FinalExam-F08-Solution

# FinalExam-F08-Solution - MAE 101 Final Examination December...

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MAE 101 Final Examination December 9, 2008 Instructor: Ajit Mal TA: Massimiliano Repupilli DO ALL WORK ON THE EXAM ATTTACH ADDITIONAL SHEETS AS NEEDED WRITE CLEARLY AND AVOID UNNECESSARY VIRBIAGE WE MUST BE ABLE TO READ AND UNDERSTAND YOUR WORK IN ORDER TO ASSIGN GRADES USE SYMBOLS AND NOTATIONS USED IN CLASS OR IN TEXT ONLY ABSENCE OF OR INCORRECT FBD’S WILL RESULT IN SEVERE LOSS IN CREDIT CORRECT ANSWERS WITHOUT SUPPORTING ANALYSIS WILL NOT GUARANTEE CREDIT SOLUTIONS Problem 1(15) ______ Problem 2(15) ______ Problem 3(15) ______ Problem 4(15) ______ Problem 5(15) ______ Problem 6(15) ______ Problem 7(15) ______ TOTAL (105) _______ NAME ____________________________________

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MAE-101 Final Exam - Solutions Fall 2008 2 Problem 1 The 200 kg cylinder is hung by the two AB and AC , attached to the top of the wall. A horizontal force P perpendicular to the wall holds the cylinder in the position shown. Determine the magnitude of P and the tension in each cable. Pb Type: 3D-Equilibrium of a Particle ‘A’ - FBD: Ext Forces: P <P,0,0> = G AA W< 0 , - W , 0 > = G Coordinates: ( ) () A 1.2,2,0 B 0,12,8 C 0,12,-10 = = = O x y z T AB P B A T AC C W A
MAE-101 Final Exam - Solutions Fall 2008 3 - Equilibrium Eq’s: 0 F = G G : 0 AB AC A TTW P + ++ = G GG G G (vector form) Resolving the Equilibrium Vector Eq’s into the 3 Cartesian axes yields, (scalar form) ˆ i: ˆ j: ˆ k: 0 0933 0 0846 0 0 778 0 70456 1962 0 0 622 0 7046 0 AB AC AB AC AB AC .T P . T . T −⋅ + = +⋅ = ⋅− ⋅= Finally, solving for the three unknowns, 1402 1238 235 AB AC TN PN = = = Tension within Cable AB: 1. AB ˆ ˆ r B A <-1.2,10,8> =−= G m 2. 22 2 1 2 10 8 AB AB AB r <-1.2,10,8> m ˆ r .m λ == G G 3. 0 0933 0 778 0 622 AB AB AB AB ˆ TT T . , . , . = =< > G N Tension within Cable AC: 1. AC ˆˆ r C A <-1.2,10,-10> G m 2. 222 1 2 10 10 AC AC AC r <-1.2,10,-10> m ˆ r G G 3. 0 0846 0 7046 0 7046 AC AC AC AC ˆ T . , . , . = > G N

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MAE-101 Final Exam - Solutions Fall 2008 4 Problem 2 The beam CD in the frame will safely support a maximum compressive axial load of 3 kN and the hinge at A can support a maximum reaction force of 2 kN . Based on these criteria, determine the maximum safe value of F .
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## This note was uploaded on 01/20/2010 for the course MAE 101 taught by Professor Orient during the Fall '08 term at UCLA.

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FinalExam-F08-Solution - MAE 101 Final Examination December...

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