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# ws 13 - V MEEN 221 Summer 2002 Worksheet 2 Dr A Palazgolo(l...

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Unformatted text preview: V MEEN 221 Summer 2002 - Worksheet 2 Dr. A. Palazgolo (l) HWS2 Due at Beginning of Next Class Ch2 (58, 84), Ch 3 (3, 8, 10, 23, 37) (2) Attendance Mandatory for 10:00 am— 12:45 pm , unless excused by instructor. Quizzes may be given at any time during this period. (3) Subjects: Concurrent Force System, Static Equilibrium, Free Body Diagram Rectangular Comgonen't-s at a Force: Let F pass through point q with coordinates (a, b, 0). Then the unit vector (3,, along the line of action of F is given by: ' A A A A 'a': b 1‘ C . . I’C‘ eF =Zt+21+gk=emz+6“,y+eEz _ Q Casgze -—‘ Fx 4 where a’ =ch2 +b2 +c2 . The vector F may be represented by _F =F éi (where F is the magnitude ofAF) A ‘ (OS 6% 5 eFa : . =FX i.+F, j+.Fz k=Fein +Feﬂjr+Feﬂk _ The orientation angles of F are given by: .K 6, =cos“'(eFx), 61, =‘cos"(e,‘;,)_, 62 =cos"(em) .Resultants by Rectangular Comgonents Let 13‘} be represented in rectangular form as: F}. =ng +Fﬁj+1~gk, j=1,2,...n Then the resultant of the concurrent force system shown above is given by: -— 0—. A A A R=2Fj =in +Ryj+Rzk i=1 “(hem .Rx :iFAjn Ry =53Frj’ R2 zinj j=l F1 ' j=l Note: _ ” [Ma/R: +123 +_R§ . 9 R _. Rt _ R ‘ Izco’s 6R? : cos 2,008 wiﬁté Ceneurrent Fortes Suppose that the rigid body in Fig. 1(a) is represented as a collection of an inﬁnite number of particles subjected to external forces 13],}?2 F; and interaction forces i- = force on article i (1116 to article '= — 7 b Newton's 3rd Law f, p 13 J J y ‘ (wherefﬂ- is the force on particle j due to particle i ) (l) ‘ Newton's second law for each particle becomes jﬁéeﬁ+gﬁj I (2) 0 _. a) 0 %=R2 +jz=lf2j where R is the resultant external force on particle i. All ai's are zero. ' since the body is stationary. Sum all equations in (2) to obtain 0=§E+iin (» i=1 j=1 ' The double summation in (3-) is zero by .eq. 1 and the ﬁrst sum equals:- ' the of all external force-s aetin on the body. Therefore (3 ‘ a roves . (Static EQuilibriwn) R (2—61 1: a) Determine the x, y and z scalar components of the force shown below, and _. 1, (—H)+\a,'7) 1C1: /\ 1’ A.» I __ \ :ibOOlbr F, 3 F J ./ Riley (2 — 66 ) TWO forces are applied to an eyebolt as shown . -(a) Determine the components of F2 (b) Write; F2 in Cartesian vector form .I (c) Determine the magniturle of the component of F2 along FI '17.: Fi=3Q.k‘U F2.’—50-KN (a; ‘3, wmeﬁrerr '. (S; “3) 1)/V\9:‘r err 32;; Pl. Q96 2-83*'Determine the magnitude R of the resultant and the angles 9 , 9 , and 9 between the x y z . line of action of the resultant and the positive x—, y-, ang-z— coordinate axes for the ﬁhree forces shown in Fig. PZ-BS; ' > res-tart >‘#sauusBLE , (3 3312) Harnlng, premature and of Input . ’ [> ca. := 3.1415931180 : v ‘ > eqns :={TE-300*9.81=0 , '1'C*coé (60fga) '-TD=0 , TC*Sin (60*ca} ~TE=0 , [ TB*cos (30*ca.)-T11*cos(40*ca)-TC*cds(60*ca)=0 , ' , TB*sin (30*ca) +‘1‘A*sin (40*ca) -TC*sini(60 *ca.) =0} : [> varsz= {TE,TC,TD,TA,TB}_: . >. solve(eqmsi,vars) , i i . - , . i '= 2943., TD = 1699141392, T C n 3398283459, TA = 1808.l%8952, T B = 3561436524} EXAMPLE 1 R(3—12) Statement: A body with a mass of 300 kg is supported by the ﬂexible cable system shown in Fig. 1. Determine the tensions in cables A, B, C, D,‘ E. Exam 1e- ~ 2% ~ w-.