Meriam, Kraige & Bolton — Statics of Particles: Problem 2_158

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/158 The combined action of the three forces on the base at may be obtained by establishing their resultant through . Determine the magnitudes of and the accompanying couple . Problem 2/158 1. Vector Representation of the Forces Based on the coordinate system shown in the figure (where is vertical, is forward-left, and is forward-right), we can express each force as a Cartesian vector: Force : Magnitude is , acting in the negative -direction. Force : Magnitude is , acting in the negative -direction. Force : Magnitude is , acting in the -plane at an angle of from the - axis towards the -axis. 2. Points of Application We identify the position vectors for each force's point of application relative to the origin : Force : Applied at the elbow between the -segment and the -segment. Force : Applied at the very end of the pipe assembly. Force : Applied at the origin . O OR M zx y F 1 400 lbx F = 1 −400i lb F 2 600 lbz F = 2 −600k lb F 3 500 lbxy45 ∘ x y F = 3 500(cos45i+ ∘ sin45j)= ∘ 353.55i+353.55j lb r O(0,0,0) F 1 3-fty3-ftx r = 1 0i+3j+7k ft F 2 r = 2 3i+3j+7k ft F 3 O r = 3 0i+0j+0k ft 3. Calculation of Resultant Force ● Calculation Process 1. Present Final Formula: 2. Substitute Values: 3. Partial Operations: 4. Final Calculation: ● Final Conclusion: The magnitude of the resultant force is . 4. Calculation of Accompanying Couple The couple is the total moment about point . ● Calculation Process 1. Present Final Formula: 2. Substit