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.

 

[PJC01]

Sure, I'd be happy to help clarify this concept for you. In physics, work is defined as the product of a force and the displacement of the object in the direction of the force. So, when we say "work done by a general variable force," we are referring to the work done by a force that changes in magnitude (strength) as the object moves.

The statement you mentioned is saying that the direction of the force remains constant throughout the object's motion, but the strength of the force may vary. This means that the force is always acting in the same direction, but its intensity may increase or decrease. For example, imagine pushing a shopping cart up a hill. The force you apply to the cart is always in the forward direction, but as the slope of the hill changes, the force needed to push the cart may increase or decrease.

Additionally, the statement mentions that the magnitude of the force at any given position does not change with time. This means that as the object moves, the force acting on it remains constant at that particular position. Going back to our shopping cart example, if you stop pushing the cart at a certain point on the hill, the force acting on the cart would remain the same until you start pushing it again.

I hope this helps clarify the concept of work done by a general variable force. Let me know if you have any other questions!