If the positive energy is the capacity to perform work
what about the negative energy?
there's no such thing as negative kinetic energy (KE)
and potential energy (PE) is always relative
for example, we usually take electric potential energy to be zero at infinity, which means that (for positive charges) it's always negative!
negative potential energy simply means less capacity to perform work than if the potential energy was 0
(there's always some capacity to do work! )
A bound system can be regarded as having negative energy. For example, the ground state energy of a hydrogen atom is about -13.6eV (*). This means it takes 13.6eV energy input to free the electron from the proton.
(*) This isn't the total energy because it doesn't include the rest energy of the proton and electron. The total energy is positive.
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