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Unformatted text preview: NAME: SQLQI lOﬂ ME 270 — Spring 2010
Examination No. 1 Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Signature: INSTRUCTIONS Begin each problem in the space provided on the examination sheets. If additional space is required,
use the yellow paper provided to you. Work on one side of each sheet only, with only one problem on a sheet.
Each problem is worth 20 points. Please remember that for you to obtain maximum credit for a problem, it must be clearly presented,
Le. . The coordinate system must be clearly identified. 0 Where appropriate, free body diagrams must be drawn. These should be drawn separately
from the given figures. . Units must be clearly stated as part of the answer. 0 You must carefully delineate vector and scalar quantities. if the solution does not follow a logical thought process, it will be assumed in error. When handing in the test, please make sure that all sheets are in the correct sequential order
and make sure that your name is at the top of every page that you wish to have graded. Instructor’s Name and Section: Section 1: J. Jones 9:30 — 10:20 am. Section 2: S. Dyke 2:30 — 3:20 pm. Problem 1
Problem 2
Problem 3 Total ME 270 EQUATIONS
(You probably will not need all of these equations) 5;: _ , F=r i=ep'sﬂ
lrl T1
EB=ABCOSQ v=vo+act
1
=AxBx+AyBy+Asz s=s0+v0t+2act2
A”=}1ﬁ v2=v§+2ac(s—so)
"0:7“? , M0=Fd ' 213%;
2F=0 E lP=0
E " :2
M0: rx y rz ﬁ=5ci+yj+z7c
1% F), I:
Ma="aM0 vzfﬁr+reﬁ9+2k
M02170 (FXF) 9:15;:
uax uay “a2
Ma: rx ry r2 a=ﬁ+yf+2k
I: F), F;
M’a=ﬂd{auar a=vut+Fun
_W _ 2_ 2 #_ .. .2 a .. _. a "a
m—— , g—32.17ﬁ/S —9.807m/s a—(r—re )ur+(r8+2r6)u9+zk
g
3
d 24
I+[—y]
dx
p: 2 Eszmic',EFy=mj},ZFz=m'z'
ﬂ
dx2
d . .. .
VE : a=ﬂ=V—v ZF=m(i‘—r62),2Fé=m(r9+2f6),ZF=m§
0’: dt ds r 2
v2
2F=mv,2F=m—~,EF=0 EBM — [BIA E=FEF I fstaﬂ'cSJuSN fslide:iuKN
Ila/Al
£=dem yzjydm 27:!de
~ __ 2mg“ ~ ... 23%;; ~_ 2771:;
x— m, y— 2m 2 2m]
EJMA EJ326114 2:]sz
M4 [an jdA P = pgh
= d d dos
W ,0 ghd If [3 = [3(a) , then: i = —‘8— (chain rule of differentiation)
d: do: dt
2=jci+jzi g=ii+3>1
=fgr+r9g9 =(f—r92) gr+(ré+2i*9) g,
= V E: 2
= V E; + v—En
p
Trigonometric Identities
Annotated reference triangle.
secza=1+tan2a, sin2a+cosza=1, csc2a=1+cot2a, sin2a=25incxcoscx,
cos 2:): = cos2 06 — sin2 a
 2 2 2 . a b 3
Law of cosmes: g = a + b — Zab cosy Law of smes: , — sm 06 sin )3 sin y  NAME:
ME 270 — Spring 2010 I PROBLEM 1 (20 points) — Prob. 1 questions are all or nothing. I .
PROBLEM 1A. (5 points) ' . FIND: Determine the projection of force FAB in the
 ”direction of cable AC. Note force FAB is given by
FAB = 9.62§+ 3213+ 6.41 Elbs. Express the resulting
projection both as a scalar magnitude & a Cartesian vecto 3o 2:  8? +10k =0 15
lég . 4t. *O.bl'¥? +0 ’5qu“ E; . mo .. JAM4%! +m+l= 1.47 [iv+1. PROBLEM 1B. (5 points) ” ' FIND: Determine the equivalent forcecouple system at
point A Assume the thickness of the frame' Is
negligibly small. (Hint. This' IS n_ot a static
equilibrium problem ) R= 35(sm36i' C0530”)— 40? +25: ' 2m
“.42 5C. '— 50‘3alb5. A  ~85Co530° (2.) ~20“) +256) . A
(Mi—‘3 4056, Ib ft NAME:
ME 270 — Spring 2010 PROBLEM 1c. (5 points) IGIVENtThe man pulls on the rope with a force of F = 20N. FIND: Determine the fOrce vector (_ FAB) & the moment that this force exerts about the base of the pole at O (M F3: 2.o (
Mo zﬁﬂ X55: 00570X (HAWK5:33} PROBLEM _1 D. (5 points)
GIVEN: The 70N force acts on the end of the pipe atX. FIND: Determine the maximum magnitude of the moment 0.9m
about point A that the TON force shown can exert on the pipe. At what angle (between 0° 5 6 s 90") will this maximum moment occur. NAME:
ME 270 — Spring 2010 PROBLEM 2. (20 points) GIVEN: Frame ABC is attached to ground by a fixed support at A. The frame is loaded with two
forces and a couple as shown and is in static equilibrium. ' FIND: a) Deterrrsy'ge tItge 1raLagnitudes of the reactions at the fixed support at A. (16 points)
0 _
b) If the 4BBNm couple was shifted toward point B, what effect would this have on the magnitude of the reactions at A? (increase, decrease, or  Circle one. (2 points) c) If the 150 lb load was shifted toward point B, would this cause the magnitude of the reaction moment to? decrease or remainthesame)_ CircIeone, (2 pom) . ‘
@ZNM —=0 c, +Zf50(4)]+505m3o°(4)' ~50cLo330(3)—I~5‘oo '. ‘ _ NAME:
ME 270 — Spring 2010 PROBLEM 3. (20 points) GIVEN: The truss shown has a pin support at joint. E and a roller support at joint. F and is loaded with
two forces as shown. (Remember 1 kip = 1000 lbs). .The truss is in static equilibrium. " FIND:
a) Determine the reaction'forces at joints E and F. (6 points) _' b) Identify all zero fo'rCe members by placing a zero on each member in the sketch provided. Select
' one ze_rOfforce member and demonstrate that it is truly a zeroforce member using the equations
_ of staticiequilibrium by applying the method of joints. (4 points) 0) Using the upper section of the truss, determine the magnitude of the forces in members FOE and
FCF using the method of sections & indicate whether each member is in tension or compression. (10 points) ...
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