Meriam, Kraige & Bolton — Statics of Particles: Problem 2_92

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/92 The force F has a magnitude of 300 lb and acts along the diagonal of the parallelepiped as shown. Express F in terms of its magnitude times the appropriate unit vector and determine its x-, y-, and z-components. Problem 2/92 1. Identify the Coordinates of the Start and End Points From the diagram, the force vector acts along a diagonal of the parallelepiped. Let point be the tail of the vector and point be the head of the vector. Point is located on the -axis at a height of 8 ft. Thus, its coordinates are ft. Point is located on the - plane. Its projection on the -axis is at 4 ft, and its projection on the -axis is at 8 ft. Thus, its coordinates are ft. 2. Determine the Displacement Vector and its Magnitude The displacement vector from point to point is calculated as follows: The magnitude (length) of this diagonal is: 3. Express F in terms of Magnitude and Unit Vector The unit vector in the direction of the force is: Expressing the force as its magnitude times the unit vector: F AB AzA(0,0,8) Bxyx yB(4,8,0) r AB AB r = AB (x − B x )i+ A (y − B y )j+ A (z − B z )k A r = AB (4−0)i+(8−0)j+(0−8)k=4i+8j−8k ft d d= = (4)+(8)+(−8) 222 = 16+64+64 = 14412 ft n AB n = AB = d r AB = 12 4i+8j−8k i+ 3 1 j− 3 2 k 3 2 F 4. Determine the x-, y-, and z-components By distributing the magnitude, we find the individual vector components: The scalar components of the force are: Final Vector Expression: or Scalar Components: ✨ Final Answer Summar