Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_22

⚡ Mecademy AIENG정역학 · ch3  Problem Statement The force on the handle of the positioning lever produces a vertical compression of in the coiled spring in the position shown. Determine the corresponding force exerted by the pin at on the lever. Problem 3/22 (a) Determination of the force exerted by the pin at ● Calculation Process 1. Present Final Formula: First, we determine the applied force using the moment equilibrium equation about the pivot . Then, we use the force equilibrium equations to find the reaction components at . 2. Substitute Values: From the diagram, the vertical distance from to the line of action of is , and the horizontal distance from to the line of action of the spring force is . The spring is in compression, exerting an upward force of on the lever at point . Taking counter-clockwise moments as positive about : 3. Partial Operations: Solve for : Now, determine the components of the reaction force at pin . Let be positive to P60 lb O O P O O M = ∑ O 0 F = ∑ x 0, F = ∑ y 0 R = O O +O x 2 y 2 O Pd = P 8 in.O d = s 3.20 in. F = s 60 lbA O P(8)−F (3.20)= s 0 P(8)−60(3.20)=0 P 8P=192⇒P= = 8 192 24 lb OO x the right and be positive upward. Sum of forces in the x-direction: Sum of forces in the y-direction: The magnitude of the resultant force at is: 4. Final Calculation: The direction of the force measured clockwise from the positive x-axis is: ● Final Conclusion: The force exerted by the pin at on the lever has a magnitude of and is directed downward and to t