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Re: Egg drop (was Re: momentum)



I found David Hamilton's three views of the egg-drop challenge very
good because he helped me see what some good teachers are trying to
accomplish with the students. Unfortunately I've been more accustomed
to reading or hearing hand-waving arguments about conservation of
energy that haven't made sense to me. And when I've had the
opportunity to ask more questions, the answers (from both students and
teachers) did not bring enlightenment.

I do have a few comments about David's posting.

In David's second paragraph when he discusses the egg's change in KE
and how we try to spread that change over greater distance, etc... I
have primarily semantic comments. First, I agree that this view is
identical to the momentum/impulse view. Although I have heard this
view described as an example of conservation of energy (which David did
not do), I believe that wording is not helpful. I believe the more
helpful way to classify this analysis is as an example of the
work-energy theorem. The work to bring the egg to rest is set equal to
the required change in kinetic energy. Work is integral(Fdx). We can
graph the process using a force-versus-distance graph. The area under
the curve is the change in kinetic energy, and we can have large force
and small distance (which breaks the egg) or small force and large
distance (which might save the egg). This graph is nearly identical to
the impulse graph (force-versus-time) and the goals are the same: keep
the graph area constant while reducing the magnitude of the force. And
I believe this graphical approach with either F-versus-t or F-versus-x
can be used even in non-calculus-based courses.

It is not surprising that the impulse/momentum and work-energy views
yield nearly the same treatment. The analysis is easier if we use
calculus, but non-calculus approaches can yield similar results.

dW = Fdx = (dp/dt)dx = (mdv/dt)dx = (mdv)(dx/dt) = (mdv)(v)

integrate to get:
delta-W = 1/2 m v^2.

That is, we typically derive the work-KE theorem from Newton's second
law as shown above. If momentum has been introduced prior to KE, then
we start with F = dp/dt. If not, then we start with F = ma. Once we
remember that the work-energy theorem utilizes F = dp/dt and then we
realize that the rearrangement of this (dp = Fdt) leads to the
definition of impulse, we see how exactly correct David is when he says
the impulse/momentum treatment and the "work/energy" (my words)
treatment are identical.

In David's third paragraph about conservation of energy, David has
helped me see that some teachers are not necessarily treating the egg
drop as an example of conservation of energy (i.e. "this proves energy
is conserved"), as much as they are trying to ask the question (and
then control) "where does the energy go." We ask, is most of the
original kinetic energy of the egg eventually going to end up as
thermal energy in the container (with possible survival of the egg) or
is it going to end up as thermal energy in the egg (with destruction of
the egg)? I accept this as a valid viewpoint.

I have two further comments about this last viewpoint. (1) I would
hope that teachers use it carefully and that they also bring the other
two viewpoints into the discussion. As mentioned, my experience is
that this third view is often the only view presented, and it has not
always been presented very clearly. (2) Although David's example of
using toothpicks and glue is a good one, it does primarily emphasize
the third view, and it appears to require the destruction of the
vehicle. If I were judging an egg-drop contest, I would give "extra
credit" to students who designed a container/vehicle that could be
reused. Although, in the end, the KE still needs to transfer primarily
to thermal energy in the vehicle, requiring that the vehicle be
reusable might make the students look harder at the first two views.

Probably Jim Birdsong was trying to tell me the same thing that David
Hamilton told me, but I didn't get it. Sorry Jim.

Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817