Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_46

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The 10° wedge is driven under the spring-loaded wheel whose supporting strut C is fixed. Determine the minimum coefficient of static friction for which the wedge will remain in place. Neglect all friction associated with the wheel. Problem 6/46 (a) Minimum coefficient of static friction ● Calculation Process 1. Present Final Formula: For the wedge to remain in place against the tendency to "pop out" due to the vertical load, the friction force at its base must balance the horizontal component of the normal force from the wheel. Since friction at the wheel is neglected, the only friction is at the wedge-ground interface. 2. Substitute Values: Substitute the given wedge angle . 3. Partial Operations: Consider the free-body diagram of the wedge. Let be the normal force from the wheel (acting at to the vertical) and be the normal force from the ground. Sum of vertical forces: Sum of horizontal forces: , where is the friction force from the ground. Impending slip condition: 4. Final Calculation: Substitute the expressions for and into the slip condition: μ s μ s μ = s tanθ θ=10 ∘ μ = s tan10 ∘ N 1 10 ∘ N 2 F =∑ y N − 2 N cos10= 1 ∘ 0⟹N = 2 N cos10 1 ∘ F =∑ x N sin10− 1 ∘ F = f 0⟹F = f N sin10 1 ∘ F f F = f μ N s2 F f N 2 N sin10= 1 ∘ μ (N cos10) s1 ∘ ● Final Conclusion: The minimum coefficient of static friction required for the wedge to remain in place is . ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 6/46 μ = s = cos1