Conservative Force: Is F Dependent on Velocity?

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Discussion Overview

The discussion revolves around the nature of conservative forces, specifically whether a force that depends on the velocity of an atom can be classified as conservative. Participants explore definitions, examples, and implications of velocity-dependent forces in the context of physics.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants question whether a force dependent on velocity can be considered conservative.
  • One participant suggests that the definition of a conservative force is crucial to the discussion.
  • Another participant states that velocity-dependent forces are generally not conservative, citing the Lorentz force as a potential exception.
  • A participant presents an example with the force F = -av and argues that integrating this force shows it depends solely on the start and end points, implying it is conservative.
  • In response, another participant argues that the work done by the force depends on the path taken, indicating that it is not conservative.
  • There is a clarification that 'a' refers to acceleration due to the force.
  • One participant emphasizes that the work done varies with different paths, providing a specific example to illustrate their point.
  • Another participant reiterates that velocity-dependent forces are generally not conservative, adding that forces acting perpendicular to velocity may be exceptions.
  • There is a misunderstanding regarding the conservation of force, with one participant asserting that force is always conserved, which is corrected by another participant who clarifies the definition of a conservative force.

Areas of Agreement / Disagreement

Participants express differing views on whether velocity-dependent forces can be classified as conservative. There is no consensus, as some argue for the conservative nature of certain forces while others challenge this perspective.

Contextual Notes

Participants reference specific examples and definitions, but there are unresolved assumptions regarding the implications of velocity dependence and the conditions under which forces are considered conservative.

johann1301
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If F is a force acting on a atom and is dependent on the velocity of the atom. Is the force conservative?
 
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What do you think -- what is the definition of a conservative force?
 
Velocity dependent forces are generally not conservative and exception is the Lorentz force due to a magnetic field acting on a charged particle although some would strictly speaking not consider this force conservative either.
 
Lets say

F=-av

If i integrate this, isn't it soley dependent on the start and end point? And thus, its conservative..?
 
a is just a constant.
 
V is dependent of time since v = a*t = m*a. Isn't it clear therefore that the work in reaching a specific position will depend on the path traveled. The longer the path the more time and thus more work.
 
my a is the acceleration due to the force
 
johann1301 said:
Lets say

F=-av

If i integrate this, isn't it soley dependent on the start and end point? And thus, its conservative..?
Certainly not. Consider ##a=-1 \; N/(m/s)## and an object which goes out a distance of 1 m at 1 m/s and then back at 1 m/s and another which goes out the same 1 m distance at 1 m/s and then back at 10 m/s. The force does 2 J of work for the first path and 11 J of work for the second. Furthermore, the work is non-zero, so both differ from the path which just stays at the endpoints.
 
gleem said:
Velocity dependent forces are generally not conservative and exception is the Lorentz force

... or any other force always acting perpendicular to velocity (e.g. coriolis force).
 
  • #10
Are you asking if force is always conserved? From my understanding yes f=mv thus it will always equation out to your mass and velocity on the other side of the equals sign?
 
  • #11
audire said:
Are you asking if force is always conserved? From my understanding yes f=mv thus it will always equation out to your mass and velocity on the other side of the equals sign?
That is not at all what is being asked.

A force is "conservative" if the work done on an object by that force as it moves along any path that loops back to where it started is always equal to zero. Note that in this context we are talking about a force "field" as in http://en.wikipedia.org/wiki/Field_(physics)
 

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