Negative Force-potential energy relationship?

In summary, force is the negative derivative of potential energy because it refers to the force that causes the potential energy, not the force that changes it. In the case of gravitational potential energy, the F in the equation represents the gravitational force, which is negative. This is why when a positive force is applied to an object, the potential energy increases even though the force is positive. This concept applies to other conservative forces as well.
  • #1
SharKCS11
3
0
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), Ug goes up, right?
I'm new to this forum, so sorry if I posted this in the wrong section...
 
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  • #2
SharKCS11 said:
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), Ug 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.
 
  • #3
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?
 
  • #4
SharKCS11 said:
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.
 
  • #5
Ok, thanks. That cleared up a lot.
 
  • #6
Welcome to PF! :smile:
 

What is a negative force-potential energy relationship?

A negative force-potential energy relationship is a concept in physics that describes the relationship between the force applied to an object and its potential energy. In this relationship, as the force increases, the potential energy decreases. This is because potential energy is defined as the energy that an object possesses due to its position or configuration, and as the force acts on the object, it changes its position or configuration, resulting in a decrease in potential energy.

How is a negative force-potential energy relationship represented mathematically?

The negative force-potential energy relationship is represented mathematically as the negative derivative of potential energy with respect to displacement. This can be written as:
F = -dU/dx
where F is the force, U is the potential energy, and x is the displacement.

What are some real-life examples of a negative force-potential energy relationship?

A common example of a negative force-potential energy relationship is a spring. As a force is applied to a spring, it compresses or stretches, resulting in a decrease in the potential energy stored in the spring. Another example is a ball that is thrown into the air. As the ball rises, it gains potential energy due to its height, but as gravity pulls it back to the ground, the potential energy decreases.

Are there any exceptions to the negative force-potential energy relationship?

Yes, there are some exceptions to this relationship. One example is an object moving in a circular path at a constant speed. In this case, the force is perpendicular to the displacement, resulting in no change in potential energy. Another exception is a conservative force, where the change in potential energy is dependent on the initial and final positions of the object, rather than the force applied.

How does the negative force-potential energy relationship relate to the conservation of energy?

The negative force-potential energy relationship is closely related to the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed. In this relationship, as potential energy decreases, the corresponding increase in kinetic energy maintains the total energy of the system, thus conserving energy.

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