Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_3

⚡ Mecademy AIENG정역학 · ch3  Problem Statement A carpenter holds a 12-lb 2-in. by 4-in. board as shown. If he exerts vertical forces on the board, determine the forces at A and B. Problem 3/3 (a) Force exerted at A ● Calculation Process 1. Present Final Formula: We model the board as a rigid body in static equilibrium. To find the force at point , we sum the moments about point . 2. Substitute Values: From the diagram, the board has a total length . Assuming the board is uniform, its weight acts at its center of gravity , which is at the midpoint, from the left end . Distance from to is . Distance from to is . Let be the magnitude of the force at . To balance the clockwise moment created by the weight acting at about point , the carpenter must push downward at to create a counter-clockwise moment. Taking counter-clockwise as positive: 3. Partial Operations: 4. Final Calculation: ● Final Conclusion: The carpenter must exert a force of downward at point . AB M = ∑ B 0 L=2+ ′ 6= ′ 8 ftW=12 lb G4 ftA BAd = AB 2 ft BGd = BG 4− ′ 2= ′ 2 ft F A A GBA F (2 ft)− A (12 lb)(2 ft)=0 2F − A 24 lb⋅ft=0 2F = A 24 lb⋅ft F = A 12 lb 12 lbA (b) Force exerted at B ● Calculation Process 1. Present Final Formula: To find the force at , we apply the equilibrium of vertical forces. 2. Substitute Values: Let upward forces be positive. We have the upward force at ( ), the downward force at (), and the downward weight of the board (). 3. Partial Operations: 4. Final Calculation: ● Final Conclusion: The