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Is it possible to have a situation where...

Is it possible to have a situation where mechnial energy (E ) - potential energy `(E_p)` is negative, i.e., `(E - E_p) lt 0` ?

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No. We know that `E = E_p + E_k.` Therefore, `E_k = (E - E_p). Since E_k` is never negative, `(E - E_p)` is also never negative and as such `(E - E_p)` is never less then zero.
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