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I'm feeling very confused about which sign to the potential should I choose. A specific exercise I've had trouble with is in this link. in this exercise a double Atwood machine is given. when I tried calculating the potential, I drew gravity pointing downwards, and the axis system I chose was y pointing downwards and x pointing right. I chose the reference plane to be the canter of the top pulley (marked in green in the picture). so when I calculated the total potential energy V, for all the masses, I got the same expression as in the article, but in an opposite sign. What did I miss?

Thank you very much for your help.

enter image description here


edit: that's how I tried to solve this: enter image description here

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    $\begingroup$ Can you show your work? $\endgroup$ Feb 5, 2020 at 12:24
  • $\begingroup$ @FissionChips I've added my solution (at least what Iv'e tried to do). thank you! $\endgroup$ Feb 5, 2020 at 13:12

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Co-ordinate systems for 1D vectors are always tricky. A handy technique to validate your co-ordinate system is to track the potential energy of a particle under free fall (in your co-ordinate system).

The direction of $g$ has to be such that the potential energy is decreasing as energy has to be conserved. (Kinetic energy depends only on the magnitude of $v$ which keeps increasing under free fall). This is violated in your co-ordinate frame unless $g\to-g$. If you do so, then your Lagrangians will match.

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