Meriam, Kraige & Bolton — Statics of Particles: Problem 2_146

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/146 Replace the two forces acting on the pole by a wrench. Write the moment M associated with the wrench as a vector and specify the coordinates of the point P in the y-z plane through which the line of action of the wrench passes. Problem 2/146 1. Identify Force Vectors and Application Points From the diagram, we observe two forces of magnitude acting at different heights on the pole. The pole is aligned with the -axis, and the origin is at its base. Based on the geometric labels and orientation: Lower Force (): Applied at height . There is a dashed line of length parallel to the -axis. The force acts at the end of this dashed line, in the positive - direction. Application point: Force vector: Upper Force (): Applied at height . There is a dashed line of length parallel to the -axis. The force acts at the end of this dashed line, in the positive -direction. Application point: Force vector: 2. Calculate Resultant Force () and Total Moment about () ● Resultant Force: The magnitude is . The unit vector in the direction of the resultant is: T zO F 1 z=3aa yx r = 1 0i+aj+3ak F = 1 Ti F 2 z=3a+a=4a ax y r = 2 ai+0j+4ak F = 2 Tj ROM O R=F + 1 F = 2 Ti+Tj R= = T+T 22 T 2 u = R = R R i+ 2 1 j 2 1 ● Total Moment about the origin : Summing these moments: 3. Determine the Wrench Moment Vector () The moment associated with the wrench is the component of parallel to . Expressing the wrench moment as a vector: 4. Locate Point in the Plane The