MECH 230 Final Given + Solution, Spring 2012

W.Najm~ J. Kasamani AMERICAN UNIVERSITY OF BEIRUT FACULTY OF ENGINEERING AND ARCHITECTURE MECH 230 - DYNAMICS- FINAL EXAM.- FALL 2011 NAME: IDNo: Jan.30,2012 2.5 hours open book Exam. • Solve in sequence on the answer booklet. • The question sheet in not considered in grading. • Write clearly. Clarity is important in grading. • Vectors are indicated in bold. • Take g=9.81 m/s2 or g=32.2 ftls2; No.1- (20%) The cable from drum A turns the double wheel B, which rolls on its hubs without slipping. At the shown instant, the angular velocity and the angular acceleration of A are respectively 4 rad/s and 3 rad/s2 respectively, both in the counterclockwise direction. Note that the centers of pulleys A and C are fixed. 5% 1- Determine the angular velocity of the double wheel Bat the instant shown. 5% 2- Determine the angular velocity of the drum C at the instant shown. 1 0% 3- Determine the angular acceleration of the double wheel B at the instant shown. No.2- (20%) Link OA has an angular velocity of 8 rad/s as it passes the position shown. 1 0% 1- Determine the angular velocity of link CB. 10% 2- Determine the Corriolis component of acceleration of pin A. No.3- (20%) The uniform 1 00 kg beam is freely hinged about its upper end A and is initially at rest in the vertical position with 8=0°. A force of 300 N is applied on the attached cable as shown. 5% 1- Draw the free body diagram and the kinetic diagram at the instant 8=0°. Page 1 of 2 E E 0 C'J ~ c A B 80mm p ~~I - - -- V i v I UfE i=Q~ A iNS~ER I / o n I I ,.. / I'L I :.....vo I •V) rl Pl- r/.. 1l. t: D. f- i-1-c ~\ v ' - ' Ll J - ~ ' !'/ ~ ,..,... './ i} j/..s "- .. -t-1lr - 1 -}f 1 I -r-J --t---+--------1--+--+- -f----- -+-+-+--H-----J----t---\JV. 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I ': I J \ I~ _-t--+~~'--t- , -k-91=-~:.-----t"---t-JIJ-f---H--"',.__,:='-I"""'-"~-'-,P-/-+--+-+-~ ...... ~&-+-+-Hir-, 17 n+---+--+-+-+--l-l--+-l-~-+---+-+-~-)(+---l---l-l-+-+--l-----, -+ } oO ( ~~(}) --- ·-;~b~ L' ~ e '$ r\-- - _,_ --~ {, tD~ ' "' - i .., h r->1 ") - I :>. >9 f :~~ . ., ' 1.::;" .~· ~:..... 71 / I I I I u / 1 : ~3MSN'If t od 3Sn L l'~-/~+-+rt--+-+-+-r~~+-+-t--+-+-+-r-r~-+-+-~-+-+-l-~--+--+-+-+--l-+-+-l-~-~41-+-+--l~ I 5% 2- Determine the initial angular acceleration of the beam at the instant 8=0°. 5% 3- Determine the horizontal and vertical components of the reactions at pin A at the instant 8=0°. 5% 4- Determine the angular velocity of the beam when 8=15°. No.4- (20%) The uniform 3 kg bar ABC is initially at rest with end A bearing against the stop in the horizontal guide. When a constant couple M=8 N.m is applied to end C, the bar rotates causing the end A to strike the side of the vertical guide with a velocity of 3 m/s. There is energy loss due to friction in the guide and the roller. 1 0% 1- Determine the angular velocity of the bar when it is in the vertical position . 10% 2- Determine the energy loss due to friction. No.5- (20%) The 320 kg flywheel of a small hoisting engine has a centroidal radius of gyration of 600 mm. The power is cut off when the angular velocity of the flywheel is 1 00 rpm clockwise. Block B has mass of 100 kg. 10% 1- Draw the impulse and momentum diagrams of the system. 5% 2- Determine the time required for the system to come to rest. 5% 3- Determine the tension in the cord C. Page 2 of2 A --~ ') {!"' L!? M L l- 1: G - ~~ rlrl ~ J.~ 'h-br7 - +--+--+-- Jl --p ;::: ~ fV, lvl {, l o.\ ~ ,.,, L~ l ,\I ~ II- lm' :;; su ... Jr'tf - ,/I '"11 h. ) G I! ...:(. I ' d 'n /~ 17 .~ lfl l ~ I I P _i 1::',1 / ~ - 1--7 -- I g. - ~ I' _$. 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