University:
Angelo State University
Course:
ENGR 2301 | Engineering Mechanics - Statics
Academic year:

2024
Views:

156

Pages:

7
Author:

unrememberedx6wyi

Problem 2.131 y 360 mm C D 450 mm O 500 mm B z A 320 mm 600 mm x A container of weight W = 1165 N is supported by three cables as shown. Determine the tension in each cable. Problem 2.131 y Solving Problems on Your Own 360 mm C D 450 mm O 500 mm B z A 320 mm 600 mm x 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 = F ? = (d x i + dy j + dz k) d Problem 2.131 y 360 mm C D Solving Problems on Your Own 450 mm O 500 mm B z A 320 mm 600 mm x 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. Problem 2.131 Solution Draw a free-body diagram of the particle. y 360 mm C D ? F=0 O TAC 500 mm z 450 mm B TAD A 320 mm TAB 600 mm TAB + T AC + T AD + W = 0 x W = _ (1165 N) j 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 Problem 2.131 Solution y 360 mm C D O TAC 500 mm TAD z Resolve each of the forces into rectangular components. 450 mm A W = _ (1165 N) j TAC = TAC ? AC = TAC B 320 mm TAB 600 mm x TAB = TAB ? AB = TAB AB = AB 600 450 j TAB = = i+ 750 750 = (0.6 i + 0.8 j) TAB ( ) 600 _ 320 AC 15 j _ 8 j = 680 j k TAC = TAC 680 AC 17 17 ( ) ( ) AD 500 600 360 i+ k TAD = TAD = TAD ? AD = TAD = j+ 860 860 860 AD 25 30 18 = i+ k TAD j+ 43 43 43 ( ( ) ) Problem 2.131 Solution y 360 mm C D O TAC 500 mm z Set the resultant, or sum, of the forces exerted on the particle equal to zero. 450 mm TAD A W = _ (1165 N) j B 320 mm TAB 0.6 TAB _ 25 TAD = 0 43 600 mm x Substitution into ? ?F = 0, factor i, j, k and set their coefficients to zero: TAB = 0.9690 TAD 15 30 T _ 0.8 TAB + TAC + AD 1165 N = 0 17 43 _ 8 18 T = 0 T + 17 AC 43 AD + TAC = 0.8895 TAD (1) (2) (3) Problem 2.131 Solution y 360 mm C D O TAC 500 mm z 450 mm TAD A W = _ (1165 N) j B 320 mm TAB 600 mm Substitution for TAB and TAC from (1) and (3) into (2): x 15 30 x 0.8895 + )TAD _ 1165 N = 0 17 43 TAD = 516 N 2.2578 TAD _ 1165 N = 0 ( 0.8 x 0.9690 + From (1): TAB = 0.9690 (516 N) TAB = 500 N From (3): TAC = 0.8895 (516 N) TAC = 459 N