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The kinetic energy formula for lagrange doesnt make sense

  1. Nov 28, 2014 #1

    grandpa2390

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    1. The problem statement, all variables and given/known data
    This is a real basic question I am sure. Maybe I just missed something.
    so in the book, t = the kinetic energy . only for a pendulum, they add kinetic energy of x dot squared, plus kinetic energy of y dot squared.

    2. Relevant equations
    T = 1/2 m v^2
    a^2 + b^2 = c^2
    3. The attempt at a solution
    This doesn't make sense. At first I thought maybe they were splitting velocity into x and y components.
    but T(velocity) is not equal to T(x component of velocity) + T(y component of velocity). if I am traveling in a straight line at 5 m/s, 1/2m(5)^2 is not equal to 1/2m(3)^2 + 1/2m(4)^2. what is the xdot and ydot a measure of
     
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  3. Nov 28, 2014 #2

    haruspex

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    Are you a betting man?
     
  4. Nov 28, 2014 #3

    grandpa2390

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    No I am not. And I get the feeling you are about to tell me that it's a good thing. lol because 3^2 +4^2 does equal 5^2 .... this is what I get for forcing myself out of bed to study... sry for the inconvenience. It made sense earlier when I was awake. Then I take a nap. force myself up, and I am writing a formula that says exactly what I said wasn't making sense. lol.

    They only hope I have to hold onto is that my professor says that you aren't a physicist unless you occasionally write something stupid.

    edit: I know what i was thinking. the variable itself v being plugged in, and then just replacing it with components added. x and y. 3 + 4 != 5 but i guess thats why v is squared in kinetic energy. so that the kinetic energy of components can be added. you cant say .5m(x+y)^2 but u can say the other
     
    Last edited: Nov 29, 2014
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