Meriam, Kraige & Bolton — Statics of Particles: Problem 2_139

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/139 The pulley and gear are subjected to the loads shown. For these forces, determine the equivalent force–couple system at point O. Problem 2/139 1. Analysis of Force Vectors and Positions First, we define the position vectors for the points of application of each force and express the forces in vector notation using the given coordinate system. Origin: Point is at . Gear Force (): Magnitude: Angle: from the vertical (-axis), pointing downward and toward the positive - direction (to the left in the diagram). Vector form: Application point: Located on the gear at a distance from and at the right side of the gear (radius in the direction). Position vector: Pulley Forces (): Both forces are horizontal and point to the right (negative -direction). Upper belt tension: at . Position . Force . Lower belt tension: at . Position . Force . 2. Determine the Resultant Force ● Calculation Process 1. Present Final Formula: x−y−z O(0,0,0) F G F = G 1200 N 10 ∘ yz F = G −1200cos10j+ ∘ 1200sin10k ∘ x=220 mmO 75 mm−z r = G 0.220i−0.075k m F ,F P1P2 z F = P1 800 Ny=+100 mmr = P1 0.330i+0.100j mF = P1 −800k N F = P2 200 Ny=−100 mmr = P2 0.330i−0.100j mF = P2 −200k N R R=F=∑F + G F + P1 F P2 2. Substitute Values: 3. Partial Operations: 4. Final Calculation: ● Final Conclusion: The resultant force is . 3. Determine the Resultant Moment about Point O ● Calculation Process 1. Present Final Formula: 2. Substitute Values: 3. Partial Operations: 4. Final