Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_90

⚡ Mecademy AIENG정역학 · ch4  Problem Statement The 80-kg ventilation door with mass center at is held in the open position shown by means of a moment applied at to the opening linkage. Member is parallel to the door for the 30° position shown. Determine . Problem 4/90 (a) Determination of the required moment M ● Calculation Process 1. Weight Calculation: The weight of the door acts at its mass center . Substituting the given values: 2. Moment of Weight about Pivot O: The door is inclined at 30° to the vertical. The horizontal distance from the pivot to the mass center is . 3. Linkage Geometry and Equilibrium Analysis: Let be the unit vector along the door . Since is parallel to , its position vector is . The points and are defined by and . The linkage is a two-force member. The force exerted on the door at is along the line . The vector . The moment produced by the linkage on the door about must balance the weight moment: ODG MAAB M G W=m⋅g W=80 kg× 9.81 m/s= 2 784.8 N OD OGx = G 0.8sin30 ∘ M = W W⋅(0.8sin30) ∘ M = W 784.8 N⋅0.4 m=313.92 N⋅m (Clockwise) u = d sin30i− ∘ cos30j ∘ ODABOD =r AB 0.9u d CA =r OC 0.4u d =r A −0.6iBCF BC CBC = BC −r C =r B −r C ( +r A )=r AB 0.4u − d (−0.6i+0.9u )= d −0.5u + d 0.6i O = M O,link ×r OC F = BC (0.4u )× d ( T )= L BC BC (0.4 u × L BC T d (−0.5u + d The moment produced by the linkage on member about is: Comparing the two moments: Since must equal for equilibrium, the magnitude of the moment applied at to balance the linkage force is: ● Fin