Defining Mechanical Energy: A Scientist's Perspective

[jmsmith]

Hello,

What would be a good definition of mechanical energy? I currently encounter the following two:
1) "Mechanical energy: energy that is mechanical"
2) "Mechanical energy: the sum of kinetic energy and potential energy."

I am disatisfied with the first definition due to the obvious redundancy. I am disatisfied with the second definition because it seems obviously wrong to me. What about forms of kinetic energy and potential energy that are not mechanical (thermal, chemical, nuclear, etc)? How exactly do we define kinetic energy, potential energy, and mechanical energy to be consistent with each other and the world? If that second ME definition is truly appropriate, what am I mis-understanding?

Also, a side question (possibly relevant to the questions above): How do we classify the energy carried by mechanical waves? How does the energy carried by mechanical waves relate to mechanical energy (if at all)?

 

[montecarlo]

Hello. The first definition is tautological and cannot give any additional info! The second definition is fine. Remind this, too: kinetic + potential = mechanical = energy that is conserved in presence of conservative forces.
Thermal energy is ultimatively kinetic energy. With nuclear energy you enter the subatomic world and you get energy-mass conversion, so this is beyond the domain and definitions of classical physics.
Is that alright? Please ask for more if I am ambiguous or obscure.

 

[Dr.D]

The definition of mechanical energy as the sum of kinetic and potential energies is workable.

Do not include thermal energy, even though that is kinetic energy at the molecular level, because it is not recoverable directly.

You asked about other forms of kinetic and potential energy that are not mechanical (thermal, chamical, nuclear, etc). Nuclear is again essentially thermal energy, so it is kinetic energy of a sort but not what should normally be considered mechanical energy. Chemical energy is potential energy because it is stored energy, just as energy might be stored in a spring. I'm not sure what you are asking when you say, "What about...?" Well, what what about? They are not mechanical energy.

Energy carried by mechanical waves is definitely mechanical energy. It carries kinetic and potential energy.

 

[jmsmith]

Thermal energy is ultimatively kinetic energy.

I think this is where I have the problem: Mechanical energy = kinetic energy + potential energy. However, we do not include certain forms of kinetic energy (such as thermal energy) or potential energy (such as chemical energy) in the equation. This seems to be inconsistent to me. What do you think?

(As an aside: I am more involved on the science education side than the science research side. Therefore, I am concerned with having a definition that makes sense, not just to me, but to students as well.)

 

[Dr.D]

The definition is essentially based on what forms of energy will be naturally involved in a mechanical process, without making provisions for combustion, nuclear reactions, etc. to occur. Thus if we limit the process to things like blocks sliding on guides, impacts, geared mechanisms, various machines, etc., these involve only kinetic and potential energy. To drive them it is often necessary to put energy in from some other source, such as an electric motor, but the electrical energy is not considered a form of mechanical energy. It goes through an electro-mechanical conversion process to become mechanical energy in the system in that case.

 

[jmsmith]

Thank you for keeping up the replies Dr.D. I think that we generally have the same "sense" of mechanical energy. However, I don't think that I could give a useful and accurate definition of mechanical energy to student.

A side question: What kind of energy do machines have as we make them smaller and smaller? Is there a point when we would begin to think of a microscopic machine has a form of energy other than mechanical energy?

 

[alxm]

Remember that energy is a relative property. There really isn't such a thing as 'absolute' energy. When you speak of energy, you are always speaking of energy of one state relative the energy of another state.

So it follows naturally then, that when you speak of the energy of a system, you're only speaking of the energy that changes, or which is relevant to whatever is changing in your system. E.g. if the temperature is constant, there is no reason to include thermal energy in your description of the system.

 

[Dr.D]

Your question about "smaller and smaller" suggests the nature of your problem in formulating a definition. You seem to want a definition that applies to everything, and that, while perhaps desirable, may not be feasible. If you keep your definition to macroscopic machines, then I don't think there is really much problem. If you want to go to microscopic machines, then I don't don't know what to say to you; I don't deal in such things myself. I've gotten by 50 years with the understanding of mechanical energy that I tried to convey to you, but then I never had any interest at all in MEMS. I might suggest to your students that they start with things big enough that they can see them and understand those well before they try to understing microscopic machines.

Classically, mechanical energy consists of kinetic energy of moving masses and the potential energy stored in the gravitational field and in the deformation of elastic bodies.

 

[Astronomer@14]

I am amazed that my feeble mind even understands half of this topic! I am an eighth grader writing an essay on the forms of energy. And I was wondering if someone could please speak in simple words and maybe I could understand this better. What makes this energy be released and how does it work really? I am sorry that I can't narrow my question down any further because I am truly nowhere now!

 

[Dr.D]

Astronomer, consider a really simple case as an example of energy release.

Suppose you swing a hammer in order to drive a nail. While you are swinging the hammer, your muscles are doing work on the hammer in order to increase its kinetic energy. Just before it hits the nail, it is moving pretty fast and has considerable energy stored as kinetic energy. When it hits the nail, the nail moves into the wood, doing work against friction. This causes the nail to get hot as the friction work is converted to heat. If you put you finger on the nail head right after you hit the nail, you will feel that it is quite warm. Thus the work done by your muscles has caused the nail to be driven into the wood and the energy finally is dissipated as heat.

Hope that helps.

 

[Astronomer@14]

Thank you so much! That actually clears things up a lot. Actually right before I was checking my email, I remembered my textbook, although with both explanations I seem to be in a lot better position now to do my work. Thanks again.