Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_28

⚡ Mecademy AIENG정역학 · ch6  Problem Statement Determine the magnitude of the horizontal force required to initiate motion of the block of mass for the cases (a) is applied to the right and (b) is applied to the left. Complete a general solution in each case, and then evaluate your expression for the values . Problem 6/28 (a) Magnitude of when applied to the right ● Calculation Process 1. Present Final Formula: To initiate motion to the right, the block must overcome friction from both the horizontal floor and the bar at contact point . From the equilibrium of the bar (pivoted at ): At impending slip, , leading to: From the horizontal and vertical equilibrium of the block : Substituting gives the general solution: 2. Substitute Values: Using , , , , and : P m 0 PP θ= 30,m= ∘ m = 0 3 kg,μ = s 0.60, and μ = k 0.50 P A ABB M = ∑ B 0⟹ mgLcos θ + 2 1 f Lsinθ− A N Lcosθ= A 0 f = A μN sA N = A 2(1−μ tanθ) s mg m 0 F = ∑ y 0⟹N = f m g+ 0 N A F = ∑ x 0⟹P=f + f f = A μ N + sf μ N = sA μ (m g+ s0 2N ) A N A P=μ gm + s ( 0 1−μ tanθ s m ) θ=30 ∘ m=3 kgm = 0 3 kgμ = s 0.60 g= 9.81 m/s 2 P= (0.60)(9.81) 3+ [ 1−0.60tan(30) ∘ 3 ] 3. Partial Operations: 4. Final Calculation: \[P = 5.886 \left( 3 + \frac{3}{0.6536} \right) = 5.886(3 + 4.590) = 5.886(7.590) \approx 44.67 \text{ N}\) ● Final Conclusion: The magnitude of the horizontal force required to initiate motion to the right is . (b) Magnitude of when applied to the left ● Calculation Process 1. Present Final Formula: When the block is pulle