Force Vector Directed along a Line
Learning Goal:
To find a force’s directional components that act along a cable and to find the coordinates of a point on a cable that has a force vector applied to it.
Three-dimensional Cartesian force vectors are used throughout engineering mechanics. The generic force vector is represented as follows:F=Fxi+Fyj+Fzk
where F is the force vector and Fx, Fy, and Fz are the vector’s i, j, and k components, respectively. The force vector has a magnitude F=F2x+F2y+F2z−−−−−−−−−−−−√. The vector’s direction is described by a unit vector u, where u=F/F.
Part A
As shown, a force vector F with a magnitude of c = 33.0 lb is applied at point A and is directed toward point C. (Figure 1) The distance a is 2.00 ft and the distance b is 5.50 ft . What are the i, j, and k components of F?
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