Cálculo de Forças em Cartesiana

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1 - Forças em cartesiana a (-2,-6,3) + F3=400N = 300 N N Fuy = : Y + = 400 7 3K + + - - + = = + + = + 81 + N N de equilibrio 1 114,29) it 1 = 114,23 N - + = = 582,97 N III (K) = N # Intensidode F2 (582,97)2 + N]= = = 114,29 = 607,82 60382 = = 582,97 = 607,82 602,82 = = 128,52 = cost ) 607,82 607,82 2 de (F2) = = F3x F2 4 5 3 30° Fx the 11 = Fxi + 800y 800N + F2= - - = - - ; - - Equações de equilibrio + (400) = + F23/5 it - + 400 + - I = 692,82 = I + =0 + F2 - 400 + F2 - 400 + 400+ =461,88+ +III - = - + 400 - 30° = - 400 : = - + 800 sen 30° 461,88 + = + 800 461,88 + = - = 800 - 461,58 = 338,42 F2 = 338,42 2,293 = 147,59 = + 800 + = = 563,86 = 800,0 N N F2 = 147,59N N = 563,86N N3 10m forcas em cartesiana 8m 1,2m 1 P= N I A B FAB 2 - = - N (m/s) W 3 FAC A= 2 , = C-A = Z (0, 12, -10) = + - = 14,193 + 101 14,193 14, 4 FAB = UAB = = B-A = dAB UAB = - 1,2i + + = + 101 + 8K + (8) 12,862 = 12,862 + de equilibrio P+ W + FAB FAC = 0 (Pi) + 12,862 + + 14,193 = 0 Pi- - FAB 12,862 1,2 i + FAS + FAB 8 - FAC it FAC K = 0 12,862 12,862 14,193 14,193 14,193 - FAB 12,862 1,2 - 1,2 it (-1962 12,862 10 + FAC. 14,193 10 + FAB 12,862 - 14,193 ) = I = P - FAB 1,2 - FAC 1,2 = 0 12,862 14,193 FAB 1,2 + FAC 1,2 12,862 14,193= - 1962 + 10 + FAC. 10 = 0 12,862 14,193 FAC. 10 = 1962 - 10 14,193 12,862 FAC = 14,193 10 (1962 - FAB. 12,862 10 ) FAL = 1962 - FAB. 10 12,862 FAC = 2784,67 - 1,103 FAB FAB 8 - 10 =0 12,862 14,193 10 FAB. 8 14,193 12,862 FAC = FAB. 8 14,193 12,862 10 FAC = 0,883 FB 0,883 FAB = FAC = 2784,67 - 1,103 FAB 0,883 FAB = FAB = 2784, 67- 1,103 FAB 1,103 + 0,883 FAB = 2784, 67 = = 1402, 15 N] (1,103+0,883) = 2784, 67 - 1,103. FAB = = 2784, = 1238, 10N] P= 1,2 + 1,2 = 12,862 14,143 12,862 14,193 = 50 N]45 A FAD 5,6m FAB A. (0,5.6,0) (0, 5.6, m B D m FAC = -4,2m m FAB = 259 4,2m c Las 2 forças em cartesiana 1 = Pf 4) = 5) 2 FAB. UAB = UAB # vetor unitario = B-A = + + - dAB + = -4,2 7 7 = 1 i - 7 FAB 4,2i 7 = 155, - / = -FAB 3 FAC = # vetor unitorio = : + = 7,4 FAC = FAC 7,4 = 7,4 FAC 7,4 7,4 FAC = FAC. 4 FAD = . # vetor unitario (Um) : = = dAD dAD UAD = 6,5= FAD. 6,5 - = - FAD. 6,5 5,6 - 6,5 3,3 K FAD = - FAD. 0,50769K de = P+ FAO = 0 + (-155, (FAC. - + ( = 0 (-155,4 + FAC. 0,32432) it - FAC. 0,75676 - + 0,56757 - FAD =0 = I = -155,4 + 0,32432 = FAC = = 479. 16 0,32432 E 0,75676 - 0,86154 - P= FAC. 0,75676 + 86154 + = 0,56757 - = FAD 0,50769 = 0,56757 = 535, 67 ] 0,50769 P= = 0,75676 + + 207,2 = 479,16. 0,75676 + 535,67. 0,86154 + 207,2 = 1031,31 4 FAC = 479, 16 N = 535, N P = 1031,31 N5 P+ FAB + FAD = FAB. + 0,32432i = (-FABO, + FAC. -FAB. 0,8 - 0,75676 + 0,56757 - 1 0,6 + FAC = 0,6 800 - 0,8 0,75676 - 0,86154 =0 800 FAC. 0,6 .0,8 - FAC 0,75676 - 0,86 154 0,86154 = 800 - 0,8 - 0,75676 0,6 FAD = 800 - 0,43243 FAC - 0,75676 952, 0,50193 FAC - 0,86154 FAO = 952,57 - 1,38025FAC FAC - FAD. 0,50769 = 1,1179 FAC 0,50769 1, = FAD = 952,57 - 1,38025 FAC FAC = 952,57 - 1,38025 FAC + 1, 1174 FACE 2,4982 FAC = 952,57 FAC 952,57 = 381,30 = FAC = 381,30 = 426, 25 FAB = 0,32432 = 0,32432 = 206, 0,6 0,66 Posiwes Y C 450 A= (0,-600,0) mm D = mm FAC 320mm B IX mm z FAD "FAB 600 mm +360) mm A M Forças em cartesiana = - 11651 N 2 UAB # vetor unitario (UAB) = rAB = = 0) + = dAB dAB Um3 = + = + (450)2 + 750 FAB = FAB ( 750 + = 750 450 it FAB 750 600 3 = FAC. # vetor