Meriam, Kraige & Bolton — Statics of Particles: Problem 2_115

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/115 The two forces acting on the handles of the pipe wrenches constitute a couple M. Express the couple as a vector. Given Data from the Figure: Force magnitude: Wrench handle length (from pipe center to force application): Offset distance along the pipe axis: Problem 2/115 1. Define the Coordinate System and Force Vectors We establish a right-handed Cartesian coordinate system as shown in the diagram: The -axis is horizontal and perpendicular to the pipe. The -axis lies along the centerline of the pipe. The -axis is vertical. Based on the visual arrows, the force on the left wrench points vertically upward ( direction), and the force on the right wrench points vertically downward ( direction). The two forces form a couple because they are equal in magnitude, opposite in direction, and act along parallel lines. Left Force: Right Force: 2. Identify Position Vectors Let the origin be at the intersection of the pipe centerline and the plane of the left wrench. The coordinates for the application points of the forces are: For : Point 1 is at , , . F=150 N d = x 250 mm=0.25 m d = y 150 mm=0.15 m x y z +z −z F = 1 150k N F = 2 −150k N O F 1 x=−250 mmy=0z=0 r = 1 −0.25i m For : Point 2 is at , , . The vector from the application point of to the application point of is: 3. Calculate the Couple Moment Vector The moment of a couple is a free vector calculated by the cross product of the position vector between the forces and the force vec