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Classical mechanics - Energy balance confussion

  1. Jul 9, 2015 #1
    Hi everyone.
    I'm confused with the balance of energy in this situation (I'm comparing the mechanical energy, initially, at rest, at a height = h, and then, at the end, at height = 0). It doesn't seem to be fine, maybe I missed something.
    I'd appreciate some help - Everything is in the .jpg below.

    There are 2 relevant equations:
    1. The work done by a nonconservative force is equal to the change in mechanical energy. (Wnc = Delta E)
    2. W = Force (dot) distance.
    Also, take into account that h / sin(theta) is equal to the hypotenuse of the inclined plane.
     

    Attached Files:

    Last edited: Jul 9, 2015
  2. jcsd
  3. Jul 9, 2015 #2

    Doc Al

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    Staff: Mentor

    It's a bit difficult to follow. And since you put your work in a jpg instead of typing it here, it is hard to comment.

    One thing: You seem to mix up the height h with the distance along the surface.
    And another: You may have mixed up some signs.
     
  4. Jul 9, 2015 #3
    Hmmm, right. y(t) gives me the displacement along the surface (not the height).
    Give me some minutes and I'll have the equations fixed.

    * EDIT: Doc Al, you were right. I rewrote the equations by hand and everything fits well now, thanks.
    I just had to change the limits in one integral at the beginning of the deductions.
     
    Last edited: Jul 9, 2015
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