Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_17

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The 80-kg man with center of mass G supports the 34-kg drum as shown. Find the greatest distance x at which the man can position himself without slipping if the coefficient of static friction between his shoes and the ground is 0.40. Problem 6/17 (a) Greatest distance x without slipping ● Calculation Process 1. Formula: First, identify the forces acting on the man and the drum. For the drum to be in equilibrium, the tension in the cable must equal its weight. For the man, the equilibrium equations in the horizontal and vertical directions are: The slipping condition is defined by the relation: Substituting the force expressions, the impending slip occurs when: 2. Substitution: From the given data: Mass of man, Weight of man, Mass of drum, Tension in cable, Coefficient of static friction, Height of pulley, Height of hands (assumed at level G), T F = ∑ y 0⟹N+Tsinθ−W = m 0⟹N=W − m Tsinθ F = ∑ x 0⟹F−Tcosθ=0⟹F=Tcosθ F≤μ N s Tcosθ=μ (W − sm Tsinθ) m = m 80kg W = m 80×9.81=784.8N m = d 34kg T=34×9.81=333.54N μ = s 0.40 h = p 5m h = g 1m Based on geometry: Substituting into the slipping condition: 3. Calculation: Rearranging to solve for : Divide by 313.92: Square both sides: Using the quadratic formula : 4. Result: ● Final Conclusion: The greatest distance at which the man can position himself without slipping is . ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 6/17 sinθ= = x+(h −h ) 2 pg 2 h −h pg x+16 2 4 cosθ= x+16 2 x 3