Meriam, Kraige & Bolton — Statics of Particles: Problem 2_128

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/128 The special-purpose milling cutter is subjected to the force of 1200 N and a couple of 240 N · m as shown. Determine the moment of this system about point O. Problem 2/128 1. Coordinate System and Position Vector Analysis First, we define a right-handed Cartesian coordinate system based on the axes labeled at point . The -axis is vertical (pointing up), the -axis is horizontal (pointing into the page to the right), and the -axis is horizontal (pointing into the page to the left). In this frame, the unit vectors are , , and respectively. From the diagram, we can determine the position vector from the origin to the point of application of the force at the center of the milling cutter: The shaft first extends along the -axis by a distance of . It then bends and extends parallel to the -axis by a distance of . Assuming the shaft lies in the horizontal plane (since no vertical offset is indicated for the shaft itself), the position vector is: 2. Force Vector Analysis The force has a magnitude of . It is applied in a plane parallel to the plane. The diagram shows the force makes an angle of with the vertical direction (the negative -axis). The force points downwards and "forward" (in the direction of the positive -axis). We can resolve the force into its components: (The force is in the plane) Oyx z ijk rO z200 mm=0.2 m x250 mm=0.25 m x−z r=0.25i+0.2k m F1200 Ny−z 60 ∘ y z F = x 0y−z F = y −1200cos60= ∘ −1200(0.5)=−600 N F = z 120