Understanding Parallel Force: Definition, Equation, and Examples

[BrooklynBees]

It's not a specific problem, but I'm wondering what "parallel force" is defined as.
The equation we were given is work = parallel force x distance.
I was thinking that parallel force is probably the sum of the forces acting in the direction of motion, but some problems we've done in class seem to show otherwise.
Now I'm wondering if parallel force has to be parallel to the original surface?
I would love if someone could clear this up for me.

 

[cryptoguy]

A parallel force is the force (or its component) that is parallel to another vector (in this case, displacement). The force has to act parallel to the displacement, not necessarily in the same direction.

 

[Doc Al]

It's not a specific problem, but I'm wondering what "parallel force" is defined as.
The equation we were given is work = parallel force x distance.

The work done by a force equals the component of the force parallel to the displacement times the displacement. So "parallel force" means the force in a direction parallel to the displacement direction.

 

[nicksauce]

The 'parallel' force is given by the dot product

$$F_{||}=\vec{F}\cdot \hat{r} = |\vec{F}||\hat{r}|\cos{\theta}$$, where $$\theta$$ is the angle between the vectors.

In more intuitive terms, you can break the Force vectors into the sum of one that is parallel to the distance vector and one that is perpendicular. For example, if the distance vector is along the x-axis, and the Force vector makes a 30 degree angle with the x-axis, then there will be a parallel force component $$\vec{F}=|\vec{F}|\cos{30}\hat{x}$$ and a perpendicular force component $$\vec{F} = |\vec{F}|\sin{30}\hat{y}$$