Understanding the Concepts and Formulas for Energy: Potential and Kinetic

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In summary, energy is a measure for work. Energy can be converted into other forms of energy, but when work is being done, something is converted to KE.
  • #1
Avalon_18
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While I was doing some practice questions it hit me "what is energy". I also don't understand how the formulas for potential and kinetic energy were derived. Was it due to their definitions or is there some reason behind their respective formulas.
 
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  • #2
Energy is a measure for work: if you do some work to move a book from the bottom shelf to the top shelf, the difference in potential energy of the book is the work you have done. Establishing a zero point for energy is awkward because in the real world all we have is energy differences.
 
  • #3
An interesting question to which I do not know the answer! My recollection is that I first thought about energy when learning about Joule and work-heat equivalence. But maybe I'd met KE before and not thought much about it.

If you do have a concept of KE, then PE seems obvious. When an object falls, it gains speed and hence KE due to the acceleration caused by gravity. So when an object is high up, it has the potential to gain KE by falling. Or if an object has speed, KE, then it has the potential to rise up against gravity.

Quantitatively the change in KE with height when moving in a gravitational field works out at mgh, so that becomes the PE.
 
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  • #4
Avalon_18 said:
While I was doing some practice questions it hit me "what is energy". I also don't understand how the formulas for potential and kinetic energy were derived. Was it due to their definitions or is there some reason behind their respective formulas.

There are many videos online on the subject "what is energy?". Perhaps what they all have in common is that it is not, in general. easy to define. One simple approach is to leave it essentially undefined, but list the different forms it can take: kinetic, potential, chemical, thermal, nuclear, radiation.
 
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  • #5
Avalon_18 said:
While I was doing some practice questions it hit me "what is energy". I also don't understand how the formulas for potential and kinetic energy were derived. Was it due to their definitions or is there some reason behind their respective formulas.
There are several equally valid definitions used in different branches of physics. In Newtonian mechanics energy is defined as the capacity to do work. In thermodynamics an approach like @PeroK is used, energy is defined as kinetic energy (##\frac{1}{2}mv^2##) and anything that can be converted to kinetic energy. In Lagrangian mechanics it is defined as the conserved quantity associated with time translation symmetry of the Lagrangian.
 
  • #6
Do all forms of energy manifest as motion?
 
  • #7
BeedS said:
Do all forms of energy manifest as motion?
Can you think of any that don't? See the list in post #4.
 
  • #8
PeroK said:
Can you think of any that don't? See the list in post #4.
No
kinetic = Motion
potential = potential to move
chemical = Motion caused by interactions of atoms / particles
thermal = Motion of heat energy
nuclear = motion of particles and subatomic
radiation = Motion of photons
 
  • #9
BeedS said:
No
kinetic = Motion
potential = potential to move
chemical = Motion caused by interactions of atoms / particles
thermal = Motion of heat energy
nuclear = motion of particles and subatomic
radiation = Motion of photons

I might question whether potential, chemical and nuclear are directly "motion".
 
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  • #10
BeedS said:
Do all forms of energy manifest as motion?
No. KE and thermal energy of an ideal gas are motion. Thermal energy of other materials would have some of its energy in internal degrees of freedom corresponding to motion, but could also have non motion internal degrees of freedom if available. Most other forms of energy are not necessarily manifested as motion, although of course they can all be converted into KE. For example, electromagnetic energy can move (radiation) but you can also have static electromagnetic fields which hold energy without moving.
 
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  • #11
Avalon_18 said:
While I was doing some practice questions it hit me "what is energy". I also don't understand how the formulas for potential and kinetic energy were derived. Was it due to their definitions or is there some reason behind their respective formulas.
Does your textbook say anything about this stuff? It would help if we can use it as a starting point for discussion. Is this a grade-school or university textbook? The university level textbooks that I've used all make at least some attempt at this.
 
  • #12
Avalon_18 said:
While I was doing some practice questions it hit me "what is energy".
A quantity that is conserved in an isolated system over time.

