Meriam, Kraige & Bolton — Statics of Particles: Problem 2_20

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/20 Determine the scalar components and of the force along the nonrectangular axes and . Also determine the orthogonal projection of onto axis . Given values from diagram: Magnitude of force: (directed horizontally to the right). Angle of axis relative to the horizontal: (counter-clockwise). Angle of axis relative to the horizontal: (clockwise). Problem 2/20 (a) Determination of Scalar Components and ● Calculation Process To find the scalar components of a force along non-rectangular axes, we use the parallelogram law of vector addition. We can construct a force triangle where the sides are the components and , and the diagonal is the resultant force . 1. Identify the internal angles of the force triangle: The angle between the force and axis is . The angle between the force and axis is . The total angle between axes and is . In the force triangle formed by , , and a line parallel to , the angle opposite the resultant is . By geometry, the side is opposite the angle between and axis , which is . The side is opposite the angle between and axis , which is . 2. Apply the Law of Sines: R a R b R abP a Ra R=800 N a30 ∘ b110 ∘ R a R b R a R b R Raθ = a 30 ∘ Rbθ = b 110 ∘ abα=30+ ∘ 110= ∘ 140 ∘ RR a R b Rγ=180− ∘ (30+ ∘ 110)= ∘ 40 ∘ R a Rb110 ∘ R b Ra30 ∘ = sinθ b R a = sinθ a R b sinγ R 3. Calculate : 4. Calculate : ● Final Conclusion: The scalar components of the force along the nonrectangular axes are and . (b) Determination of the O