Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_1

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The 85-lb force is applied to the 200-lb crate, which is stationary before the force is applied. Determine the magnitude and direction of the friction force exerted by the horizontal surface on the crate. Problem 6/1 (a) Magnitude and Direction of the Friction Force 1. Formula: First, determine the normal force from vertical equilibrium: Then, calculate the maximum possible static friction force : Finally, compare the applied force with to determine if motion occurs. 2. Substitution: Given values: , , . Normal force: Maximum static friction: 3. Calculation: Calculate maximum static friction: Check for motion: Since the applied force is less than the maximum static friction force (), the crate does not slip and remains stationary. Determine actual friction force: From horizontal equilibrium : 4. Result: directed to the left. P F N F = ∑ y 0⟹N−W=0 F s,max F = s,max μ N s PF s,max W=200 lbP=85 lbμ = s 0.50 N=200 lb F = s,max 0.50×200 lb F = s,max 100 lb P=85 lb 85 lb<100 lb F =∑ x 0 P−F=0⟹F=P=85 lb F=85 lb ● Final Conclusion: Since the applied force of is less than the maximum static friction capacity of , the crate remains at rest. The static friction force required to maintain equilibrium is exactly equal to the applied force, which is to the left. ✨ Final Answer Summary (a) to the left Mecademy AI Solution · ENGProblem 6/1 85 lb 100 lb 85 lb F=85 lb