# Question #4e99f

May 18, 2016

This is probably relating to questions where the force is applied at an angle to the direction in which an object is moving

#### Explanation:

I am second guessing the problem here but I assume you have seen work done equations as
$W = F S$
and also
$W = F S \cdot \cos \theta$

The definition of work done is:

work done = force x distance moved in direction of force

If this relates to a problem along the following lines, such as "what is the work done on the object if the weight is pulled along in the horizontal direction by a distance S?"

Then in the above, the force can be resolved into a horizontal component ($F \cos \theta$) and a vertical component ($F \sin \theta$).

Work done in the vertical direction is nil (no distance is travelled in the vertical direction) whereas work done in the horizontal direction would be $W = F S \cdot \cos \theta$

A more technically correct definition of work done is that it equals the dot product of two vectors, force and displacement. Hence:
$W = \vec{F} \cdot \vec{S}$
The solution to this is
$W = F S \cdot \cos \theta$ where F and S are the magnitudes of the force and displacement (identical to the above)

Does this help?