Meriam, Kraige & Bolton — Statics of Particles: Problem 2_134

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/134 An oil tanker moves away from its docked position under the action of reverse thrust from screw A, forward thrust from screw B, and side thrust from the bow thruster C. Determine the equivalent force–couple system at the mass center G. Problem 2/134 1. Define the Coordinate System and Identify Force Vectors We establish a right-handed coordinate system with the origin at the mass center . According to the diagram: The x-axis is longitudinal, with the positive direction pointing toward the bow. The y-axis is lateral, with the positive direction pointing toward the starboard (right) side. The z-axis is vertical, with the positive direction pointing upward. Based on the problem description and diagram, the force vectors are: Screw A (Reverse thrust): Screw B (Forward thrust): Bow thruster C (Side thrust): 2. Calculate the Resultant Force The resultant force is the vector sum of all applied forces: 3. Identify Position Vectors for Each Force G F = A −50i kN F = B 50i kN F = C 8j kN R R= F= ∑F + A F + B F C R=(−50i)+(50i)+(8j) R=8j kN From the dimensions provided in the figure, we determine the position vectors relative to the mass center : Screw A: Located aft, to the port (left), and below . Screw B: Located aft, to the starboard (right), and below . Bow Thruster C: Located forward on the centerline and below . 4. Calculate the Resultant Moment about Mass Center G The resultant couple (moment) is the sum of the moments of each