Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_89

⚡ Mecademy AIENG정역학 · ch4  Problem Statement Compute the force in link of the lifting tongs, which cross without touching. Problem 4/89 (a) Analysis of the link force ● Calculation Process 1. Establish Coordinate System and Geometry: Let the origin be at the top pivot point on the vertical axis of symmetry. Based on the dimensions provided in the diagram: Points and are 12" below and 18" from the centerline: and . The gripping points and are at the bottom. The total vertical distance from is ". The grip width is 30", so they are 15" from the centerline: and . The tongs cross without touching, forming two main arms: and . Link is horizontal and located 20" below the line , at ". Find the position of pin on arm . The equation of line is: At , the x-coordinate of is: ". Thus, . By symmetry, . 2. Free-Body Diagram of Arm : Consider the equilibrium of arm . The total load is 800 lb, so each side supports 400 lb vertically. AB AB (0,0)E CDEC= (−18,−12)D=(18,−12) FG E12+20+24=56 F=(−15,−56)G=(15,−56) ACGBDF ABCDy=−12− 20=−32 AACGCG y−(−12)= (x− 15−(−18) −56−(−12) (−18))⟹y+12= − (x+ 33 44 18) y= − x− 3 4 24−12= − x− 3 4 36 y=−32A−32=− x− 3 4 36⟹ x= 3 4 −4⟹x = A −3A=(−3,−32)B=(3,−32) ACG ACG At : Reaction forces from link . Since link is a two-force member, the force acts along the line with slope . At : Forces from the load. At : Horizontal force from link . Assume tension (force to the right on arm ). 3. Moment Equilibrium Equation: Sum of moments about point to eliminate the unkno