Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_51

⚡ Mecademy AIENG정역학 · ch6  Problem Statement Determine the torque which must be applied to the handle of the screw to begin moving the 100-lb block up the 15° incline. The coefficient of static friction between the block and the incline is 0.50, and the single-thread screw has square threads with a mean diameter of 1 in. and advances 0.4 in. for each complete turn. The coefficient of static friction for the threads is also 0.50. Neglect friction at the small ball joint . Problem 6/51 (a) Torque required to move the block up the incline 1. Formula: First, find the axial force required to push the block up the incline. From equilibrium: Then, find the torque required for a square-threaded screw to provide this axial force: where the lead angle is given by . 2. Substitution: Weight Incline angle Block friction coefficient Screw mean diameter Screw lead Screw thread friction coefficient Calculate axial force : M A P P=W(sinθ+μ cosθ) s M M=P tan( α + 2 d φ)=P 2 d ( 1−μ tanα s ′ tanα+μ s ′ ) αtanα= πd L W=100 lb θ=15 ∘ μ = s 0.50 d=1 in. L=0.4 in. μ = s ′ 0.50 P P=100(sin15+ ∘ 0.50cos15) ∘ Calculate : Substitute into the torque formula: 3. Calculation: Numerator of the fraction: Denominator of the fraction: 4. Result: ● Final Conclusion: The torque required to begin moving the block up the incline is ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 6/51 tanα tanα= π(1) 0.4 M=P ( 2 1 ) 1−0.50 ( π 0.4 ) +0.50( π 0.4 ) P=100(0.258819+0.50×0.965926)=100(0.258819+ 0.482963)