unitario (UAC) = = = + = dAc dAc = - = (600)2 (320)2 680 ( 320 = 600 680 320 k 4 = FAD. UAD # unitario UAD= = == - + + = + 360K dAD (600)2 (360) 860 = = + 860 860 500 860 360 de equilibrio W + FAn =0 + 750 + 750 + 680 600 L- - 680 860 860 600 360 =0 750 450 - 860 it 1165 600 FAB 600 750 + 860 ( -FAC 680 320 1 360 860 K Gro I FHB 450 - FAD 500 =0 750 860 FAB 450 = 500 FAB = 500 750 750 860 860 450 FAB = 0,96899 H -1165 + FAB 600 + 600 + FAC 600 =0 750 860 680 FAB 600 = 1165- - FAn 600 - FAC 600 750 860 680 FAB = 750 600 (1165 - FAO 860 600 FAC 680 600 ) = 1456,25 0,87209 FAD - 1,10294 FAC 320 + 360 = 0 680 860 FAC 320 = FAO. 360 680 860 FAC = 360 680 = 0,88953 FAD 860 320 (I) = 0,96899 = 1456,25 0,87203 - 1,10294 FAC substituindo (III) em 0,96899 = 1456,25 -0,87209 FAD - 1,10294. 0,88953 FAO 0,96899 FAO + 0,87203 + 0,9811 1456,252, = 1456, 25 = 1456,25 = 516,0 2,8222 = 0,88953. = 459,0 N, = FAO : 516 = 500,0 7 mm A= 240, mm = Q=0 mm of FAC A mm FAB = 305 N B 960 em notacao cartesiana 1 P= = Pi 2 UAB # = vetor unitario B-A = (0-960 dAB = dAB dAB UAB = - = - 1060 FAB = FAB. (- 960 + = - FAB. 1060 :- FAB. 1060 240 + FAB. 1060 380 k 3 = FAC. # vetor unitario C-A = (0-960) it = - a dnc MAC - = (-240) 1040(- 1040 - 1040 960 i - FAC 1040 1040 320 k 4 FAD = # vetor unitario = = D-A = + 220K dAD MAD = - 960 it = - 960 + + 1220 FAD = 960 1220 + - - 1220 960 it 1220 720 1220 de equilibrio P+ FAB FAC = D (Pi)+ (- FAB - FAB 1060 240 FAB 1060 380 + 1040 1040 240 - 1040 k) 1060 (- 960 it FAD - 220 =0 1220 1220 1220 (P - FAB 1060 960 1040 960 - 960 )i+ + (- FAB 1060 240 - FAC. 1040 1220 720 ) + (FAB 1060 380 - 1040 320 - 1220 220 = 0 I Fx(i) FAB 960 - FAC 960 - 960 =0 1040 1220 P = FAB 48 + 12 + 305.48 53 13 61 P= 48 + 12 + 240 53 13 240 - 240 + = =0 1060 1040 1220 FAB 240 FAC 240 + 1060 1040 1220 FAB 12 = - FAC 180 53 13 FAB = 53 12 13 3 + 180)= - 53 52 FAC + 795 (tr)FAB 380 - FAC 320 - 220 1000 1040 1220 FAB 380 FAC 320 + 1040 1220 FAB 19 = 55 53 13 FAB = 53 19 4 13 +55) FAB = 212 FAC + 2915 (III) 247 19 e (III) - 53 795 = 212 FAC + 2915 52 247 19 212 FAC + 53 FAC = 795 - 2915 52 19 1, 8775 FAC = 641, 58 FAC = 641,58 = 341, 72 N 1,8775 = 212 FAC + = 212 341, 2915 19 = 446, 71 247 19 247 FAD = 305 N FAB 48 + FAC 12 + 240= 496,71. 53 48 + 13 240 53 13 P= = ON8 AT A= = (0,2.7,0) m = m 0,6m (0.9,0,19) m 1,8m = -1.8) = em cartesiana 1 P= 2 = FAB. UAB # vetor unitario MAB = - dAB = - = 3,172 3,172 = 3,172 3,172 + 3,172 k FAB =-1235, + 3 = # vetor unitario MAC= = ΓAC = = = = + 3,422 = = 3,422 0,9 - fre 3,422 + 3,422 1,9 k 3,422 4 FAD = FAD. "AD # vetor unitario = D-A = dAD dAD um = 3,3= FAD. - 3,3 - = 3,3 - 3,3 3,3 Equações de equilibrio EF=0 : =-0 - 794, 3,422 0,9 3,422 + 3,422 1,9 + 3,3 3,3 3,3 1,8 =0 FAC 3,422 0,9 + 3,3 + (P-2383,35 - 3,422 2,7 - 3,3 2,7 ) (794,45 1,9 - FAD 3,422 3,3 I -1235, 81 FAC + 0,6 = 3,422 3,3 = 1235,81 - FAC. 0,9 3,3 3,422 = 3,3 (1235,81 - 0,9 ) 0,6 3,422 FAD = 6796,96 - 1, 4465 (I) P - 2383,35 - 2,7 - =0 3,422 3,3 P= = 2383,35 FAC. 0,789 + 0,8182 III =0: 794,45 + 1,9 - =0 3,3 1,8 = + 0,555 3,3 Fpn = 1,8 3,3 (794,45 -1 FAC. 0,555) FAD = 1456,49 1,0175 (III) igualando (I) e (III) 6796, - 1, 4465 = 1956,49 + 1,0175 FAC 1, = 6796, 96 - 1456, 49 2,464 FAC = FAC = 5340,47 2,464 = 2167, 40= 1456,49 + FAC. 1,0175 1456, 2167,4. 1,0175 = 3661, 82 P= = 2383,35 + + FAD. 0,8182 P= 2383,35 + 3661, 82. 0,8182 N,