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Published byDominick Gailey Modified about 1 year ago

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Problem 2.137 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. y x x 20 in A B O z z P Q

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y x x A B O z z P Q 1. Draw a free-body diagram of the particle. This diagram shows the particle and all the forces acting on it. 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 2.137

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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. y x x 20 in A B O z 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 2.137

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Problem 2.137 Solution y x x 20 in A B O z z P Q AB = AB = _ x i _ (20 in) j + z k 25 in Draw a free-body diagram of the particle. N y j N z k T AB AB P i A Free Body: Collar A F = 0: P i + N y j + N z k + T AB AB = 0 Substitute for AB and set coefficients of i equal to zero: P _P _ T AB x 25 = 0 (1)

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Problem 2.137 Solution N y j N x i _ T AB AB Q = (60 lb) k Free Body: Collar B F = 0: (60 lb) k + N x i + N y j _ T AB AB = 0 Substitute for AB and set coefficients of k equal to zero: 60 _ T AB z 25 = 0 (2) (a) Since x = 9 in.: (9 in) 2 + (20 in) 2 + z 2 = (25 in) 2 z = 12 in From eq. (2) : 60 _ T AB (12) 25 = 0 T AB = 125.0 lb (b) From eq. (1) : P = (125.0 lb)(9 in) 25 in P = 45.0 lb B

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