Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_9

⚡ Mecademy AIENG정역학 · ch6  Problem Statement Determine the coefficient of kinetic friction which allows the homogeneous body to move down the incline at constant speed. Show that this constant-speed motion is unlikely to occur if the ideal roller and small foot were reversed. Problem 6/9 (a) Determination of the coefficient of kinetic friction ● Calculation Process 1. Present Final Formula: We consider the square block in dynamic equilibrium since it moves at a constant speed. Let be the weight of the block, the normal reaction at the ideal roller , and the normal and frictional reactions at the foot . Taking coordinates down the incline and normal to the incline, the equilibrium equations are: From these, we derive: 2. Substitute Values: Substitute : 3. Partial Operations: Using and : μ k 30 ∘ μ k WN A AN ,F BB Bxy F = ∑ x 0⟹Wsinθ−F = B 0 F = ∑ y 0⟹N + A N − B Wcosθ=0 M = ∑ A 0⟹N (b)− B W cos θ − ( 2 b )W sin θ = ( 2 b )0 μ = k = N B F B cosθ+sinθ 2sinθ θ=30 ∘ μ = k cos30+sin30 ∘∘ 2sin30 ∘ sin30= ∘ 0.5cos30= ∘ ≈ 2 3 0.8660 μ = k = 0.8660+0.5 2(0.5) 1.3660 1 4. Final Calculation: ● Final Conclusion: The coefficient of kinetic friction required is . (b) Analysis of the reversed configuration ● Calculation Process 1. Present Final Formula: If the roller and foot are reversed, the foot with friction is now at (trailing edge) and the roller is at (leading edge). The moment equation about the new roller position is: This gives the normal force at the friction point : The required