Question

Given: Cables AB, AC, and AD are supporting a crate weighing 1200 newtons. Assume that all coordinates are measured in cm. Also, assume that the total effect of the four smaller cables connecting the crate to point A is simply a single force pointing in the-z direction. D(45,-65,0) PC(-60,0,0) B(0.70.0) Find: What is the magnitude of the tensile force in each cable? A(0.0.-115)

Answer 1

Let the tensions in A B, A C and A D are T_1, T_2 and T_3 respectively. AB^rightarrow = 70 j + 115 k^^and Vertical-bar AB^rightarrow Vertical-bar = 134.63 cm unit vector along AB^rightarrow = 70/134.63 j^^+ 115/134.63 k^^= 0.52 j^^+ 0.854 k^^so T^rightarrow_1 = 0.52 T_1 j^^+ 0.854 T_1 k^^AC^rightarrow = minus 60 i^^+ 115 k^^and Vertical-bar AC^rightarrow Vertical-bar = Vertical-bar 29.7 Vertical-bar so unit vector along AC^rightarrow = 0.463 i^^+ 0.886 k^^AD^rightarrow = 139.553 unit vector along AD^rightarrow = 0.322 i^^minus 0.466 j^^+ 0.824 k^^so T^rightarrow_3 = 0.322 T_3 i^^minus 0.466 T_3 j^^+ 0.824 T_3 k^^so for equilibrium rightarrow minus 0.463 T_2 + 0.322 T_3 = 0 = T_3 = 1.438 T_2