## Potential energy and work.

If you are holding an object off the ground and let it go, we say that it's potential energy is transformed into kinetic energy as it falls, but the total amount of energy stays the same. However, the gravitational force is doing work on the object, which seems like it would increase the amount of energy in the object.

Similarly, when we lift a stationary object up, we say that it's potential energy increases. Yet two forces were acting on the object as we lifted it. The force from our hand did positive work, but the gravitational force did an equal amount of negative work. So how does the energy increase?

Basically, I've suddenly realized that I don't really understand the definitions of work and potential energy.

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Hi Opus_723!

potential energy is defined as (minus) the work done by a conservative force (such as gravity)
 Quote by Opus_723 If you are holding an object off the ground and let it go, we say that it's potential energy is transformed into kinetic energy as it falls, but the total amount of energy stays the same. However, the gravitational force is doing work on the object, which seems like it would increase the amount of energy in the object.
from the PF library …
Is potential energy energy?

There is confusion over whether "energy" includes "potential energy".

On the one hand, in the work-energy equation, potential energy is part of the work done.

On the other hand, in the conservation-of-energy equation (and conservation of course only applies to conservative forces), potential energy is part of the energy.
you're double-accounting … if you want to treat mgh as energy, then you can't treat gravity as a force

 Okay. I was thinking it was something like that, where I was just fuzzy on how it's defined. Thanks for the clarification.