Meriam, Kraige & Bolton — Statics of Particles: Problem 2_1

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/1 The force F has a magnitude of 600 N. Express F as a vector in terms of the unit vectors i and j. Identify the x and y scalar components of F. Problem 2/1 (a) Scalar components of the force F ● Calculation Process 1. Present Final Formula: From the geometric representation of the force in the 2D Cartesian plane, the scalar components are given by: where is the magnitude of the force and is the angle measured from the positive - axis. The negative sign for reflects that the force is directed into the fourth quadrant (downward). 2. Substitute Values: Given and : 3. Partial Operations: Calculate the trigonometric values: Perform the multiplications: 4. Final Calculation: Rounding to four significant figures: F = x Fcos(θ) F = y −Fsin(θ) Fθx F y F=600Nθ=40 ∘ F = x 600cos(40) ∘ F = y −600sin(40) ∘ cos(40)≈ ∘ 0.7660 sin(40)≈ ∘ 0.6428 F ≈ x 600×0.76604=459.626N F ≈ y −600×0.64279=−385.673N F = x 459.6N F = y −385.7N ● Final Conclusion: The scalar components of the force are and . (b) Vector expression of the force F ● Calculation Process 1. Present Final Formula: A vector in 2D is expressed in terms of its scalar components and unit vectors and as: 2. Substitute Values: Using the scalar components calculated in the previous step: 3. Final Calculation: Simplify the expression: ● Final Conclusion: The force expressed as a vector is . ✨ Final Answer Summary (a) Scalar components: , (b) Vector expression: Mecademy AI Solution · ENGProble