Fall 2006 Retest 1 Soln

# Fall 2006 Retest 1 Soln - RENSSELAER POLYTECHNIC INSTITUTE...

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Unformatted text preview: RENSSELAER POLYTECHNIC INSTITUTE TROY, NY RETEST ND. 1 INTRODUCTION TO ENGINEERING ANALYSIS NAME: SECTION: RIN: l—of—ﬁ ._.—-"'—'__"'-.___.—o--—-'H__l__,__ 8 Problem 1 (40 Points).i W Given the following system of equations with unknewne x, y and z: x] + x2 + x3 = —3 2x] + 2X3. = 13 3X2 4" 3X3 = 21 l. 1Write dawn the augmented matrix (T paints} 2. Determine the reduced raw—echelon fenn at the augmented matrix by Gauss—Jordan elimination (24 points) 3. Write the 1values efx], K2 and x3 (9 points} N'DTE: No credit will be given in Parts 2 and 3 unless you show ALL intermediate work in Part 2. 2—ef-6 SOLUTION AND GRADING KEY 1 1 41 1.1 2 13 3 3 21 [3. 1 2 IL} 1 2 ﬂ 1 {1 {1 1 1 1 -3] ﬂ 1 ﬂ —1'.? .1 1 1 [email protected]+a@ I 11 ﬂ 1 ﬂ {1 1 ﬂ {1 Problem 2 (ﬁll points} Two cables are tied together at H and are loaded as shown. a. Draw the ﬂee bod},r diagram {FED} of the supporting hook at B. This FED must he a new ﬁgure; do not do it on top of the ﬁgure shown. (ll) points). b. Write the cable force vector, Tﬂm in Cartesian vector form, where the magnitude of the fate vector is left as a variable {it} points). I c. Write the cable force vector THC, in lCartesian vector form, where the magnitude of the force vector is left as a variable (1G points]. cl. Determine the unit vector, ems, along the line ﬁ'om point A to C (Ill points}. e. Using the vector dot productj calculate the angle between the two cables (it) points). it". 1|Write {but do not solve) the two equations needed to calculate the tensions in the cables, TE”.l and TH; (1U points} SDLUTIDN AND GRADING KEY a. Free bodyr diagram of hook at E [{SEEJSDG] Ai-4ﬂﬂi3ﬂﬂl b. T (moo—oﬁﬁaoo—o)j+(o—o)ki T m gm —...—__.._. =i —.4oo* aoo' =rm —o.e' (1.6 L r—{4ﬂﬂf “3%): +00): J 5W( I+ J) ( I+ ’ .i S ’4' {3‘ / 0 .3 J4? FW‘ T L (525)1 +{Sﬂu}2 +133)2 J r25( '+_ f) ( H i) . e me vector rom to , t v1 e 3? engt o vector to get umt vector: I” (525 — How +{5oo — 3oo) j + (o — on?! _ (9251+ zoo j) a” Z L #0925)! + (zoo)2 + (o)2 J 94:5 . =3:?3.3Ltﬂ~2111 . (A) N Peri" e. [Joe the dot produot formula in the form Tharj 0 TH, = TNT”. mania) and solve for cosﬂx) Tm .Tﬂ: Tm (418i+ﬂ.ﬁj)-TH.(ﬂ.T24i+ﬁ.ﬁQUj) eo3[o)=—= —--—'— =r r THAI—'51:: TJMTM.‘ (a) f D 0 rd"? {—ﬂ.8]{ﬂ.?24} + (nexoeem = 41165 :> oos{rx] = 9.95” f. Apply static equilibrium for a concurrent force system using the FED in part {a}: 2 Fr. = u T1.M + TM, + W = {1' r,“ (—ﬂ.8i+ o.5j)+ rm. (ﬂ.?24i+ ﬂ.ﬁ§ﬂj)— 3w = o (oerm + I].T24Tm_.)i + (norm + worm. — awn = n which yields the two scalar equilibrium equations: f 3 ? our“ +o.r24rm_. :11} [ ll.) I a )7 o ru—Jfr our“ + moor”. = 3m ( ﬂ ...
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## This note was uploaded on 01/26/2009 for the course ENGR ENGR1100 taught by Professor Spilker during the Fall '09 term at Rensselaer Polytechnic Institute.

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Fall 2006 Retest 1 Soln - RENSSELAER POLYTECHNIC INSTITUTE...

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