Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_5

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The 180-lb exerciser is repeated from Prob. 3/21. The tension is developed against an exercise machine (not shown) as he is about to begin a biceps curl. Determine the minimum coefficient of static friction which must exist between his shoes and the floor if he is not to slip. Problem 6/5 (a) Determination of the minimum coefficient of static friction 1. Formula: To prevent slipping, the required friction force must not exceed the maximum static friction . The minimum coefficient of static friction is found at the impending slip condition: From the equilibrium of the exerciser treated as a single body: Horizontal equilibrium: Vertical equilibrium: 2. Substitution: Given and : 3. Calculation: Calculate the numerical values for the total friction and normal forces: 4. Result: T=15 lb F F= max μ N s μ = s N F F =∑ x 0⟹F=Tcos20 ∘ F =∑ y 0⟹N=W−Tsin20 ∘ W=180 lbT=15 lb F=15cos20 ∘ N=180−15sin20 ∘ F=15×0.93969=14.095 lb Tsin20= ∘ 15×0.34202=5.130 lb N=180−5.130=174.87 lb μ= s = 174.87 14.095 0.080605 μ ≈ s 0.0806 ● Final Conclusion: The minimum coefficient of static friction required between the exerciser's shoes and the floor to prevent slipping is . ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 6/5 μ = s 0.0806 μ = s 0.0806