- Hiqu “BALI-r‘akiiaflB #533: - 8QL°€EB I: 29*}?- fiino?‘ [PM = ‘4»sz mwg -= 4}. 1567069075 Sugar: —- bog-DEF” :. -Q..5;)L(Ll.D-567§) 3 ‘2103 5 a giving: = augfibxgm, —.m(—2.51’4;)x Q3 ; 45.36 2 SQbS‘h-im‘e. ‘H‘teéfi back Info 0) u. m 3 - Iafifi-headmgsawm’tz—LIaswa/fiflnogmsss2 Equa‘te. 433‘} -(a.q3o/Eb:-a7.03 -? 649-6 = in??? ‘ _‘ "‘ 09 l 5 3(66' mée‘L 4. (5) State in words Newton’s Second Law. n7h€ QCCe/efq'fym find par/m4: I: PWPWTAM/ +0 .Hm ragga“ .porce qdm M (7‘ and 45 H) vibe d1M¢+IM {93+ JhLS Jbfleg” 5. (5) The parallel-link swihging plate is an ample of what type of rigid body motion. ‘ Curt/i lmear‘ Trans Limb ‘9} me .32: -' -- Parallel-link swinging plate ...
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This note was uploaded on 04/25/2010 for the course ES 9111 taught by Professor Morrison during the Spring '07 term at Clarkson University .

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Exam 3 2005 - ES 223 — Rigid Body Dynamics Exam DI March...

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