Egg drop (was Re: momentum)

["David J. Hamilton" <djhamil@TELEPORT.COM>]

Michael,

Your arguments about the physics of the collision were very helpful to
me.  However, I'm having trouble with your insistance that an egg drop
challenge is primarily a momentum change problem.  It seems equally
approachable from either a momentum or an energy analysis.  In fact there
are two energy analyses that are useful.

Change in momentum view:  The impulse required to change the momentum of
the egg+container is fixed; therefore, increasing the time of impact
reduces the average force on the egg.  This is a preferable treatment
when delta-t is of concern.  When designing a container, I wish to build
a device that will expand the time of impact.

Change in KE view:  The work required to change the KE of the
egg+container is fixed; therefore, increasing the distance over which the
egg is stopped reduces the average force on the egg.  This is a
preferable treatment when delta-y is of concern.  When designing a
container, I wish to build a device that will expand the "stopping
distance" of the egg. This explanation is identical in form to the change
in momentum view.  I see no "built-in" preference for examining the time
of impact vs. the distance over which the impact occurs.

Conservation of energy view:  In my version of the egg drop, students may
use only wooden toothpicks and Elmer's glue.  This makes the collision
quite inelastic.  I tell my students that the KE of the egg+container
must "go" somewhere (Sorry, Jim -- it's a useful metaphor).  It is
preferable that the energy is used to break the toothpicks than to break
the egg.  (I challenge my students to explain how energy is conserved
while breaking a toothpick.)

Any one of these explanations is sufficient for planning a strategy for
an egg drop.  Why should one be the preferred explanation?  Why not ask
students to understand all three?

Dave

Michael Edmiston writes:

> Jim Birdsong says...
>
> <quote>
> You wrote that discussing an egg drop vehicle experiment in terms of
> energy
> is wrong.  I heartily disagree.  It is very instructive for students to
> design ways to not only increase the time of the impact (as you stated)
> but
> to decrease the required momentum change by decreasing the kinetic
> energy of
> the vehicle (through drag force or rotation).  I don't find physics can
> be
> compartmentalized so much as you state.  Energy and momentum should be
> considered together by students, because they "occur" together."
> <end quote>
>
> In the rules I have seen for egg drop experiments, drag devices (like
> parachutes) are not legal.  The egg-carrying device must hit the floor
> after a free fall.  All entries in the contest must hit the floor at
> the same velocity.
>
> Even if this were not so, I would not view that we are trying to reduce
> the momentum change by reducing the kinetic energy.  I would view that
> we are trying to reduce the momentum change by reducing the impact
> velocity.  Granted, reducing the impact velocity, reducing the required
> momentum change, and reducing the impact kinetic energy amount to the
> same thing.  There just isn't any reason to invoke kinetic energy.  If
> there's no reason to invoke it, why cloud the issue with extraneous
> physics?
>
> This whole experiment can be carried out, and properly designed
> egg-vehicles can be built, without ever mentioning energy.  This is
> true regardless of whether reduced impact velocity is allowed or not
> allowed.
>
> I certainly agree that many aspects of our physics equations and
> conventions occur simultaneously in most experiments.  And it is
> sometimes useful to examine everything going on.  Obviously it is
> worthwhile to bring energy considerations into discussion of collisions
> because we find it useful to divide collisions between elastic
> collisions and inelastic collision.  If we have elastic collisions,
> then conservation of kinetic energy gives us additional equations to
> analyze the motion (in addition to the momentum equations).  But once
> we establish the collision is inelastic, then we don't have any
> conservation of energy equations that can bring any more insight into
> the motion; we only have the momentum equations.  (Unless we somehow
> can know the percentage of elasticity... something we typically would
> not know until after we solve the momentum equations.)
>
> In contrast to considering everything that "occurs together" I would
> say that is important to guide students to view experiments with the
> goal of trying to ascertain the most critical aspects.  We don't want
> them to lose sight of the forest because of the trees.  Thus, my beef
> with bringing KE into the egg drop experiment is that it is not needed,
> and worse, it can obfuscate the fact that this is primarily a delta-p =
> F(delta-t) experiment.  Seat belts, air bags, catching baseballs,
> egg-drop experiments are all good examples for teaching
> impulse/momentum.  They are not very good examples for teaching
> conservation of energy.
>
> A science booklet published by the State of Ohio Department of
> Education intended to help high-school science teachers actually
> recommends the egg-drop experiment as a way to teach conservation of
> energy, and it never mentions momentum or impulse.  As I read it, it
> just doesn't make any sense.  The writers of that booklet clearly lost
> sight of the forest because of all the trees.
>
> 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


David J. Hamilton, Ed.D.          *  And gladly woulde he learn,
Portland Public Schools           *  and gladly teche.
djhamil@teleport.com              *        - Chaucer