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I have been trying to find the value of theta at which a string goes slack in a vertical circle, by letting the diameter of the circle be the zero potential

diagram

My question is would the gravitational potential above and below the zero potential have opposite signs?

I am well aware that potential energy is a scalar quantity however when I apply the conservation of energy $$K.E_{initial} + P.E_{initial}= K.E_{final} + P.E_{final}$$

The only way I get a satisfactory answer (one that matches the answer on the book) is when the potential energies have opposite signs.

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  • $\begingroup$ Is it perhaps that the change in potential energy overall would be a net gain and not a net loss? $\endgroup$
    – Filthyscrub
    Commented Apr 8, 2021 at 18:17
  • $\begingroup$ And if so would alternating signs above and below the potential line account for this? $\endgroup$
    – Filthyscrub
    Commented Apr 8, 2021 at 18:18
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    $\begingroup$ What string? Is it acting on a object? What would cause it to go slack? $\endgroup$
    – R.W. Bird
    Commented Apr 10, 2021 at 15:13

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The zero potential plane also called Datum plane is the plane where gravitational potential is considered to be 0. Now if you where 5 m above this plane initially and came down to 4 m your potential energy would reduce from mg $\times$ 5 to mg $\times$ 4. In short potential energy decreases with decreasing height.Now when you go below datum plane why should the rule be any different ? But we know that potential energy is 0 at this plane .So if you go below this plane your potential energy should decrease i.e become negative .

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