Meriam, Kraige & Bolton — Statics of Particles: Problem 2_74

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/74 Determine the height above the base at which the resultant of the three forces acts. Given values from diagram: Top force: acting to the right. Middle force: acting to the left. Bottom force: acting to the right. Spacing: Three vertical segments of each, separating the forces and the base . Problem 2/74 1. Determination of the Resultant Force ● Calculation Process To find the resultant force, we sum the horizontal components of the three applied forces. We define the positive -direction to the right. 1. Present Final Formula: 2. Substitute Values: Taking right as positive (+): 3. Final Calculation: ● Final Conclusion: The resultant force has a magnitude of and acts to the left. 2. Determination of the Total Moment about Base ● Calculation Process We calculate the sum of the moments of each force about point . Let's define the vertical distances from base : hB 300 lb 650 lb 250 lb 30 ′′ B R x R=F = ∑ x F + 1 F + 2 F 3 R=300 lb+(−650 lb)+250 lb R=300−650+250=−100 lb R100 lb B B B Distance to force: Distance to force: Distance to force: We use the convention that a force acting to the right creates a clockwise (negative) moment, and a force to the left creates a counter-clockwise (positive) moment about point (using standard coordinates where ). 1. Present Final Formula: Using vector notation 2. Substitute Values: Using a sign convention (CCW is positive): 3. Partial Operations: 4. Final Calculation: 3. Calculation of the Height