Reconciling Potential Energy and Work: Understanding the Relationship

In summary, potential energy is energy that is stored due to a difference in an object's potential energy and actual energy. It is considered to be part of the work done in an equation, but is considered energy in the conservation of energy equation.
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Opus_723
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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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  • #2
Hi Opus_723! :smile:

potential energy is defined as (minus) the work done by a conservative force (such as gravity)
Opus_723 said:
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 :wink:
 
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Okay. I was thinking it was something like that, where I was just fuzzy on how it's defined. Thanks for the clarification.
 

1. What is potential energy?

Potential energy is the energy that an object possesses due to its position or condition. It is a form of energy that is stored and has the potential to be converted into other forms of energy, such as kinetic energy.

2. How is potential energy calculated?

The formula for calculating potential energy varies depending on the type of potential energy. For gravitational potential energy, the formula is PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the object's height above a reference point. For elastic potential energy, the formula is PE = 1/2kx^2, where k is the spring constant and x is the displacement from equilibrium.

3. What is the relationship between potential energy and work?

Work is defined as the transfer of energy from one object to another. When an object moves from a higher potential energy to a lower potential energy, work is done on the object. The amount of work done is equal to the change in potential energy. In other words, work and potential energy are directly proportional.

4. Can potential energy be negative?

Yes, potential energy can be negative. This usually occurs in situations where the reference point for measuring potential energy is chosen arbitrarily. For example, if the reference point is set at the top of a hill, an object at the bottom of the hill would have negative potential energy.

5. How is potential energy related to the conservation of energy?

According to the law of conservation of energy, energy cannot be created or destroyed, only transferred or transformed. Potential energy is a form of energy that can be converted into other forms, such as kinetic energy. Therefore, potential energy plays a crucial role in maintaining the total energy of a system and is closely related to the principle of conservation of energy.

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