Meriam, Kraige & Bolton — Statics of Particles: Problem 2_110

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/110 The 4-lb force is applied at point A of the crank assembly. Determine the moment of this force about point O. Problem 2/110 ● 1. Identify the Position Vector From the provided diagram, point is at the origin . Point is the location where the force is applied. Based on the dimensions given: The main arm of the crank lies along the -axis, with a length of . Thus, the - coordinate of point is The handle pin at point is vertical (parallel to the -axis) and has a height of . Thus, the -coordinate of point is There is no displacement along the -axis for point , so . The position vector from to is: ● 2. Express the Force as a Cartesian Vector The force has a magnitude of . It acts at an angle of with respect to the horizontal -axis. From the orientation of the arrow and the dashed projection lines, the force lies in the plane (or a plane parallel to it), pointing in the positive and positive directions. 1. Horizontal component (y-axis): 2. Vertical component (z-axis): 3. x-component: The force vector is: r A O(0,0,0)A F x1.5 in.x A1.5 in. Az0.75 in. zA0.75 in. yAy = A 0 OA r = A 1.5i+0j+0.75k (in.) F F4 lb30 ∘ y y-zyz F = y F⋅cos(30)= ∘ 4⋅cos(30)≈ ∘ 3.464 lb F = z F⋅sin(30)= ∘ 4⋅sin(30)= ∘ 2.0 lb F = x 0 F=0i+4cos(30)j+ ∘ 4sin(30)k= ∘ 3.464j+2.0k (lb) ● 3. Calculate the Moment The moment of the force about point is given by the cross product of the position vector and the force vector: Using the determinant form: Expanding the dete