Meriam, Kraige & Bolton — Statics of Particles: Problem 2_103

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/103 If the scalar projection of F onto line OA is 0, determine the scalar projection of F onto line OB. Use a value of b = 6 ft. Problem 2/103 1. Express Force in Cartesian Vector Form From the given figure, the force has a magnitude of . Its orientation is defined by two angles: The angle with the positive -axis is . The angle of its projection on the plane with the positive -axis is . From the visual orientation, the projection points towards the negative -axis direction to satisfy the condition that its projection on is zero (since is in the positive quadrant). The components of are: Substituting : 2. Determine the height using the first condition The scalar projection of onto line is zero. Point has coordinates . The vector is: F FF=1700 lb y40 ∘ x-zz30 ∘ x OAAx-z F F = y Fcos40 ∘ F = xz Fsin40(projection in the x-z plane) ∘ F = x −F sin30= xz ∘ −Fsin40sin30 ∘∘ F = z F cos30= xz ∘ Fsin40cos30 ∘∘ F=1700 lb F = x −1700sin40sin30≈ ∘∘ −546.36 lb F = y 1700cos40≈ ∘ 1302.29 lb F = z 1700sin40cos30≈ ∘∘ 946.33 lb F=−546.36i+1302.29j+946.33k lb h FOAA(b,0,h) OA The scalar projection is zero if the dot product : (Note: This corresponds to ) 3. Calculate the scalar projection of onto line Point has coordinates . The vector is: The magnitude of is: The unit vector along is: The scalar projection of onto is: The scalar projection of force onto line is . ✨ Final Answer Summary Scalar projection of onto line : Mecademy AI Solution · ENGPro