Meriam, Kraige & Bolton — Statics of Particles: Problem 2_97

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/97 Derive the expression for the projection of the force onto the line directed from to . Problem 2/97 ● Calculation Process 1. Identify Point Coordinates: Establish a right-handed rectangular coordinate system with the origin at the bottom-back-left corner of the parallelepiped. Based on the geometry and dimensions shown in the figure: Point (top-back-left): Point (top-front-left): Point (top-back-right): Point (bottom-front-right): 2. Define the Force Vector : The force acts along the diagonal of the top face from point to point . The magnitude is . The unit vector in the direction of the force is: Thus, the force vector is: 3. Define the Unit Vector along Line : The line is directed from point to point . The magnitude is . The unit vector is: F DC F DC a,b,c Dr = D 0i+0j+ck Ar = A 0i+bj+ck Br = B ai+0j+ck Cr = C ai+bj+0k FF AB = ABr − B r = A (a−0)i+(0−b)j+(c−c)k=ai−bj ∣∣= AB a+b 22 u F u = F a+b 22 ai−bj F=Fu = F (ai− a+b 22 F bj) DCDC = DCr − C r = D (a−0)i+(b−0)j+(0−c)k=ai+bj−ck ∣∣= DC a+b+c 222 u DC 4. Calculate the Scalar Projection : The projection of onto the line is the dot product of the force vector and the unit vector of the line. Perform the dot product: ● Final Conclusion: The derived expression for the scalar projection of the force onto the line is given below. ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 2/97 u = DC a+b+c 222 ai+bj−ck F DC FDC F = DC F⋅u = DC (ai−bj) ⋅ [ a+b 22 F ] [ a+b+c 222