Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_24

⚡ Mecademy AIENG정역학 · ch6  Problem Statement Determine the horizontal force required to cause slippage to occur. The friction coefficients for the three pairs of mating surfaces are indicated. The top block is free to move vertically. Problem 6/24 (a) Determination of the required horizontal force 1. Formula: First, identify the blocks and interfaces. Let Block 1 be the top (), Block 2 be the middle (), and Block 3 be the bottom (). Calculate the normal forces at each interface: Then calculate the maximum static friction forces at each interface using . The required force to cause slippage will be the minimum of: - Case 1: Blocks 2 and 3 move together as a unit relative to Block 1 and the ground. - Case 2: Block 2 slips relative to both Blocks 1 and 3. 2. Substitution: Using : Maximum friction forces: P P 100 kg 50 kg20 kg N N = 1 m g 1 N = 2 (m + 1 m )g 2 N = 3 (m + 1 m + 2 m )g 3 F max F = i μ N ii P P = 1 F + 1,max F 3,max P = 2 F + 1,max F 2,max g= 9.81 m/s 2 N = 1 100⋅9.81=981 N N = 2 (100+50)⋅9.81=150⋅9.81=1471.5 N N = 3 (100+50+20)⋅9.81=170⋅9.81=1667.7 N F = 1,max 0.60⋅981=588.6 N F = 2,max 0.40⋅1471.5=588.6 N F = 3,max 0.30⋅1667.7=500.31 N 3. Calculation: Evaluate the two possible slippage scenarios: Case 1 (Blocks 2 and 3 move together): Check if slippage occurs between Blocks 2 and 3 in this case. The friction force needed to move Block 3 is equal to the ground friction . Since , Blocks 2 and 3 will indeed move together without slipping relative to each other. Case