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Unformatted text preview: AEM 201: Exam 1’ Name: . _ _ 1. (10 points——2 points each) a) Express the vector equation a particle must satisfy if it is in equilibrium. , ,i I 4 f. A
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b) Based on the criteria discussed in class and the text book, express the following measure in kg
to'3 significant digits: 32.556 g. ' (13“73257 ' 3 ‘2 6 x/o j:3 0) Write the identity that thecoordinate' direction angles (on. B, y) of a vector must satisfy. (50?; m "i" (.1015: “E; %~ (as, 2’ X2, / d) The absolute magnitude ofthe dot product of two vectors is maximum when theangle(s)r
between the vectors is/are:  ' ' (92c) , b M j I} 'nl: '. e) True or False: A + B = B + A if A and are vectors. "mur fur AEM 201: Exam 1 Name: _ CWID: 2. (25 points) Consider the system below. The pulleys are frictionless. A) Draw a free—body diagram at Pt D. r B) Write the equations of equilibrium at Pt D in terms of variables such as T3, F, 6 , etc. C) . IfA weighs 60 N, C weighs 50 N, 6 = 75° and d = 60°, then find the force magnitude
F and the weight at B.  Bonus (4 points) if B weighs 70 N, F = 0 and 6 = 65°, then find the minimum weight at C and the
corresponding weight at A to maintain equilibrium. ' Box final solutions for Part C and Bonus. Show all work for full credit. r (extra page) AEM 201: Exam 1 ‘AEM 201: Exam 1
Name: ' CWID: _
3. (30 points) The 15 N collar C is fixed to rod AB.
A) Determine the vector components of the weight that are parallel and perpendicular to rod AB. B) Determine coordinate direction angle AB makes with the zaxis. Place final solutions in the box. Show all work for full credit. "3 M Li] C W (9 Ex “l” (C) (0 “7g;
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, m?@..__./<.:i Vumnmmnum.w,muunutmmnmsmmh “713314140 + it . a
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’3 N 499W A.) ill/him} ; ernxztlmwmmmmrm «7/ zitlaz 2n ,..——ru. .7..‘~..,..._.,m...‘_.....m~ Cog 5.: :3 Cos AEM 201: Exam ’1 Name: , CWID: 4. (35 points) Bar CA is in compression because of the pulling force P. Determine the magnitude of
the cable tensions TB and Tc as well as the force vector P to keep the system in equilibrium if bar
0A exerts a 3000 lb force at Pt A. Be sure to sketch a free—body diagram. Place final solutions in
the box. Show all work for full credit. . 3" , amp—45m?
 "ammmmmamu,,._nm,.m.m_ﬁ;mwobfn’fzfg'éwm‘igWDWm., :95 ‘6" ~‘33in‘an? i)? TEE/5 mi Name: (extra page) AEM 201: Exam’l CWID: w LL <4 gm? 7%.. '7“ AEM 201: Exam ZB Name: CWID:
1. (10 points—~2 points each) Circle the best answer.
i) The following system shown below represents a(an) system.
SOON
__l_\)_s_.taticilly_dstsrminafs ._ D) unstable ) none of these ' ii) iv) During a scalar formulation of a resultant moment, the sense of direction of a moment is found using which
of the following: “"\
(ByThe Right—hand Rule
E) none of these A) Static Equilibrium
D) The Moment Theorem C) Pythagorean Theorem if i, j and k are unit vectors for a righthanded system along the X, y and z coordinate axes, respectively,
then k X] = ‘ A) IX k. B) 0 C) i E) none of these A couple moment is created when two forces are A) parallel B) opposite in sense C) equal in magnitude D) separated by a distanceéﬂall ofthese What is the equivalent concentrated load and where does it act retative to Pt A for the force distribution
shown below? . I 1,. i
do "a? ” /Z, Wmm?’ A) WoL/2, U6 B) WOUZ, U3 C) Wot/2, 2113 D) WOU4, U3 69mm, 2L/3 AEM 201: Exam 25 Name:  CWID: 2. (26 points) If the force vector F = —5i + 15j + 10k N determine the moment produced about the
pipe segment AB. Express your answer as a Cartesian vector. ' Box or underline final solutions. Show all work for full credit; a FBD is not necessary. AEM 201: Exam 28 Name: CWID: 3. (32 points) Structure ABCDE is supported by a roller at D and a frictionless, moment—resistant
collar at A that slides along rod FG. The weight'of A8005 is negligible. Determine the support
