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Exam I 2009 - ES 223 — Rigid Body Dynamics Exam I NAME:39...

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Unformatted text preview: ES 223 — Rigid Body Dynamics Exam I February 18, 2009 NAME :39 Mi] 071/ Closed book and closed notes. Show all work and enclose your final answer with a box. Problems will be raded for artial credit on] if the work is neat and all intermediate steps are clearly shown and presented in an easy to follow format. If you apply Newton '5 Second Law or Imgulse in a solution: you must show a FBD. All solutions must Show a coordinate system. Equations: Uniformly accelerated rectilinear motion: Acceleration due to gravity: _ 2 v=vo+at g—9.81m/s 2 1 g = 32.2 fi/sec s = so + v0! +—art2 2 Conversion: v2 = v02 + 2a(s — SD) in: hr = fl Normal/tangential g path} coordinates: 3 - 6 s A K : ver 2 ' ' miley ) = fi‘ g = v— é” + 13.63, (for circular motion) ( hour xl.47 see p v = r9 2 v ~ - 1 . . an=—=pfiz=vfl an=L=r92=v6 P r ar=13=§ al=fi=rt§ a = on2 + of Polar coordinates: Quadratic eguation: A ' A 2 __ y=fer+r993 ax +bx+c—0 g=(r_ra'2)é, +(r9'+2w‘)é5 x:—bi\/b2-4ac 2a (for circular motion) Vr = 0 Power v9 = r6 P =E'2 ' 2 or = —-rt9 pomp“ a9 = r6). m P. Work-energy: T: + U192 = T2 T1 + V3] + V9! + U11): = j?"2 + V32 + Vt,2 U: Ii'dfi T=—mv2 142 U = —%k(x§ — x12) (Spring) =mgh V = k):2 i ‘ 2 S' F = kx (Spring) Imgulse-momentum: fz! g1+ jzgdz = g Q = my fig + Imam: 11:02 flo=r><m£ E=QX£ Coefficient of restitution: e = (van —(v:),, (V1 )n “ (V2 )n Selected integrals: I dx =lin(a+bx) a+bx b Isinm + bx)dx = —% cos(a + bx) Icos(a + bx)dx = ésinm + bx) Friction force F: Fmax=us N (static. friction) F=uk N (kinetic friction) 1. (30) If the coefficients of static and kinetic friction between the 20 kg block A and the 100 kg cart'B are both the same value of 0.40, determine the acceleration of each part if P = 60 N. Ignore the mass of the pulley and assume the pulley and cart wheels are frictionless. Hkflps=0.40 P=60N Find: tip. and a3 Fm“: 14st = 0.4 (1%.2) —..—.> Fm“: 75mg N ajSume sipping occurs: For" H l iiF-Kimnmfi at) mesa r 30 up. @i a“: 2.07s urn/6.. a. I weapon—amt elmgwrzas mg» l 2. (30) The rotation of the 0.9 m arm 0A about 0 is defined by the relation t9= 0.15t2, where 6is expressed in radians and t in seconds. Collar B slides along the arm in such a way that its distance from 0 is r = 0.9-0.12:2, where r is expressed in meters and I in seconds. ©o\ar Cod‘fc‘l‘ 3’10;th .5 After the arm has rotated through 30" (0.524 rad), determine A (a) The velocity of the collar in vector form. er- (b) The acceleration of the collar in vector form e= 0.514 > 0.156% 1-,: Law 5 - r g; 0.31: @f [.8515 , 6: 05M {Wad/5 er 0.3 ' {‘2 0.9-042+? @tél-quJ l1“ 0.‘-l8\ m (1:. -03.th “ r —O-Ll‘/Cl "Y; F: ~0'7-Ll I A. are: ta + was. = — aweé‘wtrD-Wlwwl Ea _. 0"le 5r 4— 0.170 go “/5 Inna—W '—nl~r"w)v'r w... .7”, t. q. A. 935% §:_{~é"jé‘r + (fe'+g\r9 ea 4. 0.1L; ~(0.u3:)(o.%1)j {1+[0.qar)(o.s)+a.eo.wo(0.5bfi Ea a3: “ 03Q| Er- “0359 @e mgr, 3. (35) A 2.5 lb block B 13 moving with a veiocity v0 of magnitude vo= 6 fi/sec as it hits the 1 5 1b sphere A which 18 at rest and hanging from a cord attached at 0 Knowing that ,uk— 0. 6 between the block and the horizontai surface and e= 0. 8 between the block and sphere, determine after Impact the following. (a) The maximum height I: reached by the Ephere. “t (b) The distance x traveled by the block. . ”61‘er \W‘Pa‘ri pw‘GiQM do ~Fm& 2L6-*“J_ .. ag ”If“ 0W5} ’Ué, : m AVA * M6735 ; m M" 1+ m 6 1%! _ * |~— . —4 END) 1%? 742’“) 32 L if”); (7357* m) 15;: 104671119 CocH 01F rash-H441“. e: We VA $an ’63:, (:0— M77173) Ufi' 'm 0 _.. 6 153‘. 1.95 {AL/Sec ) my; 1.410—lu'lo7095) :3 131;; (.15 $7M V w Wom Enerfin‘a’? 0 7,: 2° /F:r A: T +\/%’.+\/2|+ :‘u‘riu. Ta- VWVT—ij “5 " ‘5 3L}- : : Dr O i 31.2.. (6‘75) ' (3'25L ( )(A) BLm aslb For E) I 21-11.- mayo >~TJS+N 0 => N= 3515 #:TN F3144”: (0.6)(3-5) => F: i5 lb ~ 0 a +— :.- 32.30%) zc-rx o em 4. (3) State in words Newton’s second law. )NQ, accemmiww 3'? 0% (qu‘l‘lole LS Plpov+wflal 4o 44x6; T‘ESuH’Ihfl -pa{‘c-e.,« 515‘ alarm m H“ and {fix/n +he dweohow ~H‘\ if3 1-ofce... 5. (2) According to your textbook, what term is used to describe an imaginary set of rectangular axes assumed to have no translation or rotation in space? (Bewitd or as4rovxowumt {e4erance #mwre, (,9 L71) ...
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