# B What is energy?

#### Avalon_18

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.

#### BvU

Homework Helper
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.

#### Merlin3189

Homework Helper
Gold Member
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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#### PeroK

Homework Helper
Gold Member
2018 Award
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.

#### Dale

Mentor
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.

#### BeedS

Do all forms of energy manifest as motion?

#### PeroK

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Gold Member
2018 Award
Do all forms of energy manifest as motion?
Can you think of any that don't? See the list in post #4.

#### BeedS

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

#### PeroK

Homework Helper
Gold Member
2018 Award
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
I might question whether potential, chemical and nuclear are directly "motion".

#### Dale

Mentor
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.

#### jtbell

Mentor
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.

#### A.T.

While I was doing some practice questions it hit me "what is energy".
A quantity that is conserved in an isolated system over time.

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.

#### BeedS

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?
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?

#### Dale

Mentor
What work doesn't involve moving something?
None. $dW=F\cdot dx$

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.

#### BeedS

Sure, but it is still energy.
Yes in a stable configuration.
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

#### Dale

Mentor
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.

#### Twodogs

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.

#### Dale

Mentor
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.

#### Twodogs

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.

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