Several respondents to my posting on momentum
conservation have understandably gagged on the use of
the term "dissipated energy". I should have explained
the context in which it is used. The treatment of
"energy with less work" developed by Modeling leaders
emphasizes the introductory study of energy based on
these questions: Where does it come from? Where does
it go? How does it enter or leave a system? What does
it do? "Work" is not treated as a separate entity but
rather as the process of workING which simply
represents the transfer of energy into or out of a
system by mechanical means (action of a force).
Typically the system is chosen to include the surface
on which an object moves. Similarly we try to only use
the words radiatING (not radiation) and heatING (not
heat) to focus on the process of energy transfer while
avoiding the reinforcement of the incorrect concept
that there are different "kinds" of energy. So that is
why we speak of energy storage MODES rather than
different kinds of energy. That is, energy can be
stored in the movement of an object's CM (Ek), in a
gravitational field due to the object's elevation
above a reference level (Eg), or in a distorted spring
(Eel). There was a clear need to account for the
inefficiencies present when shifting energy from one
storage mode ("bin") to another. The word chosen was
"dissipated" (Ediss). When this topic is presented, it
is made VERY clear that this energy is not lost, but
is distributed throughout the system, typically
showing up as a temperature increase. It is energy
that still exists but is difficult to recover and put
to "use" in the form of Ek, Eg, or Eel. Perhaps
"irrecoverable" or "dilute" would be a better word?
But I think the word is less important than the
concept. I have used a physical analogy of Eg, Ek, and
Eel "buckets" between which energy may be "poured",
but each transfer is always accompanied by a little
"spillage" of energy into another (lower) container
from which it is very difficult to recover the energy
(the Ediss). Maybe I'm a bit like the newly converted
religious zealot, but I think that this approach
provides much more clarity and is still scientifically
correct. It completely avoids the pseudowork issues
(eg, "work done" by friction) that Sherwood and Chabay
have addressed. Instead we speak of "energy dissipated
by friction". I suppose we could say "energy converted
to increased internal kinetic energy which shows up as
a temperature rise", but I think Ediss is simpler and
creates no difficulties within the context it is
presented. This approach also bypasses the classical
work-energy theorem which is often presented as a
special case that only "works" when there is no
friction. Pie charts are employed as a visual way to
keep track of energy changes in a system during a
sequence of events. If no energy enters or leaves
(equivalent to the more traditional statement "no work
done by or on the system"), then the size of the pies
stays constant although the Ediss slice of the pie
always gets larger. If the process involves an object
coming to rest at the reference elevation, the entire
"final" pie is Ediss - not lost energy, but energy
that is no longer available (at least not easily).
Anyway, there were a couple of very helpful replies to
my original questions (thanks to David Emigh and Bob
Sciamanda). Does the following recapitulation make
sense? During the Pasco cart collision, momentum is
transferred during the entire time of contact (during
which forces act) but the motions of the CMs of the
cars (ie, the velocities) are only changed during a
portion of the contact time. That is, the integral of
Fdx occurs over a different (ie, shorter) time than
that during which there is momentum transfer. During
the "rest" of the time energy is "dissipated"
internally producing an increased internal energy
which does not contribute to CM motion. This sounds
pretty good to me, except that the "v" in "mv" is the
same as the "v" in "0.5mv2"; they're both the velocity
of the object's CM. Comments?
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