Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_31

⚡ Mecademy AIENG정역학 · ch6  Problem Statement Determine the distance s to which the 90-kg painter can climb without causing the 4-m ladder to slip at its lower end A. The top of the 15-kg ladder has a small roller, and at the ground the coefficient of static friction is 0.25. The mass center of the painter is directly above her feet. Problem 6/31 (a) Determination of the distance ● Calculation Process 1. Present Final Formula: First, we determine the geometry of the ladder. Let be the angle between the ladder and the horizontal. From the diagram, the base is and the length is : The height of point is . From vertical equilibrium: At impending slip, the friction force at is: From horizontal equilibrium: Finally, we use the moment equilibrium equation about point : 2. Substitute Values: Given: , , , , base distance . s θ 1.5 m 4 m cosθ= 4 1.5 Bh=Lsinθ= L−1.5 22 F = ∑ y 0⇒N − A m g− L m g= p 0⇒N = A (m + L m )g p A f = A μ N = sA μ (m + sL m )g p F = ∑ x 0⇒f − A N = B 0⇒N = B f = A μ (m + sL m )g p A M = ∑ A 0⇒N (Lsinθ)− B ( m g )( cos θ )− L 2 L (m g)(scosθ)= p 0 m = p 90 kgm = L 15 kgL=4 mμ = s 0.25 =1.5 m cosθ= = 4 1.5 0.375 Substituting these into the moment equation: 3. Partial Operations: Divide the entire equation by : 4. Final Calculation: ● Final Conclusion: The maximum distance the painter can climb along the ladder without causing it to slip is approximately . ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 6/31 Lsinθ= = 4−1.5 22 ≈ 13.753.7081 m N = A (15+