— Determine the resultant of the 4‘ Forces and its line of action with respect to the axis of the plane. Fi‘ez 9 swig 9\ «(fireman 84 _..CHAPTER 3 STATICS OF PARTICLES » TABLE 6—1 TWO-DIMENSIONAL REACTIONS AT SUPPORTS AND CONNECTIONS 1. Gravitational attraction The gravitational attraction of the Earth on a body (see Fig. 6-1) is the weight W of the body. The line of action of the force W passes through the center of gravity of the body and is directed toward the center of the Earth, Cylinder supported by smooth surfaces Fig. 6-1 2. Flexible cord, rope, chain, or cable A ﬂexible cord, rope, chain, or cable (see Fig. 6—2) always exerts a tensile force R on the body. The line of action of the force R is known; it is tangent to the cord, rope, chain, or cable at the point of attachment. Free—body diagram Figure 3-1 Free-body diagmm for a cylinder supported by two smooth surfaces. A rigid link (see Fig. 6-3) can exert either a tensile or a compressive force R on the body. The line of action of the force R is known; it must be directed along the axis of the link (see Section 6-3.1 for proof). Fig. 6-3 A ball, roller, or rocker (see Fig. 6-4) can exert a compressive force R on the body. The line of action of the force F. is perpendicular to the surface supporting the ball, roller, or rocker. Block held on a smooth inclined surfnce with a ﬂexible cable Free-bod) diagram Figure 3-2 Free-body diagram for a block held on a smooth inclined sur- face with a ﬂexible cable. (b) Constructing a Free-Body Diagram i i Step1. Dedde which body or combination of bodies is to be 1 shown on the free-body diagram. Step 2. Prepare a drawing or sketch of the outline of this isolated I or free body. Step 3. Carefully trace around the boundary of the free body and , identify all the forces exerted by contacting or attracting I bodies that were removed during the isolation process. , Step 4. Choose the set of coordinate axes to be used in solving [ the problem and indicate their directions on the ﬂee-body ; diagram. Place any dimensions required for solution of I the problem on the diagram. l @0) [> #EXAMPLE 2 (R. c3—40) d: 5.60.04“ > W1:=5*9.81 : Theta := arccos(2/3*b/d -1) : éy/ <§\$ven) [ Thetan:=subs(d:100,Theta): ' ‘l . w . v a [> Df:= WA/sin('1‘hetan): ' MAPLE 'COﬂE ‘ [> Az=WA*cos(Thetan)/sin(Thetan): > plot({n£,1inesty1e=1,p.,11nesty1e=2},b=200.‘.290,1£it1e="n and A Forces vs. b , with d = 100nm",l_abels=["b in m","rorce in N"],thickhess=2,axgs=box)a‘ -‘ :I' , ’ DandAForcesya b , With d,=100mm’ cheinN \‘¢?‘ ,2; ‘47 40 200 2%] 24) ‘4“ ﬂ ,_ > # EXAMPLE. 3 c3—39 FROM Riley > ThetaI. :é arcsin(ld/10_) :_ ' ThetaR:=a.rctan (d/ (30—10mm (arcsin' (d/lO) ) ) ) : > de1:= -sin('1'heta.L +' ThetaR) . V v . >_'1'L:= -1000*cos(ThetaR)/de1: P:= -1000*cos (ThetaL) Idel: MP; 9.6 CODE‘ vs. d ",1abe13=["d in ft. " ,"For_ces in lbs . "] ,thickness=2 ,a3es=box) ; > : P and TL Forces vs. d 6000 ‘ P44300011»: = meaeéi- Forces in lbs. 2000 [ I: - ‘ > plot‘({TL,1inestj1eé1,P,linestyle=2},d=1..10,title¥"P and n. Edrces 1000 a: 3 C3 --3 ‘83 m: 59G R0? F;,‘o\ CQBXQ +2nJth. ...
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ws 13 - V MEEN 221 Summer 2002 Worksheet 2 Dr A Palazgolo(l...

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