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AEM2012_Exam3_Spring2008_Soln

# AEM2012_Exam3_Spring2008_Soln - AEM 2012 — Examination#3...

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Unformatted text preview: AEM 2012 — Examination #3 — Spring 2008 Problem #1: Two identical billiard balls can move freely on a horizontal table. Ball A has a velocity volas shown and hits ballB, which is at rest, at a point C deﬁned by 6 = 45°. Knowing that the coefﬁcient of restitution between the two balls is e = 0.8 and assuming no friction, determine the velocity vector of each ball after impact. I. §, VA- V01 L‘ A l‘ L13 LVAB" + CVB\,\ a WAIEA+ (VB/>n (2,2) (VA'L : ngiv ‘1; \IO (43 (Va, (,0: so“ m H13 2 . " \f A \n- 6&7)“: (-2 [6/0“ 6/33.” KvP-.\r\ = Q/A’ln+<vl3’)q (“3“ (VA, \A = E (“'93 VD 645% (VA)M=' YA?‘ 04L; yﬂ 1 New; AEM 2012 —— Examination #3 ~ Spring 2008 Problem #2: Disk C with radius 2 meters rolls with out slipping with a constant velocity of vc = 1 m/s i. Rigid rod AB with length 5 meters is is connected to disc C at point B and slides along on a horizontal surface at point A. Calculate the angular 2 m . CE acceleration (XAB of rod AB. A\</ i .. A A A -- ‘ .D Vex = kip-*wek" r 3 =2 ~wcr—i N ii... a ._.._. A“Sr&~ = ‘Mlsi Track (:35 S K Rolling without slip point of contact 8% A ’ 9 _ A G VA} " 1/3 + wngl" V. :h/v, " . ’.‘ ’t = 21 +WA3K xC-BL-Ll‘n A h A —.-. 2i - Swim 1, +Ll‘JAgi T g cm ‘ as: 4‘ o(ma, L y‘ (- mag “JAB ~A/B 'V OK A- ~ 3 o ‘ I‘ A I: QM " 6%: + ol‘MKXC-rSL-Llay A A A A 1 . L . , . .. and“ A ' / _. _, 2- “at “W “ if “3‘ - .. z .1 '- .. '3“; ‘ ?( 1'.) " ~ it; 5‘ A - _L ‘53 .. ihg ‘ b 31' K L sm/\ CD I! 6‘ la AEM 2012 — Examination #3 - Spring 2008 Problem #3: The below conﬁguration is released from rest. Yo—Yo A has mass 4 kg, a radius of gyration k = 1m, an inner radius 13- = 1m, and an outer radius of r0 = 3m. Pulleys B and C are massless and D has mass 9 kg. The cable passes over all pulleys with zero friction. If disk A rolls without slipping along the incline, calculate the tension T in the cable and the acceleration up of mass D at the instant of release. Further if the coefﬁcient of static friction between the disk and the incline is us = 0.6, decide if the assumption that the disk initially rolls without slip is valid. F805 ' _ 2‘ _ X Mass TA I: ”'3 u LL i 0 ’M9ch w: MPaXIL-Sinei -°°591) Uﬂﬁsi T F; N, in“): (6:0,) «A, 0‘0 0 SF": T+F “ “£153”: MAG»), m kiMMQAicS'. IF=M—m usasza):oLz) A 5‘ / 7 “a; A “Y 98: 99+ OKRKX (‘gx "WAEE/A Rape Con 5%hiﬁt“ ’1 (6-5»): 1" ag "‘ DIR r». (5.): W (a5)! = - 3&5 C7.) Vic- Rwos‘. / _—-—-—__...._____—~. A ,. A l f H s | ~ “.319 L'-‘ “4.2%: Last é d/Ati. a.m , O‘N+ MFR-XV." A JV? ~. A 4; o :' CLPJ a “0‘ (9" ‘ - C’ﬂ Egan»: + ‘7 mks: 1:5”, (“\$0554.45 at, (am. an .. - «An, Ln Problem #3: (continued) Solve \$15M : val T =' ‘10.qu // MQ 0( =' ~21.c.3 ‘33—— !) \$1. // Chuk- RWOS; AEM 2012 — Examination #3 -— Spring 2008 l ) (“Hahn (‘0: 3M Rib“ m“: Hug) mu: CH4? N Neuk \OAKQN vs. Rwos =\O-Hol\l// z: 33.9% N// W! éﬁsN J /J_S= mo. mania-am 2.- 310.3th g Lagg’. ...
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