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Exam I 2006 (Part 1) - ES 223 Rigid Body Dynamics Exam I...

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Unformatted text preview: ES 223 - Rigid Body Dynamics Exam I February 1, 2006 NAME/SECTION 5a IL! 7L/ M 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. Coordinate systems that you use must be clearly drawn. Equations: Uniformly accelerated rectilinear motion: Acceleration due to gravig: _ 2 v=v0+at g—9.81m/s 2 g = 32.2 fi/sec s = s0 +v0t+§at2 v2 = v02 + 2a(s — so) Normal/tangential (path) coordinates: 3 = vé, v 2 . ‘ A (for circular motion) g = ———e,, + ve, . ,0 v = r0 2 V . . V2 . . an=—=P,32=Vfl an=——=r62=v0 P r a,=13=s° a,=13=r§ a = an2 + a,2 Polar coordinates: Quadratic equation: ax2+bx+c=0 ___ ——b-|_-\/b2 —4ac g=fé,+r0é9 g: (F—r92)é, +(ré+2r'é)éa x 2a (for circular motion) v, = Power: V0 = r 6 P = E'X a, — —r6l2 PW“! 1. (30) The rectilinear motion of a particle is described by the following: 5 v = 7s5 m/s Find the acceleration of the particle when s = 2 m. ads-.Vchr :/ 1/ a: MS»: = lvs 3%)(95 j a: awn“ gar S: D. 7’ a: 5427(1) 3 2. (5) State in words Newton’s First Law. a b a 4,1 M ”w 7L I W ran/1am; m Mafia/Vt, q 13ko 4+ fQS'I‘ remams ml res‘l" unless odeJ bran bk; an uan/qnce Jon 6 3. (35) A small projectile is fired from point 0 with an initial velocity u = 500 m/s at the angle of 60° from the horizontal as shown. Neglect atmospheric resistance. Compute the radius of curvature p of the path of the projectile 30 seconds after the firing. Find: Radius of curvature p of the path 30 seconds alter the projectile is fired. “0%? if 7‘ v1 Q. :“QJ‘ ___ 2; .— / $93-$71? n 7°- ’> ID Qn / N [7/ % an 50) we need an and 7/“ some 41W 11': when 13—305, L152 praJeOHe Mail/aim mzvgcob w: 500cc: (n0 = 2.50 m/s 7r? (2m ~c5t= “Boos/n00 “93430) - Bra. 7m/5 fiecquse 'U’ ,5 pasn’avc) Pradeu‘: I-e Is 5741/ aomfi «f, 4. (30) An extensible robotic manipulator with a small spherical payload is shown below. The angle of rotation 0 and extension distance r are functions of time as given below. When t = 2 seconds, find the magnitudes of the velocity and acceleration of the payload. Find: v and a when t = 2 s. (be sure to express your final answer as the magnitude) b Er polar Coora’lmaiLQS t9 = 0.1+ 0.5t + O.()7t2 rad r = 2+0.4t m (t in seconds) 9: 0411057: +0,o7t7’ 40v £=1 ,9:/.33rw/ é‘ 0.5+ adv-t afar {:13 = 0,78 Fad/5 “é: 01/9 Tad/51 F‘ Q‘Wd-Hrf: {or i=z,r=;2.a> m " Qfiw Q _.. s w M W WWW». 12f: rad réee 6v: ‘r'~r9")€,+(ra+2re)ea :' O'Llar'l’ <1?)(0I78)29 ="[O L? 8)(0t78)jer 33" o M'e‘r + RPM 33 1~[(2.2?)(o.m)+2(043(07afler3 'U" \lo.q"’+;\\8q" = -l7DL1€ + [bib Be inf: 9.32 “‘15) a- a."\lH‘w~\) +00%) ‘a. = 1.5?84 (Vt/$2.1 ...
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