Goldstein classical mechanics discrepancy?

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SUMMARY

The discussion centers on a discrepancy in Goldstein's classical mechanics text regarding the nature of frictional forces in conservative fields. The text states that "friction or dissipative forces are never conservative since F dot ds is always positive," which contradicts the understanding that friction typically acts opposite to displacement, resulting in negative work. Participants agree that Goldstein's statement may be misleading and suggest that it should indicate that frictional forces are never conservative since F dot ds is always non-zero. This highlights a common confusion in classical mechanics literature regarding the characterization of dissipative forces.

PREREQUISITES
  • Understanding of classical mechanics principles
  • Familiarity with conservative and non-conservative forces
  • Knowledge of vector calculus and dot products
  • Experience with classical mechanics textbooks, particularly Goldstein's
NEXT STEPS
  • Review the concept of conservative versus non-conservative forces in classical mechanics
  • Examine the definitions and implications of work done by frictional forces
  • Study alternative classical mechanics texts for varying interpretations of dissipative forces
  • Explore the mathematical formulation of work and energy in the context of friction
USEFUL FOR

Students of classical mechanics, educators teaching physics, and anyone seeking clarity on the treatment of frictional forces in theoretical frameworks.

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Homework Statement



In Goldstein's text, he discusses conservative fields and then states that "friction or dissipative forces are never conservative since F dot ds is always positive."

From what I recall, most frictional interactions occur in directions opposite the displacement, and would, hence, result in negative values of the dot product. Shouldn't, then, the text read isntead: friction or dissipative forces are never conservative since F dot ds is always non-zero?

I have checked a few other classical mechanics texts and they all seem to have statements along the same lines- so I feel there is a detail I am missing here.

Homework Equations


The Attempt at a Solution

 
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I still have my 1st edition of Goldstein that I used in a course 42 years ago. I found the quote on page 3 and lo and behold I see that I had circled the word "positive" and added a question mark in the margin! I think Goldstein meant to use the word "negative" here (even though you can construct scenarios where a force of friction does positive work).
 
That's remarkable TSny, thanks for checking!
 

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