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Re: [Phys-L] defining energy



On 10/29/2013 5:14 PM, Bruce Sherwood wrote:
For a very simple example, consider stretching a spring with equal and
opposite forces applied at the ends. The net force is zero, the
displacement of the center of mass is zero, the pseudowork is zero, and the
change in the translational kinetic energy is zero. There is however real
positive work done by both forces, both of which act through displacements
in the direction of the force, and there is an increase of internal energy
of the system (the spring).



OK, let me continue with that example. Suppose that yesterday in class, I showed that a student applies an unopposed force as he pushes a crate on a frictionless table. By my definition (W=FD), he has done work. And since I can show that in this context, W=delta(.5mv^2), I call .5mv^2 the "motion-related work-changed quantity".

Now, today in this spring example, suppose that two students each pull the spring d/2. I'll have to introduce the idea of area under a graph for varying quantities (these are pre-calculus students) but in any case, the students will have done work. In this context, W=delta(.5kx^2). So now I call .5kx^2 another work-changed quantity, the "spring-related work-changed quantity".

Then tomorrow, I show a student lifting a mass at constant speed. Again, they have done work and now W=delta(mgh) so I call mgh the "position-in-a-gravitational-field work-changed quantity".



It seems to me that I am building a collection of quantities that have in common that they can be changed by work. I group them together under the abstraction "energy", a term that is short for "work-changed quantity". And since my definition of Work (F dot D for beginners, integral F dot dx for the next year) does not make use of the term "energy", there is nothing circular about this scheme. It seems to fall in with the way Feynman's story about the blocks talks about energy -- a collection of calculated quantities that are together conserved - as careful experimentation shows.

And as JD said, we can swap in P delta V later...


So to sum up: A student asks me: "I see the formula, but what _IS_ work?" I say: work is the number you calculate using F dot D.

Then the student asks: "I see all of these energy formulas. But what _IS_ energy?" I say: energy is the name we give to the collection of things we call specific types of energies, each of which can be changed by doing work -- which is why we care about the quantity F dot D enough to give it its own name!

Then we are ready to talk about what we mean by energy conservation (as opposed to what it means in colloquial use).