Meriam, Kraige & Bolton — Statics of Particles: Problem 2_100

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/100 Determine the angle between the 200-lb force and line . Problem 2/100 (a) Angle Between Force and Line OC ● Calculation Process 1. Present Final Formula: The angle between two vectors and can be determined using the dot product formula: Let be the force vector and be the position vector along line . Based on the dimensions provided in the diagram: Origin is at . Point is the bottom-front-right corner with coordinates inches. The force is directed from to the top-front-right corner (point ) with coordinates inches. Thus, the vectors are: The 200-lb force acts in the direction of . The angle between the force and line is equivalent to the angle between vectors and . 2. Substitute Values: First, calculate the dot product of the two vectors: Next, calculate the magnitudes of each vector: θOC θAB cosθ= ∣A∣∣B∣ A⋅B FOCOC O(0,0,0) C(24,12,0) FOB (24,12,8) = OC24i+12j+0k in. = OB24i+12j+8k in. FOBθ OCOBOC ⋅ OB = OC(24)(24)+(12)(12)+(8)(0) ∣∣= OC 24+12+0 222 ∣∣= OB 24+12+8 222 3. Partial Operations: Dot product: Magnitude of : Magnitude of : 4. Final Calculation: Substitute the partial results into the cosine formula: Calculate the angle: ● Final Conclusion: The angle between the 200-lb force and the line is approximately . Angle ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 2/100 ⋅ OB = OC576+144+0=720 in 2 OC ∣∣= OC = 576+144 ≈ 72026.833 in. OB ∣∣= OB = 576+144+64 = 78428 in. cosθ= = 28⋅ 720 720 ≈ 28 720 ≈ 28 26.8328