# Work

Every field of endeavor attaches particular and peculiar definitions to common words. What does "work" mean in ordinary conversation? In Physics (and Engineering and Science in general) "work" means something very specific,

Work = Force x distance

W = F d

Great force exerted with no distance moved means no work is done!

Units?
Force in Newtons

distance in meters

1 N-m = 1 J = 1 joule

Actually, we can say "Work = Force x distance" only when the Force and the distance moved are in the same direction.

If the force and the displacement do not lie along the same direction, then we must take the component of the force parallel to the displacement and multiply that by the displacement. It is only the component of the force parallel to the displacement that contributes to the work done.

This means the general form of the definition of work is

W = F d cos

Another way of describing this is called the "dot product" or the "scalar product",

Where we are using the mathematical notation of

A and B are vectors and S is a scalar. This is called the "scalar product of two vectors" or the "dot product" since it is indicated by a dot.

where is the angle between vectors and .