A question about linear drag force

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Discussion Overview

The discussion revolves around the concept of linear drag force in classical mechanics, specifically how velocity relates to position in the context of projectile motion. Participants explore the formulation of the equations of motion under the influence of drag and the implications of velocity being expressed as a function of position.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant cites a textbook definition of linear drag force and questions the relationship between velocity and position, suggesting a misunderstanding of how these variables interact.
  • Another participant asserts that velocity does not depend on location in a direct functional sense, but acknowledges that location may influence certain parameters.
  • A third participant clarifies that velocity is defined as the time derivative of position, indicating that while they are related, velocity does not functionally depend on position in the way the original question implied.
  • A later reply expresses gratitude for the clarification but raises a question about whether there are scenarios where velocity might depend on position.

Areas of Agreement / Disagreement

Participants exhibit differing interpretations of the relationship between velocity and position, with some asserting that velocity does not depend on position while others question if such dependencies could exist under certain conditions. The discussion remains unresolved regarding the potential for velocity to depend on position in specific contexts.

Contextual Notes

The discussion does not address specific scenarios where velocity might depend on position, leaving this aspect open for further exploration. There is also a lack of consensus on the implications of the definitions provided.

shanname
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My classical mechanics textbook says that, for a projectile, the linear drag force is given by f = -bv and the second law is written as m[itex]\ddot{r}[/itex] = mg - bv (a second order differential equation) which can be rewritten as m[itex]\dot{v}[/itex] = mg - bv (a first order differential equation) because the forces depend only on v and not on r. But I can't figure out why this is the case. Doesn't v depend on r?
 
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No. Velocity doesn't depend on location as such, only to the extent that location may effect some of the parameters.
 
##\mathbf v ## doesn't "depend" on ##\mathbf r## in the sense that it is some (unknown) function of ##\mathbf r## and probably some other variables as well.

The point is that ##\mathbf v## is just another name for ##\mathbf{\dot r}##, (that's what "velocity" means!) and differentiating, ##\mathbf{\dot v}## is identically equal to ##\mathbf{\ddot r}##.
 
Thank you, AlephZero. I believe I understand. I mean, I know that v is just another name for [itex]\dot{r}[/itex] and the like, I just thought it could be rewritten in terms of v for that reason. No one ever explained that this is true specfically because v did not "depend" on r... is it ever the case that v does depend on r?
 
sorry, didn't realize I wasn't bolding [itex]\dot{r}[/itex].
 

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