Meriam, Kraige & Bolton — Statics of Particles: Problem 2_65

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/65 The system consisting of the bar OA, two identical pulleys, and a section of thin tape is subjected to the two 180-N tensile forces shown in the figure. Determine the equivalent force– couple system at point O. Problem 2/65 ● 1. Analysis of Forces and Geometry The system consists of a bar of length at an angle of with the horizontal. Two identical pulleys of radius are centered at points and . Point is the origin . Force 1 (): A force acting horizontally to the left, tangent to the top of the upper pulley at . Vector form: Line of action height: Force 2 (): A force acting horizontally to the right, tangent to the bottom of the lower pulley at . Vector form: Line of action height: ● 2. Calculate the Resultant Force The resultant force is the vector sum of all external forces acting on the system: 1. Formula: 2. Substitution: OAL=100 mm45 ∘ r=25 mmOA O(0,0) F 1 180-N A F = 1 −180i N y = 1 Lsin45+ ∘ r=100sin45+ ∘ 25≈70.71+ 25=95.71 mm F 2 180-N O F = 2 180i N y = 2 −r=−25 mm R R= F= ∑F + 1 F 2 R=(−180i)+(180i) 3. Final Calculation: Since the resultant force is zero, the given force system is a couple. ● 3. Calculate the Resultant Moment at point O The moment of the couple is the same about any point. Calculating it about : 1. Formula: Since the forces are horizontal (), the moment is simply . 2. Substitution: Moment due to : (Counter-clockwise) Moment due to : (Counter-clockwise) 3. Partial Operations: 4. Final Calculation (conv