Avalon_18 said:
I also don't understand how the formulas for potential and kinetic energy were derived. Was it due to their definitions or is there some reason behind their respective formulas.
All the formulas for energy where defined such that the total energy is conserved in an isolated system over time.
 
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  • #14
Dale said:
although of course they can all be converted into KE
That is when work is being done, something is converted to KE. What work doesn't involve moving something?
Dale said:
For example, electromagnetic energy can move (radiation) but you can also have static electromagnetic fields which hold energy without moving.
No work is being done with the static field (PE), when work is done the field will move(KE) the charge or whatever is being moved/worked/energized?
 
  • #15
BeedS said:
What work doesn't involve moving something?
None. ##dW=F\cdot dx ##

BeedS said:
No work is being done with the static field
Sure, but it is still energy. The question was “do all forms of energy manifest as motion” not “do all forms of work manifest as motion”. Work and energy are closely related, but they are not the same thing.
 
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  • #16
Dale said:
Sure, but it is still energy.
Yes in a stable configuration.
Dale said:
The question was “do all forms of energy manifest as motion” not “do all forms of work manifest as motion”. Work and energy are closely related, but they are not the same thing.
So all forms of work manifest as motion? Judging by your "None. dW=F⋅dx" reply, then yes?
And I need to look into my understanding of work and energy.
Thanks
 
  • #17
BeedS said:
So all forms of work manifest as motion? Judging by your "None. dW=F⋅dx" reply, then yes?
Yes, the dx term is motion of the object on which work is done.
 
  • #18
Good question. I think you should hang on to it for a while. We can measure energy with incredible precision. We can describe its permutations with strict accounting. I don't know that we can say 'what' it is for the time being.
 
  • #19
Twodogs said:
I don't know that we can say 'what' it is for the time being.
Sure we can. I gave three definitions for what it is in post 5.
 
  • #20
Dale said:
Sure we can. I gave three definitions for what it is in post 5.

truth -- the quality or state of being true.
• that which is true or in accordance with fact or reality.
• a fact or belief that is accepted as true.

Certainly, you give a workable definition. Regards.
 
  • #21
BeedS said:
And I need to look into my understanding of work and energy.
Energy = current motion (Since everything is moving, energy is the current motion caused by previous work done)
Work = change of motion (result of changing a objects energy through KE)

Is this better?
 
  • #22
BeedS said:
Energy = current motion
What about potential energy?
 
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  • #23
A.T. said:
What about potential energy?

And we should not forget about the rest energy ##E = m c^2##. Quite a good example of a energy not associated with a particle's motion.
 
  • #24
A.T. said:
What about potential energy?
The object with potential is still created by things moving internally(sum of the objects scaled energy(its mass)). PE is potential motion, the PE object is still moving (KE) and has a potential to change that motion through work done.
 
  • #25
BeedS said:
the PE object is still moving (KE)
What about two opposite charges at rest? They have PE without moving.
 
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  • #26
A.T. said:
What about two opposite charges at rest? They have PE without moving.
At rest relative to what? Only to the object itself and something with the same motion as the object?. The charges are still moving with the charged objects. The charges are considered part of the objects mass (PE)? Charges do contain mass? Charges do move with the object they are bound to?
 
  • #27
BeedS said:
At rest relative to what?
Yes, every object that is at rest in one frame is moving in another. It does not follow that energy is motion or that rest is a meaningless concept.

Edit: You do realize that energy is a frame-relative concept? If we are talking about energy being present in an object at rest, we are working in a frame of reference within which the energy is non-zero and and the object is at rest.
 
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  • #28
BeedS said:
At rest relative to what?
Relative to the reference frame in which you calculate the energy.
 
  • #29
What is mass?
The dimension of time might be related to energy?

In E=MC2, what does it mean? The energy bound in mass?
 
