Work Done By A General Variable Force

[Bashyboy]

As the title alludes to, I am currently reading about work. One sentence has left me very confused, thought: " Only the magnitude of this variable force changes, not its direction,
and the magnitude at any position does not change with time."
Could someone possibly help me understand this?

 

[mathman]

It seems to describe a particular force field, which is defined by two specific requirements. 1) It is constant over time. 2)The direction of the force is the same at all points in the field, but the magnitude varies with position.

 

[Bashyboy]

But it says "...and the magnitude at any position does not change with time," which would not be in accordance with the second requirement you provide. Anyways, I don't believe it is talking about force fields, because I have not read about those in my book yet.

 

[mfb]

Take a simple, one-dimensional example: A force given by F=kx^2 where x is your position and k is some constant (like "1N/m^2").

Now, the direction is always the same (in positive x-direction), the magnitude at any position (fixed x) does not change with time, but the magnitude varies with the position (different x lead to different F).
You can use the same force, just in 3 dimensions. It always points in positive x-direction.