In mechanics the work performed by a force is defined as the product of the magnitude of the force times the distance moved in the direction of the force.
From Fig. 3.14 we see that, since the component of along the line of force is , where is the distance travelled, the work is , and thus work can be evaluated as an innerproduct.
Example 3.9:
A force is applied to a particle which is moving along a wire where and are straight, and the points and are and . Find the work done.
Solution:
Along the line the work done is ,
Along the line , , and the work done is
The total work is thus