Problem y C D A container of weight W = 1165 N is supported O

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Problem 2.131 y C D A container of weight W = 1165 N is supported O 600 mm 320 mm 450 mm 360 mm 500 mm D O C B A x y z A container of weight W = 1165 N is supported by three cables as shown. Determine the tension in each cable.

F d y Solving Problems on Your Own C D A container of weight O 600 mm 320 mm 450 mm 360 mm 500 mm D O C B A x y z Problem 2.131 Solving Problems on Your Own A container of weight W = 1165 N is supported by three cables as shown. Determine the tension in each cable. 1. Draw a free-body diagram of the particle. This diagram shows the particle and all the forces acting on it. 2. Resolve each of the forces into rectangular components. Follow the method outlined in the text. F = F l = (dx i + dy j + dz k) F d

Solving Problems on Your Own 600 mm 320 mm 450 mm 360 mm 500 mm D O C B A x y z Problem 2.131 Solving Problems on Your Own A container of weight W = 1165 N is supported by three cables as shown. Determine the tension in each cable. 3. Set the resultant, or sum, of the forces exerted on the particle equal to zero. You will obtain a vectorial equation consisting of terms containing the unit vectors i, j, and k. Three scalar equations result, which can be solved for the unknowns.

S F = 0 TAB + TAC + TAD + W = 0 AB = (450 mm)i + (600 mm)j AB = 750 mm Problem 2.131 Solution 600 mm 320 mm 450 mm 360 mm 500 mm D C B A x y z TAD TAB TAC W = _ (1165 N) j O Draw a free-body diagram of the particle. S F = 0 TAB + TAC + TAD + W = 0 AB = (450 mm)i + (600 mm)j AB = 750 mm AC = (600 mm)j _ (320mm)k AC = 680 mm AD = (_500 mm)i + (600 mm)j + (360 mm)k AD = 860 mm

( ) ( ) ( ) ( ) ( ) 450 750 i 600 j TAB = (0.6 i + 0.8 j) TAB 600 mm 320 mm 450 mm 360 mm 500 mm D C B A x y z TAD TAB TAC W = _ (1165 N) j O Problem 2.131 Solution Resolve each of the forces into rectangular components. ( ) 450 750 i + 600 j TAB = (0.6 i + 0.8 j) TAB TAB = TAB lAB = AB = TAC AC ( ) 600 320 680 k ( ) 15 8 TAC = TAC lAC = = j TAC = j j TAC 680 _ _ 17 17 TAD AD ( ) 500 860 i + 600 j + 360 k TAD = TAD lAD = = TAD = ( ) 25 43 i + 30 j + 18 k = TAD

0.6 TAB _ 25 43 TAD = 0 TAB = 0.9690 TAD 15 17 30 43 TAD 0.8 TAB + TAC 600 mm 320 mm 450 mm 360 mm 500 mm D C B A x y z TAD TAB TAC W = _ (1165 N) j O Problem 2.131 Solution Set the resultant, or sum, of the forces exerted on the particle equal to zero. Substitution into S F = 0, factor i, j, k and set their coefficients to zero: 0.6 TAB _ 25 43 TAD = 0 TAB = 0.9690 TAD (1) 15 17 30 43 TAD 0.8 TAB + TAC + _ 1165 N = 0 + (2) 8 17 18 43 TAD = 0 _ TAC + TAC = 0.8895 TAD (3)

600 mm 320 mm 450 mm 360 mm 500 mm D C B A x y z TAD TAB TAC W = _ (1165 N) j O Problem 2.131 Solution Substitution for TAB and TAC from (1) and (3) into (2): 15 17 30 43 ( 0.8 x 0.9690 + x 0.8895 + )TAD _ 1165 N = 0 2.2578 TAD _ 1165 N = 0 TAD = 516 N TAB = 500 N TAC = 459 N From (1): TAB = 0.9690 (516 N) From (3): TAC = 0.8895 (516 N)