Particle equilibrium C 0 X Tension : angles: 2 = Cos' È= F (cosai+ cosBj+cosyk) Magnitude: [Fx+ F+F¿ B = COS' Fy IFI Y = Co 5 Fa IFI Rod Force: 0 # Better use in . FR1 then put into matrix 500 lbs BA: (3) LRA 7 6 CA : (1) LCA : 6.78 6 ft DA: (3) LDA: 7 3 - 3 TDI /LD -2 O -2 -1 3 0 -6 -2 0 TB + Tc+ TD + F=0 H ,3ft -6 -6 -1 0.6 m 0.4 m LCD: 20.570.62 = 0.78 m ?Fx: Spring: F =- KOX Pull cos' d + cosp + costr = 1 A. B = ABCose M= u·rxF Push · LAB= 0.513 Lb T = 0.0733 Tc= 0.03. 4?=0.226/ lb Tp = 0.06. 40 = 0.42 Lb Max: 500 = 974.1 Lb 0 .513 -0.6 FAC + LAC kAC = 1.5 KN/m B 0.5 0.5 m KAR = 1.2 kN/m LBA: No.53+0.42 = 0.64 m 0.5 SFy : LAC 0.4 FAB = 0 LAB 0.5 - W =0 + FAL + A 3 40kg W= 40.9.81 = 392.4 N FAL LAC -0.6 FAB LAB 0.4 FAC= 244.86 N 1200 0.20405m 0.5 0.5 244.86 301.36 = 0.2009/m 1500 FAB := 301-36 N -LAB = 313.92 0 392.4 FAB ZAB Fac 40 = 470.88 Moment forces ixj=k jxk=i kxi = j Ak -> Moment force is perpendicular to the plane and direction of force i -> Cross Product: À X B = W, A2 A3 A, A2 Magnitude : []=[A].[B] sine BA B2 B3 XB, XB2 -> 3D Cross Product: i jk +K. (RXF2-RyFx) = 2 . ( RyFa - RaFy ) - j. (RxFz -RaFx) Rx Ry Rz Fx Fy F& Parallel forus: If all forces on a plane -> Counter-clock wise = + are parallel to each other. Clock wise = M = IRFsing = 1RF1 = = Fd = RxFy - Ry Fx the Mp total is always perpendicular to FR Total. RIF FLd Wrench Example: [500 ] 142 Fg = [800k| N 300 1800 FA = [500%) N IF2 1 = 989.95 11 1 4m Pick a reference point with no moment , for example A Fe 989.95 6 m 6m Mg: - [4.800] Mc: 1: 1 = > Mp: 0 L 6.300 [ 3] FR FR Fc = (300] N () (AR·?). ? . $200 1551.02] 7648-987 11 = (MR 140 1.I = [ 1551.02 930.61 2481.63 L R=[%|=> RX FR = 11 M1 = Mg- 11 = 1. - 930.61 = 1-930.61 IFRI IFRI ,2 1800 2481.63 -681.63 Now we find a vector y=2.061 x=1.163 500 300 X Z 800 y = Mix =1648.98 XXO 3 = -800X RxF = M1 = 1-11=11-1;T= 1-CF 800 = MLY =- 930.61 C = M . E y = 300x-500Y = M12 Mx - C Fx 1. -681.63 F. My - CFy For the rigid body equilibrium Projection of vector on another AxBx+AyBy+AzBE × if = = A+B = Fa : force