Meriam, Kraige & Bolton — Statics of Particles: Problem 2_153

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/153 The control lever is subjected to a clockwise couple of 80 N·m exerted by its shaft at A and is designed to operate with a 200-N pull as shown. If the resultant of the couple and the force passes through A, determine the proper dimension x of the lever. Problem 2/153 ● Solution Strategy and Principles A system of forces and couples can be reduced to a single resultant force acting at a specific location. For the line of action of the resultant force to pass through a specific point (in this case, point ), the total moment of all original forces and couples about that point must be zero. The system consists of: An applied clockwise (CW) couple: . In standard coordinate systems, clockwise moments are negative: . A pull force . From the diagram, this force is horizontal and directed to the left. The condition that the resultant passes through implies: where is the moment of force about point . ● Calculation of Moment of Force P 1. Identify the Moment Arm: Since the force is horizontal, its moment arm about point is the vertical distance from to the line of action of . 2. Geometric Relations: The total length of the lever from the pivot to the point where is applied is . A M = c 80 N⋅m M = couple −80 N⋅m P=200 N A M = ∑ A 0 M + P/A M = couple 0 M P/A PA P AhAP AP L=x+150 mm The lever is oriented at an angle of with respect to the vertical axis. The vertical height is given by: . 3. Express the Moment: Since the force pulls to th