Work Done Over an Inclined Plane

Consider a person skiing down a slope. Assuming that the force due to friction on the skis is negligible over ice, a free-body diagram can be drawn.

The component of the gravitational force along the displacement moves the person forward. Forces perpendicular to the displacement have no role in the movement and, hence, do not contribute to the work done.

So, the work done is simply the parallel force component multiplied by the displacement.

Another way to solve this is by taking the force vector instead of its component.  

Here, the angle between the  force and the displacement is considered. Note that the final expression for work done is the same.

However, if the displacement of the skier is in the opposite direction of the force such that it starts and ends at rest, then the work done is negative.

If the angle of the inclined plane is zero, the force is perpendicular to the displacement, so the work done by the gravitational force on the person becomes zero.