Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_11

⚡ Mecademy AIENG정역학 · ch6  Problem Statement Determine the magnitude and direction of the friction force which the vertical wall exerts on the 100-lb block if (a) and (b) . Problem 6/11 (a) Friction force for 1. Formula: To determine the state of the block, we first find the normal force and the net vertical force excluding friction. We compare the required friction force for equilibrium, , with the maximum static friction force, . 2. Substitution: Given , , , , and : 3. Calculation: Calculate Normal Force: Calculate Maximum Static Friction: Calculate Net Downward Force (excluding friction): Check for slipping: Since , the block slips downward. Calculate Kinetic Friction: 4. Result: The magnitude is . Since the block slides downward, the friction θ=15 ∘ θ=30 ∘ θ=15 ∘ N F net,y N=Pcosθ F = net,y W−Psinθ(positive downward) F = req ∣F ∣ net,y F = max μ N s P=120 lbW=100 lbμ = s 0.50μ = k 0.40 θ=15 ∘ N=120cos15 ∘ F = req 100−120sin15 ∘ F = max 0.50×N N=120×0.9659=115.91 lb F = max 0.50×115.91=57.96 lb F = req 100−120× 0.2588=100−31.06=68.94 lb F = req 68.94 lb>F = max 57.96 lb F=μ N= k 0.40×115.91=46.36 lb 46.4 lb force from the wall acts upward. ● Final Conclusion: The friction force is acting upward. (b) Friction force for 1. Formula: Similar to part (a), we find the normal force and compare the required equilibrium friction with the static limit. 2. Substitution: Given : 3. Calculation: Calculate Normal Force: Calculate Maximum Static Friction: Calculate Net Downward Force (e