Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_88

⚡ Mecademy AIENG정역학 · ch4  Problem Statement A 250-N force is applied to the foot-operated air pump. The return spring exerts a moment on member for this position. Determine the corresponding compression force in the cylinder . If the diameter of the piston in the cylinder is , estimate the air pressure generated for these conditions. State any assumptions. Problem 4/88 (a) Compression force C in the cylinder BD 1. Formula: To find the compression force , we analyze the equilibrium of the pedal member by summing moments about the pivot point : where: is the moment from the return spring. is the moment from the applied foot force. is the moment from the compression force in the cylinder. 2. Substitution: First, establish the geometry relative to in millimeters (mm): Point : , Point : , Point : , (assuming and are at the same horizontal level) Next, determine the components and moments of the forces: Applied Force : at to the vertical (tilted to the right). S3-N⋅m OBA CBD45 mm C OBAO M = ∑ O M + S M + F A M = C 0 M S M F A 250-N M C O(0,0) Bx = B 25 mmy = B 85 mm Ax = A 25+125=150 mmy = A 85+100=185 mm Dx = D 225 mmy = D 0 mmOD F A 250 N15 ∘ F = Ax 250sin15≈ ∘ 64.70 N F = Ay −250cos15≈ ∘ −241.48 N M = F A x F − AAy y F = AAx (150)(−241.48)−(185)(64.70) Spring Moment : Return spring opposes depression, so it acts counter- clockwise (CCW). Cylinder Force : Acts along the line . 3. Calculation: (Clockwise) (Counter-clockwise) Summing moments: 4. Result: ● Final Conclusion: The co