Meriam, Kraige & Bolton — Statics of Particles: Problem 2_132

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/132 A table exerts the four forces shown on the floor surface. Reduce the force system to a force–couple system at point O. Show that R is perpendicular to . Given Values: Force 1 at : (downwards) Force 2 at : (downwards) Force 3 at : (downwards) Force 4 at : (downwards) All dimensions in meters (m). Forces in Newtons (N). Problem 2/132 1. Reduction to a Resultant Force at Point ● Calculation Process 1. Present Final Formula: The resultant force is the vector sum of all individual forces acting on the system: 2. Substitute Values: Each force acts vertically downward in the negative -direction ( ). 3. Final Calculation: ● Conclusion: The resultant force is . 2. Reduction to a Resultant Couple at Point ● Calculation Process M O (0,0,0)F = 1 160N (0,0.6,0)mF = 2 200N (0.9,0.6,0)mF = 3 80N (0.9,0,0)mF = 4 160N RO R=F = ∑ i F + 1 F + 2 F + 3 F 4 z−k R=−160k−200k−80k−160k R=−(160+200+80+160)k=−600kN R=−600kN M O O 1. Present Final Formula: The resultant moment about point is the sum of the moments of each force about : 2. Substitute Values: Using coordinates for each point of application: For : , For : , For : , For : , 3. Partial Operations: Using cross product rules (, , ): 4. Final Calculation: ● Conclusion: The resultant couple at is . 3. Verifying Perpendicularity between and ● Calculation Process 1. Method: Two vectors are perpendicular if their dot product is zero: . 2. Substitute Values: 3. Final Calculation: ● Conclusion: Sin