[Phys-l] What is energy? (a little long)

["Cliff Parker" <cparker@charter.net>]

Just wondering if some of you with more experience and knowledge than I will 
comment on part of my approach to describing the abstract nature of energy. 
I spend a good deal of time (most of a class period) talking with students 
about the meaning of mass.  They come to me in high school with a definition 
that is something like mass is the amount of "stuff" in an object.  The 
difference between weight and mass is not a significant problem for most of 
them.  I tell them that that was a pretty good start in middle school but is 
not good enough most of the time for us.  I ask them to tell me how they 
would find the mass of a stapler for example.  They all agree that they 
would use a triple beam balance.  I talk them into accepting the idea of 
using a simpler gravitational pan balance because I don't want to talk about 
torques etc.  They go along with that pretty well.  Then I ask them to 
consider what the pan balance "feels" or compares.  Pretty soon most agree 
that it is really feeling or comparing gravitational force or weight.  They 
know that weight and mass are not the same so they know that they would have 
just used a balance to compare weight and then they would have reported 
mass.  I suggest that this seems odd.  comparing weight and then reporting 
mass since clearly the two things are not the same.  About this time I take 
the opportunity to ask them for about the 50th time why they suppose they 
never questioned this approach before.  (I am always pointing out questions 
that they should have been asking all along, for example how do positively 
charged protons remain packed together in a nucleus, things like that)  So 
now we work on what might be a better definition of mass.  Eventually we 
come up with something like mass is the stuff in stuff that makes it 
gravitationally attracted to other stuff.  And that we really don't know 
what that stuff is because we have only measured it indirectly via 
comparison of weights.  OK, Ok, so about now they think they have a better 
understanding of this abstract thing called mass.  Then I introduce the idea 
of inertial mass.  I demonstrate an inertial balance and explain how it can 
be used to compare inertias of two or more objects.  We also discuss the 
idea that the amount of inertia an object has is related to the amount of 
mass it has.  However that object has this thing called inertia even in 
situations where we do not see this thing called weight. (the inertial 
balance works sideways and gravity doesn't care about this kind of motion, 
it can be used in free fall where gravitational balances can not, etc.)  Now 
after some prodding most are beginning to see that this thing in objects 
that we call mass is doing two different things.  We work next on coming up 
with yet another definition of mass.  This time it goes something like this. 
Mass it the stuff in stuff that makes it hard to accelerate.  Most begin to 
see that the only way we can measure mass is indirectly via weight or 
inertia.  There appears to be no way to measure mass directly.  In the end 
we come to the conclusion that not only does mass seem to have two different 
definitions but that neither one can be measured directly.  THE IDEA OF MASS 
IS FUZZY!

> From that foundation we later discuss energy.  Einstein's famous equation is 
brought into the picture.  In no way do I even attempt to explain relativity 
but we simply say that Einstein discovered this relationship between mass 
and energy.  He discovered that one can be turned into the other.  Now with 
our rather confusing foundation on the definitions of mass students seem 
willing to go along with the idea that energy is at least equally "FUZZY". 
I show a collection of about a dozen definitions of energy that I have found 
on reasonably reliable internet sights and although they all have some 
common ideas they don't really all get the job done in a nice clean way.  I 
end this presentation with a definition written by one of my clever students 
about five years ago.  It goes as follows "Energy is the stuff in stuff that 
makes stuff do stuff".  I think he got it.  At least he got what I wanted 
him to get.  Let the dissection and picking begin.

Cliff Parker