Problem 2.134 B A Two cables are tied together at C and 9 ft 5 ft 8.5 ft 12 ft 7.5 ft Two cables are tied together at C and loaded as shown. determine the tension (a) in cable AC, (b) in cable BC. B C 396 lb

Solving Problems on Your Own A 9 ft 5 ft 8.5 ft 12 ft 7.5 ft B C 396 lb Solving Problems on Your Own Two cables are tied together at C and loaded as shown. determine the tension (a) in cable AC, (b) in cable BC. 1. Draw a free-body diagram of the particle. This diagram shows the particle and all the forces acting on it. 2. 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.

TBC = 0 S Fx = 0 : + TBC = 1.088 TAC S Fy = 0 : TBC 396 lb = 0 4 7.5 12 3.5 8.5 12.5 396 lb FREE BODY C: TBC = 0 S Fx = 0 : + TBC = 1.088 TAC S Fy = 0 : TBC 396 lb = 0 Problem 2.134 Solution Draw a free-body diagram of the particle. Set the resultant, or sum, of the forces exerted on the particle equal to zero.

y Problem 2.134 Solution TBC TAC 12.5 8.5 3.5 4 x 12 7.5 396 lb (a) Substitute for TBC: 3.5 4 TAC + (1.088 TAC ) _ 396 lb = 0 12.5 8.5 (0.280 + 0.512) TAC _ 396 lb = 0 TAC = 500 lb (b) TBC = 1.088 (500 lb) TBC = 544 lb