Negative Force-potential energy relationship?

[SharKCS11]

I've been wondering for a while why force is the negative derivative of potential energy. In our books, they write that F=-dU/dx, and U=-W
I don't really understand why it should be negative. Doesn't the force need to be positive in order to increase the potential energy? For example, when you apply a positive force to an object (assuming downward is the negative y direction), U_g goes up, right?
I'm new to this forum, so sorry if I posted this in the wrong section...

 

[Doc Al]

I've been wondering for a while why force is the negative derivative of potential energy. In our books, they write that F=-dU/dx, and U=-W
I don't really understand why it should be negative. Doesn't the force need to be positive in order to increase the potential energy? For example, when you apply a positive force to an object (assuming downward is the negative y direction), U_g goes up, right?

When you apply a positive force, that means the force associated with the potential is applying a negative force. Using your example, while you exert a positive force to raise an object, the force of gravity is negative.

 

[SharKCS11]

Oh, I see, so the "F" in the equation is referring to the force that causes the potential energy, not the force that changes it?

 

[Doc Al]

Oh, I see, so the "F" in the equation is referring to the force that causes the potential energy, not the force that changes it?

Right. For gravitational PE, the F refers to the gravitational force. Similarly for other conservative forces.

 

[SharKCS11]

Ok, thanks. That cleared up a lot.

 

[Doc Al]

Welcome to PF!