Meriam, Kraige & Bolton — Statics of Particles: Problem 2_4

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/4 The line of action of the 3000-lb force runs through the points and as shown in the figure. Determine the and scalar components of . Given data from figure: Magnitude of force, Coordinates of point : Coordinates of point : The direction of the force is from to . Problem 2/4 ● Step 1: Determine the displacement vector from point to point The line of action of the force passes through points and . Based on the direction indicated by the arrow in the figure, the force acts from toward . We calculate the changes in the and coordinates: Change in : Change in : Thus, the displacement vector is: ● Step 2: Calculate the distance (magnitude) between points and The total length of the segment is found using the Pythagorean theorem: Substituting the values: ● Step 3: Determine the unit vector in the direction of the force AB xyF F=3000 lb A(−7,−2) ft B(8,6) ft AB AB A(−7,−2)B(8,6) AB xy xΔx=x − B x = A 8−(−7)=15 ft yΔy=y − B y = A 6−(−2)=8 ft AB = AB15i+8j (ft) AB dAB d= (Δx)+(Δy) 22 d= = 15+8 22 = 225+64 = 28917 ft The unit vector indicates the direction of the force : ● Step 4: Calculate the and scalar components of the force The force vector is given by the product of its magnitude and the unit vector: The scalar components are: 1. -component (): 2. -component (): ● Final Conclusion: The scalar components of the force are: More precisely: ✨ Final Answer Summary Mecademy AI Solution · ENGProblem 2/4 n AB F n = AB = d AB i+ 17 15 j 17 8