Work Done By A General Variable Force

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Discussion Overview

The discussion revolves around the concept of work done by a general variable force, specifically focusing on the characteristics of such forces, including their magnitude and direction. Participants explore the implications of a statement regarding the constancy of force direction and the variability of force magnitude with position, while also addressing potential contradictions in the description.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion over a statement regarding variable force, specifically about the constancy of direction and the time-invariance of magnitude.
  • Another participant proposes that the statement describes a force field characterized by a constant direction and a position-dependent magnitude that does not change over time.
  • A third participant challenges the second participant's interpretation, noting a potential contradiction in the description of the force's characteristics and suggesting that the concept of force fields may not be relevant to their current studies.
  • A later reply provides a specific example of a force defined by F=kx^2, illustrating that while the direction remains constant, the magnitude varies with position, which aligns with the initial statement's conditions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the statement regarding variable force. There are competing views on whether the discussion pertains to force fields and how the characteristics of the force are defined.

Contextual Notes

There are unresolved aspects regarding the definitions of force and force fields, as well as the implications of the stated conditions on the nature of variable forces.

Bashyboy
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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?
 
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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.
 
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.
 
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.
 

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