Vectors and Work

We have seen that work can be written as:

as long as the force is constant. Looking at this equation, you notice that force, F, and displacement, delta_x, are both vectors whose difference in direction is the angle theta. In other words, the right side of this equation expresses a product of the two vectors F and , which produces a scalar - the work done by the force.

In vector algebra, this is called the dot (or inner) product of the vectors. The dot product of two vectors is a scalar equal to the product of the magnitudes of the vectors times the cosine of the angle between them. Therefore, in vector language, we can write the work done by a (constant) force F on an object experiencing a displacement as:

W = F dot delta_x

last update December 13. 2003 by JL Stanbrough