Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_26

⚡ Mecademy AIENG정역학 · ch6  Problem Statement What force must the two men exert on the rope to slide the uniform 20-ft plank on the overhead rack? The plank weighs 200 lb, and the coefficient of kinetic friction between the plank and each support is 0.50. Problem 6/26 (a) Determination of the required force to slide the plank 1. Formula: To slide the plank, the horizontal component of the pulling force must overcome the total kinetic friction force from both supports. Combining these equations: Rearranging for : 2. Substitution: Given values: Weight of the plank, Coefficient of kinetic friction, Angle of the rope, 3. Calculation: Numerator: Denominator: P P F = ∑ y 0⟹N + A N − B W−Psinθ=0⟹N + A N = B W+ F = ∑ x 0⟹Pcosθ−f − A f = B 0⟹Pcosθ=μ (N + kA N ) B Pcosθ=μ (W+ k Psinθ) P P= cosθ−μ sinθ k μ W k W=200 lb μ = k 0.50 θ=30 ∘ P= cos30−0.50sin30 ∘∘ 0.50×200 0.50×200=100 lb cos30− ∘ 0.50sin30= ∘ 0.8660−0.50×0.50= 0.8660−0.25=0.6160 Final calculation: 4. Result: ● Final Conclusion: The total force that the two men must exert on the rope to slide the plank is . This force is sufficient to overcome the kinetic friction at both supports while the plank remains in contact with the rack. ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 6/26 P= ≈ 0.6160 100 162.33 lb P≈162.3 lb P 162.3 lb P=162.3 lb