What is the relationship between work and potential energy?

In summary, work is the integral of the force over a distance, while potential energy is the negative integral of the force over a distance. This relationship is expressed in the equation W=-ΔU, which shows that work is equal to the change in potential energy. Additionally, for a conservative force, the force can be expressed as the gradient of the potential energy, as shown in the equation F=grad(W). However, there is some disagreement between sources on the exact relationship between work and potential energy, as some sources show the negative sign in the equation while others do not.
  • #1
henpen
50
0
If
Work= [itex]\int[/itex]Fdx
and
Potential Energy, U= -[itex]\int[/itex]Fdx

What is Work in terms of potential (and potential and kinetic) energy?
http://en.wikipedia.org/wiki/Potential_energy#Overview and http://en.wikipedia.org/wiki/Forms_of_energy#Potential_energy don't seem to agree on this. It seems odd that as work and potential energy seem so similar that W= -[itex]\Delta[/itex]U

Also, why does Work= [itex]\int[/itex]Fdx mean that, for a conservative force, F=grad(W)?
 
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  • #2
Potential energy is stored energy. It is the energy that an object possesses due to its position in a force field or due to its configuration. Potential energy is the energy that an object possesses due to its position in a force field or due to its configuration.
 

FAQ: What is the relationship between work and potential energy?

Question 1: What is potential energy?

Potential energy is a form of energy that an object possesses due to its position or configuration. It is stored energy that has the potential to do work in the future.

Question 2: How is potential energy different from kinetic energy?

Potential energy is different from kinetic energy because it is energy that is stored, while kinetic energy is energy that is in motion. Potential energy can be converted into kinetic energy and vice versa.

Question 3: What are the different types of potential energy?

The two main types of potential energy are gravitational potential energy and elastic potential energy. Gravitational potential energy is associated with an object's position relative to the Earth's surface, while elastic potential energy is associated with the stretching or compressing of an elastic material.

Question 4: How is potential energy measured?

Potential energy is measured in joules (J). The amount of potential energy an object has depends on its mass, height, and the strength of the force acting on it.

Question 5: What are some examples of potential energy?

Some examples of potential energy include a stretched rubber band, a book on a shelf, a rollercoaster at the top of a hill, and a compressed spring. These objects have the potential to do work when released or allowed to move.

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