# SOLN_2 - 2-58 Express each force in Cartesian vector ferm...

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Unformatted text preview: 2-58. Express each force in Cartesian vector ferm. 5cos60°i + 5cos45°j +5e0560°k {2.5m + 3.54 j + 2.50 k} EN Ans (—2j}kN Ans 2-78. The forces F1 and I; act on the boll. If the resultant force FR has a magnitude of SOIb and coordinate direction angles a = 110° and B =BO', as shown, determine the magnitude of F1 and its coordinate direction angles Z 2-85. Determine the length of memberAB of the truss by ﬁrst establishing a Cartesian position vector from A to B and then determining its magnitude. rAl' (1)1 = cos‘110° + 1:05:80“ + oost 7 : 151w li',l = Fl + F, 50 cosllO° = (F2)x so c0380“ = (a), 50 c05157.44° = (1'3): —- 20 (1;), = 47.10 (1;), = 8.68 US)‘ = —26.17 1‘; = V(—17.10)1 + (8.68)2 + (—26.17)z = 3141b Ans Ans 71=COS( = 1.1 + '( tan40° - 0.8)i + (1.5—1.2)j r“, = {2.09: + 0.3j} m r” = [(2.09)2 + (0.3)2 =2.11 n1 Ans Ans ‘ 9.104 'Ihe tower is held in place by three czqu 11 the . , 15 24 famofeachcableachngonthc tow ho ' F = 400 ~' " _ _._ erus wn,determme DA 34.66! + .661 34661: N 24 FD,=800(_61+ 4 '— m: magnitude and coordinate direction angles a. H, y of me resuitant force'fhke z = 20m,y = 15m. 25.06 25.051 25.06% N 16 18 24 F = 500 ~‘_~'__ DC (3" 341 3.101? F11 = Fm + F139 + FDC = {321.66i — 16.82] - 1466.71k} N p; = ((321.66)2 + (—16.82)2 + (441515.71)2 = 1501.66N = 1.50kN Ans a _ \$03-1 321.66 77 0 1501.66 ‘ '6 p _ c054 —16.82 90 6° 1501.66 ' ' 7 = cos—l —168° 1501.66 " l“2-1081. Cable BC exerts a force pf F = 28 N 011.1116 t0P of the ﬂagpole. Determine the projection of tins force along the z axis of the pole. 6 4 12 :28—.——.——k) F- (14I 14J 14 = {IZi-aj-24k}N u_= -k ProjF=F-u=12(0)+(~'3)(0)+("24)("1)=24N AM 3 2-118. A force of F = [—40k] lb acts at the end of the pipe. Detemu‘ne the magnitudes of the components F1 and 1"; which are directed along the 'pipc’s axis and perpendicular to it 31+5j—3k _31+5j—3k J31+51+(—3)2 - {E “on = 3. ._ FEE. um=(_40k)'[ .+s; 3k] ,[4'3‘ =18.31b Am F: =VF1—Ff F2 =1/401—’18.31=35.61b Ans Ans /._____.—-————————— 2-138. Determine lh'e mag'niplde of the projectch component of the 100-lb force. acting along the and: BC of the pipe. " (0-6)|+(11-4)j+[0—(—2)]k u(:1: " J(0-6)1+(1z—4)‘+[0—(—2)l‘ II 4.5883! +0.7845]+0.l96lk 11 = Fina, - now—0.53331 +0.1u51+a19m) -(—5113351 1.13.445.“ 191512111 lb mu: Victarﬂhcunitvunoulangcﬂ is (o—m+_(o—4)(+(o-(.—z)n (0— 6)‘ +(0-4)‘+lo-(-2)P 3—0.8018i—0.53451+02673k “cl “' Injuul Coupon"! of FAlan: CB : ~(—su:sa+1u461+19.6121:)-(~o.nom -053451+03.673t) - (—51.55) (—0.11013) + (711.446) (41.5345) + (19.612) (0.2673) - 10.1 lb Au Fa =F ' “a ...
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SOLN_2 - 2-58 Express each force in Cartesian vector ferm...

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