Meriam, Kraige & Bolton — Statics of Particles: Problem 2_3

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/3 The slope of the 6.5-kN force F is specified as shown in the figure. Express F as a vector in terms of the unit vectors i and j. Problem 2/3 (a) Vector Expression of Force F ● Calculation Process 1. Analyze the geometry of the slope triangle: The direction of the force F is given by a slope triangle with a horizontal run of and a vertical rise of . To find the components of the force, we first need the hypotenuse () of this triangle: 2. Identify the magnitude and quadrant: The magnitude of the force is . By observing the diagram for Problem 2/3, the force vector starts at the origin and points into the first quadrant. Therefore, both the (horizontal) and (vertical) components will have positive signs. 3. Calculate the scalar components: We use the proportional relationship between the force components and the sides of the slope triangle: 4. Express as a vector: The vector F is the sum of its component vectors along the and axes, represented by the unit vectors and respectively: 12 5L L= = 12+5 22 = 144+25 = 16913 F=6.5 kN xy F = x F⋅ = ( hypotenuse horizontal side )6.5 kN⋅ = ( 13 12 )0.5⋅12=6.0 kN F = y F⋅ = ( hypotenuse vertical side )6.5 kN⋅ = ( 13 5 )0.5⋅5=2.5 kN xy ij F=F i+ x F j= y (6.0i+2.5j) kN ● Final Conclusion: The force F expressed as a vector is: where the scalar components are and . ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 2/3 F=6.0i+2.5j kN F = x 6.0 kNF = y 2.5 kN F=6.0i+2.5j kN