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**Problem 2.137 y x Collars A and B are connected P**

20 in A B O z P Q Collars A and B are connected by a 25-in.-long wire and can slide freely on frictionless rods. If a 60-lb force Q is applied to collar B as shown, Determine (a) the tension in the wire when x = 9 in., (b) the corresponding magnitude of the force P required to maintain the equilibrium of the system.

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**Solving Problems on Your Own**

x 20 in A B O z P Q Solving Problems on Your Own Collars A and B are connected by a 25-in.-long wire and can slide freely on frictionless rods. If a 60-lb force Q is applied to collar B as shown, Determine (a) the tension in the wire when x = 9 in., (b) the corresponding magnitude of the force P required to maintain the equilibrium of the system. Problem 1. Draw a free-body diagram of the particle. This diagram shows the particle and all the forces acting on it.

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**Solving Problems on Your Own**

x 20 in A B O z P Q Solving Problems on Your Own Collars A and B are connected by a 25-in.-long wire and can slide freely on frictionless rods. If a 60-lb force Q is applied to collar B as shown, Determine (a) the tension in the wire when x = 9 in., (b) the corresponding magnitude of the force P required to maintain the equilibrium of the system. Problem 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.

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**S F = 0: P i + Ny j + Nz k + TAB lAB = 0**

Problem Solution x P _ x i _ (20 in) j + z k AB lAB = = AB 25 in A Draw a free-body diagram of the particle. O 20 in Q z B x z Free Body: Collar A Ny j Nz k TAB lAB P i S F = 0: P i + Ny j + Nz k + TAB lAB = 0 A Substitute for lAB and set coefficients of i equal to zero: P _ TAB x 25 = (1)

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**S F = 0: (60 lb) k + Nx i + Ny j _ TAB lAB = 0**

Problem Solution Ny j Nx i _ TAB lAB Q = (60 lb) k Free Body: Collar B S F = 0: (60 lb) k + Nx i + Ny j _ TAB lAB = 0 B Substitute for lAB and set coefficients of k equal to zero: 60 _ TAB z 25 = (2) (a) Since x = 9 in.: (9 in)2 + (20 in) 2 + z 2 = (25 in) z = 12 in From eq. (2): 60 _ TAB (12) 25 = TAB = lb (b) From eq. (1): P = (125.0 lb)(9 in) 25 in P = 45.0 lb

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