Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_101

⚡ Mecademy AIENG정역학 · ch6  Problem Statement Determine the range of mass for which the system is in equilibrium. The coefficient of static friction between the block and the incline is and that between the cord and the fixed disk on the block is . Problem 6/101 (a) Analysis of Geometric Parameters 1. Formula: The wrap angle of the cord around the fixed disk is the difference between the angular directions of the two cord segments. Let be the incline angle. 2. Substitution: Direction of cord segment to fixed support: (from disk towards top-right support) Direction of cord segment to mass : (vertically downward) 3. Calculation: Convert to radians for belt friction equations: Calculate the belt friction factor : 4. Result: and . ● Final Conclusion: The wrap angle is , giving a tension ratio factor of approximately . (b) Equilibrium for Maximum mass (Impending motion UP) m 2 μ = 1 0.25 μ = 2 0.15 β θ=20 ∘ 180+ ∘ 20= ∘ 200 ∘ m 2 270 ∘ β=270− ∘ 200= ∘ 70 ∘ β=70× ∘ ≈ 180 ∘ π 1.2217 rad K=e μ β 2 K=e≈ 0.15×1.2217 1.2011 1/K=e≈ −0.15×1.2217 0.8326 β=1.2217 rade= μ β 2 1.2011 70 ∘ 1.2011 m 2 1. Formula: Sum of forces parallel to the incline (-axis, positive up) and perpendicular to the incline (-axis). For impending motion towards , , so . 2. Substitution: Substitute : 3. Calculation: 4. Result: ● Final Conclusion: The maximum mass to prevent upward slipping is . (c) Equilibrium for Minimum mass (Impending motion DOWN) 1. Formula: For impending motion down the incline, friction acts u