  • #30
folkethefat said:
What is mass?
In relativity, it is a property of an object - a quantity which is invariant for all observers. But mass can be defined in different ways too: https://en.wikipedia.org/wiki/Mass

folkethefat said:
The dimension of time might be related to energy?
No idea what do you mean by your question.

folkethefat said:
In E=MC2, what does it mean? The energy bound in mass?
I think this short video provides a nice introductory explanation:
 
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  • #31
It really is just easiest to think about it as "the capacity to do work". Essentially, work is measured in terms of energy (work and energy have the same units). This is because energy by itself doesn't mean much, it is in reference to what is it able to physically do that matters. For example, it means little to say you have a certain amount of potential energy relative to 20 feet underground below you. You certainly could possesses this capacity to do work, but it is meaningless in the context of the physical situation - you are not able to fall through the ground. Because energy can only be transformed and not destroyed, you can think of any context of energy in terms of this definition.
 
  • #32
Kavorka said:
It really is just easiest to think about it as "the capacity to do work".
Having energy around doesn't mean you can do work. When you dissipate energy, there is still the same amount of energy in the from of heat, but it cannot by itself be used to do work.
 
  • #33
Is this correct then?
Time is measured by the ordering of events. "Events" always involves a change in energy. Energy is driving the change. So energy seems to be driving that which we measure as time?
 
  • #34
folkethefat said:
Is this correct then?
Time is measured by the ordering of events. "Events" always involves a change in energy. Energy is driving the change. So energy seems to be driving that which we measure as time?
I do not agree. An "event" is simply a location in four dimensional space-time. It does not involve a change in energy. How could it, since "energy" is a conserved quantity?

In particular, energy is the conserved quantity associated with time translation symmetry by Noether's theorem.
 
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  • #35
Avalon_18 said:
While I was doing some practice questions it hit me "what is energy".

There's no definition that will help when the concept is being refined and used in different contexts. After a while the different contexts provide you with enough experience that you feel comfortable with the concept of energy. Like how we feel comfortable with the concept of money.

I also don't understand how the formulas for potential and kinetic energy were derived. Was it due to their definitions or is there some reason behind their respective formulas.

Any college-level introductory physics textbook would have good explanations of those things.
 
<h2>1. What is potential energy and how is it calculated?</h2><p>Potential energy is the energy that an object possesses due to its position or state. It is calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.</p><h2>2. What is kinetic energy and how is it calculated?</h2><p>Kinetic energy is the energy an object possesses due to its motion. It is calculated using the formula KE = 1/2mv^2, where m is the mass of the object and v is its velocity.</p><h2>3. What is the relationship between potential and kinetic energy?</h2><p>Potential and kinetic energy are interrelated. When an object is at rest, it has potential energy due to its position. As it starts moving, this potential energy is converted into kinetic energy. The total energy of the object remains constant.</p><h2>4. How do changes in height or mass affect potential and kinetic energy?</h2><p>Changes in height or mass can affect the potential and kinetic energy of an object. An increase in height or mass will result in an increase in potential energy, while an increase in velocity will result in an increase in kinetic energy.</p><h2>5. Can potential energy be negative?</h2><p>Yes, potential energy can be negative. This occurs when an object is at a lower height than its reference point. In this case, the potential energy is calculated as a negative value, indicating that the object has less potential energy than at its reference point.</p>

1. What is potential energy and how is it calculated?

Potential energy is the energy that an object possesses due to its position or state. It is calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.

2. What is kinetic energy and how is it calculated?

Kinetic energy is the energy an object possesses due to its motion. It is calculated using the formula KE = 1/2mv^2, where m is the mass of the object and v is its velocity.

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

Potential and kinetic energy are interrelated. When an object is at rest, it has potential energy due to its position. As it starts moving, this potential energy is converted into kinetic energy. The total energy of the object remains constant.

4. How do changes in height or mass affect potential and kinetic energy?

Changes in height or mass can affect the potential and kinetic energy of an object. An increase in height or mass will result in an increase in potential energy, while an increase in velocity will result in an increase in kinetic energy.

5. Can potential energy be negative?

Yes, potential energy can be negative. This occurs when an object is at a lower height than its reference point. In this case, the potential energy is calculated as a negative value, indicating that the object has less potential energy than at its reference point.

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