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Motion equation

  1. Dec 15, 2008 #1

    Im trying to make an equation for a projectiles path, but this is only over a very short distance, so the projectiles curve aren't taken into account. Im including the air resistance.
    This is what i have done:
    m*dv/dt=-k*v2 Differential: dv/v2=-k*dt integrated: -1/v=-k*t+C when: t=0 og c=-1/v0 and we get: v=m*v0/(k*v0*t+m)
    I have gotten some help doing this, but i am wondering if anyone could tell me if this is right. Another thing is that i seem to have forgotten "m", could anyone please tell me where "m" should be in the differentaded and integrated equation? i have a hard time explaing actually what i have done, but maybe you could help me.
    By the way, im from Denmark so sorry for my bad english.

    - Michael
    Last edited: Dec 16, 2008
  2. jcsd
  3. Dec 16, 2008 #2
    Anyone might be able to tell me where this: m*dv/dt=-k*v2 comes from?
    Last edited: Dec 16, 2008
  4. Dec 16, 2008 #3


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    Welcome to PF!

    Hi Michael ! Welcome to PF! :smile:

    (use the X2 tag above the reply field to make v2 :wink:)

    (and what's "og"? :confused:)

    Yes, that's fine :biggrin:

    you lost the m (though somehow you put it back in the right position :rolleyes:) when you went from

    which should have been mdv/v2=-k*dt. :smile:
  5. Dec 16, 2008 #4
    Thanks :), i was wondering where this comes from too: m*dv/dt=-k*v2
    Oh, and "og" is a danish word for "and", my bad :blushing:
  6. Dec 16, 2008 #5


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    ah, i didn't see your second post :redface:

    mmm … for me, it usually comes from the question :rolleyes:

    if you want to find why air resistance is like that, wikpedia is always a good place to start. :smile:
  7. Dec 16, 2008 #6
    I was meaning the formula m*dv/dt=-k*v2 what's the original formula? or what is it calculated from? i mean dv/dt = a ... so might be F=m*a newtons second law, but i don't know, i would appreciate some help here :)
  8. Dec 16, 2008 #7


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    oh i see! :smile:

    yes, it's good ol' Newton's second law :biggrin: … F = ma = mdv/dt …

    so if the force is given as -kv2, then that's mdv/dt = -kv2 :wink:
  9. Dec 16, 2008 #8
    Thank you very much, I appreciate it. :smile:
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