reactions at A and D for the given values: P = 25.0 lb Q =15.0lb
a = 12.0 in r b = 8.0 in c = 4.0 in' A free—body diagram (FBD) is required for this probiem, and the figure belowright may be used as
the starting point for the FBD. ' ' Bonus (5 points) Neglecting the reactions atA and D, represent the two force vectors, P and Q,
' acting on ABCED as a singleforce vector system and state where the line—of—  a‘etion'of—theresultantforcevectorwould cross ABCrelative toilét—A.    Box or underline final solutions. Show alt work for full credit. AEM 201: Exam 28 Name: ‘ CWID: 4. (32 points) Boom OAB is supported by a balland—so'cket at point 0 and two cables. Determine
the support reactions at O and the forces supported by the two cables. A complete freebody
diagram (FBD) is required for this problem, and the figure below—right may be used as the starting
point for the FBD. Box or underline final solutions. Show'ail work for full credit. AEM 201: Exam ZB Name: CWID: (extra page) (D (f? X MjSWGE,><:I> [U : + K (40 ’ 1705 F 1 7271? w 12;”? 5/31 1 if”!!! “:7 “M_W7““"T“”““W“‘ "T'J
' Liz” ‘7 7 MD ’ D 0‘ y” éﬁfW/eaj ‘n 7%, 4. gr?“ "'" I ,065:‘? Thur/i c w i 3’, 000': 
i 5.3005(T71ngfgfzit ( 3/76” ‘QCBW I: 0C Cémjzwéc f My“) .77 W2 9"“7‘4 C N.....M.......__._...u H“ 402;; ~ "" mm m : (ff/ow “~.._.___ : 3 ﬂ / K’J . 73/“? hank; Q? AEM 201: Exam 3A ' Namez' ( LA 1. (10 points) Circle the best answer. CWID: i) in the multi~f0rce member AB, internally Pt C would experience a $1.2 It i ii) When using the method of sections to solve a planar truss system, a maximum of
equilibrium equations can be used simultaneously for the section of interest. A) o 6 .C) 4 D) s E) 00 iii) The relation between the shear force and bending moment on a beam can best be expressed by independent 4?) the change in the moment is equal to the corresponding area under the shear diagram
) the change in the moment is equai to the corresponding slope of the shear diagram C) the change in the moment is equal to the corresponding area under the distributed load D) the change in the moment is equal to the corresponding slope of the distributed load
E) none of these ' iv) List the ZFMs: AEM 201: Exam 3A Name: ' ' CWID: 2. (25 points) The design shown is common in multi~span highway bridges. If the bridge supports
a uniform downward load of 9.25 kN/m, determine the support reactions at A, B and E. and the
force supported by the link CD. FBDs are required. ' Box or underline final solutions. Show all work for full credit. . 2‘16” '2 1 WC
Pr 2 AEM 201: Exam 39: “NEW cwm: (extra page) 46‘ "Zf 51%;) a“??? s"( I C?) :1 By ( “251) R AEM 201: Exam 3A
Name: . . ' CWID:
3. (30 points) Neatly draw a shear force and bending moment diagram for the beam below. Label the value of local min/max points and whether a curved segment is quadratic or cubic. Determine
the value and location of the absolute maximum shear force and bending moment. A FBD is required. 1200 kN " 600kN Bonus (4 points) Determine the shear force, Wx), and bending moment,_M(X), functions between
2 m < x < 6 m Box or underline final solutions. Show all work for full credit. I .4 ﬁrm ﬂ J0
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Name: CWID:
4.(35 points) For the truss below, determine the reaction forces at E and the forces in members BC,
DE, FG. Indicate whether each member is in tension or compression. FBDs are required. Box or underline final solutions. Show all work for full credit. Nev4 ft—b 10—4 ft—D r _.__,__.... “(wm», m.“ t. “WWm » » ma. ‘ Ft; "7:533 53; M) k y ‘1 "Mrr ‘ are; so: ? ..— ___,. w.“ r n: ' ‘ {a '7 3/, l ' 7/5"}: «ex
l' SS if lr ? N W A U d AEM 201: Exam 3A ' Name: . . CWID: . (extra page) ' 7;, “I “if Z/ a: Q 4400 w“ ,. I. f‘__w__m.% m /,__ A (as 9.513. r» {a} m3 E»: “i” m 3m K. . DE Name: \ V
(extra page) _
£1 {:3 3": t if) ’ J v’" 1% M {4v 2:. ﬂwfﬁg) AEM 201: Exam 3A CWID: ...
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 Spring '09
 Metz

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