Meriam, Kraige & Bolton — Statics of Particles: Problem 2_89

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/89 Express **F** as a vector in terms of the unit vectors **i**, **j**, and **k**. Determine the angle between **F** and the **y**-axis. Given Data: Magnitude of force: Dimensions of the bounding box: , , and . Coordinates of the origin . The force vector **F** starts at the origin . Problem 2/89 (a) Express F as a vector in terms of unit vectors i, j, and k ● Calculation Process 1. Identify the coordinates of the head of the vector: Based on the provided coordinate system, the positive -axis points towards the lower-left, the positive -axis points to the right, and the positive -axis points upwards. The force vector points from the origin to a corner point (let's call it ) at the "back-left" of the structure. Displacement along the -axis: The segment is long and points in the opposite direction of the positive -axis. Thus, . Displacement along the -axis: The segment is long and points in the opposite direction of the positive -axis. Thus, . Displacement along the -axis: The segment is long and points upwards in the positive direction. Thus, . The position vector from to is: 2. Calculate the distance from to : F=60 N 50 mm40 mm110 mm O(0,0,0) O xy zF OA x50 mm xΔx=−50 mm y40 mm yΔy=−40 mm z110 mm zΔz=110 mm OA r = OA −50i−40j+110k mm dOA d= (Δx)+(Δy)+(Δz) 222 3. Determine the force vector F: The force vector is the product of its magnitude and the unit vector in its direction: Calculate individual components: ● Final Conclusion: