Problem c 240 mm b x B A z y Collars A and B are connected by the wire AB and can slide freely on the rods shown. Knowing that the length of the wire is 440 mm and that the weight W of collar A is 90 N, determine the magnitude of the force P required to maintain equilibrium of the system when (a) c = 80 mm, (b) c = 280 mm. P W

c 240 mm b x B A z y 1. Apply the principle of virtual work. If a system of connected rigid bodies is in equilibrium, the total virtual work of the external forces applied to the system is zero for any virtual displacement of the system. 1a. Define a virtual displacement. By using a single variable, define a virtual displacement of all the forces that do work. P W Solving Problems on Your Own Collars A and B are connected by the wire AB and can slide freely on the rods shown. Knowing that the length of the wire is 440 mm and that the weight W of collar A is 90 N, determine the magnitude of the force P required to maintain equilibrium of the system when (a) c = 80 mm, (b) c = 280 mm. Problem

c 240 mm b x B A z y 1b. Express the total virtual work done by the forces and couples during the virtual displacement.  U = F.  r and  U = M  where  U is the virtual work, F is a force undergoing a virtual displacement  r, and M is a couple undergoing a virtual rotation . 1c. Set the virtual work to zero and solve for the variable. P W Solving Problems on Your Own Collars A and B are connected by the wire AB and can slide freely on the rods shown. Knowing that the length of the wire is 440 mm and that the weight W of collar A is 90 N, determine the magnitude of the force P required to maintain equilibrium of the system when (a) c = 80 mm, (b) c = 280 mm. Problem

Problem Solution Define a virtual displacement. c 240 mm b x B A z y Since AB = 440 mm we have ( 440 mm) 2 = ( 240 mm ) 2 + b 2 + c 2 b 2 = ( 440 ) 2 _ ( 240 ) 2 _ c 2 = 136 x 10 3 _ c 2 Differentiate: 2 b  b = _ 2 c  c  b = _  c = _ c b c cc c 136 x 10 3 _ c 2 P W

Express the total virtual work done by the forces. Set the virtual work to zero and solve for the variable. Virtual work:  U = 0: P  c + W  b = 0 P  c = W For W = 90 N: P = 90 c cc c 136 x 10 3 _ c 2 c c 240 mm b x B A z y P W Problem Solution

c 240 mm b x B A z y P W P = 90 c 136 x 10 3 _ c 2 (a) When c = 80 mm: P = 90 ; P = 20 N (b) When c = 280 mm: P = 90 ; P = 105 N x 10 3 _ x 10 3 _ Problem Solution