Technical Mathematics, Sixth Edition

7.6. Applications of Vectors

Any vector quantity such as force, velocity, or impedance can be resolved or combined by the methods of the preceding section. We will start with force vectors, and then cover velocity vectors and impedance vectors. As before, everything you need to solve these problems is given in this text, and you are encouraged to try problems outside your chosen field.

Figure 7.45. Resultant of two vectors.

7.6.1. Force Vectors

Our first problem is simply to resolve a vector into its components.

Example 22: A sled whose weight W is 386 lb is on an icy incline making an angle of 27.4° with the horizontal, Fig. 7-44(a). Find (a) the normal component N and (b) the tangential component T of the sled's weight. (c) What force F parallel to the incline is needed to keep the sled from sliding down the hill? Solution: We draw a vector diagram, Fig. 7-44(b), showing W acting vertically downwards, N at a right angle to the plane, and, T and F parallel to the plane. Then we resolve W into its components N and T. (c) The force F needed to hold the sled in place is just equal to the tangential component T, or F = T = 178 lb

Our next problem requires the statics equations which we first gave in Chap. 3. They are

The moment of a force about some point is the product of the ...