# Why is potential energy the NEGATIVE of the work done?

Why is the change in potential energy the NEGATIVE of the work done by a force? What is the negative sign doing there, and what physical meaning does it serve? Any input is appreciated, but a rather detailed explanation would be great, as I am having much difficulty understanding this.

navneet9431 and gracy

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NascentOxygen
Staff Emeritus
If you drop a book to splatter a cockroach, this book has done work. Useful work. In falling, the book has lost potential energy. The change in its PE is negative; PE is lower after the fall than before the fall.

HallsofIvy
Homework Helper
In other words, "conservation of energy". If you do something that does work, the potential energy must have decreased. (Remember that potential energy is always "relative" to something. The potential energy in a given problem can positive or negative depending upon the zero point. "Negative" just means "decreased".)

In other words, "conservation of energy". If you do something that does work, the potential energy must have decreased. (Remember that potential energy is always "relative" to something. The potential energy in a given problem can positive or negative depending upon the zero point. "Negative" just means "decreased".)
And the conservation here of course is reflected by an increase in the kinetic energy which is equal to the decrease in the potential energy

Thanks for the responses.

But let's say I do positive work in bringing a book up from the floor. It certainly increased potential energy, right?

Erland
Thanks for the responses.

But let's say I do positive work in bringing a book up from the floor. It certainly increased potential energy, right?
Then you are losing energy, chemical energy from your body.

Redbelly98
Staff Emeritus
Homework Helper
Thanks for the responses.

But let's say I do positive work in bringing a book up from the floor. It certainly increased potential energy, right?
And gravity -- the force associated with that potential -- has done negative work when the potential energy increases.

And gravity -- the force associated with that potential -- has done negative work when the potential energy increases.

Thank you! So really the equality means- the change in potential energy is the negative of whatever the work done by a field (electric or gravitational). Correct?

I would say also that PE variations are chosen to be the negative of work but it's a personal choice, made by the scientists because it's very comfortable: the first advantage is the concept of PE (the potential work a system can do if it owns PE) and the second is to define the Mechanical Energy as the sum of PE and Kinetic Energy (and so conservation of this sum), but no one forbids to define Mech En as the difference between KE and PE and a lot of things will change in many fields of Physics' Knowledge :surprised.