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How to show cons. of Energy from F=change of potential

  1. Apr 27, 2009 #1
    Force is equal to change in potential (r is a point in space suppose integrating between points r1 to r2 in time t1 to t2, i did not indicate this but it is not relevant for my quenstion:
    [tex]mr'' =F(r) = -\delta V[/tex]
    after multiplying both sides by dr it is obvious RHS will give potential difference, but LHS needs to be transformed to show corresponding kinetic energy difference:
    [tex]mr'' \cdot dr = m \int_{}^{} r'' \cdot r' \cdot dt = m \int_{}^{} \frac{d}{dt}r' ^{2}dt [/tex]
    :(
    The problem is there should be a 1/2 term there as well. I don't know how to integrate this LHS. Can you please help- show me clearly step by stem what is done and where this 1/2 comes in...
     
  2. jcsd
  3. Apr 27, 2009 #2

    tiny-tim

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    Hi trelek2! :smile:

    It's because d/dt (r'2) = 2 r' r'' :wink:
     
  4. Apr 27, 2009 #3
    Yes, I am a retard:P
     
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