Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_29

⚡ Mecademy AIENG정역학 · ch6  Problem Statement A clockwise couple M is applied to the circular cylinder as shown. Determine the value of M required to initiate motion for the conditions , , , , and . Friction between the cylinder C and the block B is negligible. Problem 6/29 (a) Determination of the couple M required to initiate motion 1. Formula: First, calculate the normal forces acting on both the cylinder and block , then determine the maximum static friction force each surface can provide. Use equilibrium equations to relate the applied couple to these friction forces. 2. Substitution: Calculate the weights (normal forces) using : Calculate the maximum static friction forces: 3. Calculation: Draw a free-body diagram (FBD) for each body to relate the horizontal forces. Let be the horizontal contact force between cylinder and block . For block : (where is the ground friction on ). For cylinder : (where is the ground friction on ). m = B 3 kgm = C 6 kg(μ ) = sB 0.50 (μ ) = sC 0.40r=0.2 m C B M W=mg,N=W,F = max μ N s F = ∑ x 0, M = ∑ O 0 g= 9.81 m/s 2 N = C W = C 6 kg× 9.81 m/s= 2 58.86 N N = B W = B 3 kg× 9.81 m/s= 2 29.43 N (F ) = Cmax (μ ) N = sCC 0.40×58.86 N=23.544 N (F ) = Bmax (μ ) N = sBB 0.50×29.43 N=14.715 N PCB BF =∑ x 0⟹P−F = B 0⟹F = B PF B B CF =∑ x 0⟹F − C P=0⟹F = C P F C C For cylinder : . Combining these relations, we have . Motion will be initiated when the required friction force reaches the smaller of the two static limits: Since block has the lower frictio