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A question about linear drag force

  1. Jan 20, 2014 #1
    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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  3. Jan 20, 2014 #2

    mathman

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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.
     
  4. Jan 20, 2014 #3

    AlephZero

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    ##\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}##.
     
  5. Jan 20, 2014 #4
    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?
     
  6. Jan 20, 2014 #5
    sorry, didn't realize I wasn't bolding [itex]\dot{r}[/itex].
     
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