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Re: ENERGY WITH Q



On Sat, 1 Dec 2001, Eugene Mosca wrote:

John Mallinckrodt wrote:

At time t, the center of mass of the gas
lies at a distance L/4 from the end on which you are pushing.

i) Now can you determine the distance that the container has
moved? If so, what is it?

Yes. The container has moved a distance Mv^2/F + L/8.
(IMO, the proof of this is not at all trivial without a clear
understanding of a variety of work-energy relationships.)

It seems to me this involves an understanding of only the center-of-mass
work-translational kinetic energy relation. Am I missing something?

You're right, of course. I made it more complicated than I needed
to by following this logical (but unnecessarily tortured)
sequence:

1. Use the *relationship* between W_cm ("center of mass work)
and the change in bulk kinetic energy

W_cm = change in bulk kinetic energy
= MV^2

2. Use the *definition* of w_ext (external work in the CM frame)

w_ext := F*(displacement of pt of application wrt CM)
= FL/8

3. Use the *relationship* between W-ext (external work in the
lab frame), w_ext, and W_cm

W_ext = W_cm + w_ext
= MV^2 + FL/8

4. Use the *definition* of W_ext

W_ext := F*(displacement of pt of application wrt lab)
= Fd

5. and, finally, solve for the distance d

d = MV^2/F + L/8

As you point out, however, it is enough 1) to use the relationship
between center-of-mass work and change in bulk translational
kinetic energy, 2) to correctly apply the definition of center of
mass work to determine the distance that the CM has moved, and 3)
to determine that the cylinder has moved a distance L/8 more than
the CM.

So maybe this problem doesn't require the full machinery that I
had hoped it would. On the other hand, I believe it does at least
point out the importance of the "center of mass work" (i.e.,
"pseudowork") concept.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm