Question

(25pts) The crate weighs 500lbf. The coordinates are as shown. The vectors for the tensions in cables FAB and Fac are given below: 1. FAB -FAB FAB 13 AB 2 ft (2m ji + ( 6.-jmi 3 OJA V(2-0(-6-0)(3-0 -25.el-6Facl +클Fack FAC FAC 4 ft a) Find the vector for the force in the strut FAD b) Solve for the magnitudes three forces, FAB, Fac and FAD. Write down how you set up your system of equations if you are using your calculator's solver function 25 ft 6 ft

Answer 1

SOLUTION Force Vectors: We can express each of the forces on the free-body diagram shown in Fig. a in Cartesian vector form as (2 0)i (6 0)j (1.5 0)k 4 12 FAB FAB 13 AB - 13 (-2 0) 6 0)(1.5 0) (2 0)i 6 0 (3-0)k2 FAC = F AC (2 0) + (6 0) (3 -0) (0 - 0)i [0 (6)li [0 (2.5)]k 12 FAD FAD ADJ FAD (25 13 D13 Fak W-{-500k) lb Equations of Equilibrium: Equilibrium requires 5 AB 4 13 AD 13 AD 500 k 0 Equating the I, J, and k components yields FAB 12 13 12 13 13 13 FAD 500 o Solving Eqs. (1) through (3) yields FAB- 342 lb FAC= 368 lb FAD 684 lb Ans. Ans. Ans. W 500 lb

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