Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_9

⚡ Mecademy AIENG정역학 · ch3  Problem Statement The 20-kg uniform rectangular plate is supported by an ideal pivot at O and a spring which must be compressed prior to being slipped into place at point A. If the modulus of the spring is k = 2 kN/m, what must be its undeformed length L? Problem 3/9 (a) Determination of the Undeformed Spring Length 1. Formula: For static equilibrium of the plate, the sum of moments about the pivot must be zero: The weight of the uniform plate acts at its center of mass . The spring force acts vertically upward at point . 2. Substitution: First, we determine the weights and moment arms. Mass of plate , so weight . Total width of the plate . The center of mass is at the geometric center, from the left edge. Moment arm for from : (to the right of ). Moment arm for spring force from : (to the right of ). The moment equation (taking clockwise as positive) is: 3. Calculation: Solve for the spring force : L O M = ∑ O 0 GF s A m=20 kgW=m⋅g=20⋅9.81=196.2 N w=0.12+0.48=0.60 m G0.60/2=0.30 m WOd = W 0.30−0.12=0.18 m O F s Od = A 0.48−0.15=0.33 m O W⋅d − W F ⋅ s d = A 0 196.2⋅0.18−F ⋅ s 0.33=0 F s 35.316−0.33F = s 0 Now, use the spring force-deformation relation , where the current compressed length is and : 4. Result: or ● Final Conclusion: The undeformed length of the spring must be to maintain the plate in equilibrium in the shown position. ✨ Final Answer Summary (a) (or ) Mecademy AI Solution · ENGProblem 3/9 F = s ≈ 0.33 35.316 107.018 N F = s k⋅(L−L ) c