Work energy thm and conservation

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Discussion Overview

The discussion revolves around the relationship between the work-energy theorem and the concept of conservation of energy, particularly focusing on the path dependence of work done by forces. Participants explore the implications of conservative and non-conservative forces on kinetic energy and work.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant asserts that the change in kinetic energy (K2-K1) always equals the integral of force along any path, questioning how this integral can depend on the path.
  • Another participant counters that while ∫F.dr equals K2-K1 for the net force, it does not imply path independence for non-conservative forces.
  • A participant mentions that kinetic energy depends only on the magnitude of the velocity vector, suggesting that paths with the same starting and ending velocities will yield the same work.
  • Another participant agrees with the previous point but notes that not all paths will have the same starting and ending velocities.
  • A participant expresses confusion stemming from a derivation seen in a video, indicating that the conclusion drawn about work being equal to the change in kinetic energy is only valid for conservative forces.
  • In response, another participant clarifies that as long as the force is the only one acting, ∫F.dr will equal the change in kinetic energy, regardless of whether the force is conservative.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the path independence of work done by forces, particularly distinguishing between conservative and non-conservative forces. The discussion remains unresolved as multiple perspectives are presented without consensus.

Contextual Notes

Participants highlight the dependence of work on the nature of the forces involved, with specific emphasis on the conditions under which the work-energy theorem applies. There are references to assumptions about the forces acting and the definitions of conservative forces that remain unexamined.

rattan5
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Since the change of kinetic energy, K2-K1, ALWAYS equals the integral of F.dr along any path, how can that integral depend upon the path? I realize that the integral is ONLY equal to the change in potential energy (F is the derivative of the potential) at the end points when F is a conservative force. But the integral always equals the same value K2-K1, regardless of the path from 1 to 2. Isn't that what is meant by independence of path?
 
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Just because ∫F.dr equals K2-K1 (when F is the net force) doesn't mean that it's path independent. For non-conservative forces, both ∫F.dr and K2-K1 depend on the path.
 
Since KE depends only on the magnitude of the vector, any path I take having the same starting and ending velocities will of course have the same work.
 
rattan5 said:
Since KE depends only on the magnitude of the vector, any path I take having the same starting and ending velocities will of course have the same work.
Well, that's certainly true. But not all paths will have the same starting and ending velocities.
 
Thanks for your replies. My confusion I think lies with the derivation I watched from a Yale video which went like (please notice dot product and vectors)

K = mv.v/2
dK/dt = m dv/dt.v
dK = ma.v = ma.dr/dt so
∫dK = ∫F.dr and then the lhs was set to K2-K1 to get
K2-K1 = ∫F.dr

From what you're saying, which must be true, the last step is only true for conservative forces.
 
rattan5 said:
From what you're saying, which must be true, the last step is only true for conservative forces.
No. As long as F is the only force acting, ∫F.dr will always equal ΔKE.

(If F is a conservative force, then ∫F.dr will be independent of the particular path chosen between the given endpoints.)
 

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