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Re: Energy, etc



Brian,

Thanks for your comments and clearing up some cobwebs in my mind. You
summarized the main issue here as follows:

On Mon, 9 Aug 1999, Brian McInnes wrote:

There is a similar looking equation coming for Newton's second law
being applied to the changing motion of the skater's centre of mass.
It is: F(net) delta s(centre of mass) = delta (1/2 mv(center of
mass)*2. That relates the change in kinetic energy of the body to
something that, on quick inspection, could be mistaken for the work
done on the skater but is not that. Ian Sefton, in his useful
contribution to this thread noted that this term is sometimes called
psuedo-work. Whatever we choose to call it, it certainly is not the
work done by the net force (which happens to be equal to the force
applied by the contact force from the wall) because that work is zero.

To make sure I understand you, I'd like to rephrase the problem.
Please correct me if I am wrong, but I believe my mistake here was to use
Newton's Law to derive an expression for work. As Arons' says, the
"work-kinetic energy theorem" is obtained by integration of Newton's
Second Law, but the "work-kinetic energy theorem" does *not* contain a
term called "work" (Arons' calls the term "psuedo-work"). A re-reading of
Arons suggests that he thinks the problem is the tendency for people to
equate the "work-kinetic energy theorem" with "conservation of energy".

Let me first state that I am not arguing that they are equivalent
(although I think they are much more similar than Arons seems to be
implying). In addition, I hadn't intended to argue that the "work-kinetic
energy theorem" contained a term called "work" but I admit that I ended up
doing so just out of my own stupidity. Indeed, I wouldn't say that the
wall did work, although now I realize that the wall does do "psuedo-work".

Rather, I was arguing that the work-kinetic energy theorem, as with
Newton's law, can still be applied to the situation. Although it may not
be the "best" approach, I felt that stating that it cannot be applied to
extended systems was implying that it was invalid or incorrect.

Perhaps the following problem illustrates what I mean. A block is on a
frictionless surface and attached to a horizontal spring (note: it doesn't
have to be horizontal and frictionless but it simplifies the problem). The
spring is attached to a immovable wall. If the spring is initially
compressed, then as the spring extends, the block on the end speeds up.

Question #1: As the block speeds up, is any work done on the block?

Question #2: As the spring/block system speeds up, is any work done on the
spring/block system?

The former is typical of standard textbook problems that illustrate the
"work-kinetic energy theorem". The latter is analogous to the skater
pushing against the wall. My attempt was to restate the latter question
in terms of the former. In other words, although it may be misguided to
ask if any work is done on skater (arm/body system), it is helpful (at
least to me) to see that the wall/arm is doing work on the body of the
skater in much the same way as the wall/spring is doing work on the block.

Any comments?

----------------------------------------------------------
| Robert Cohen Department of Physics |
| East Stroudsburg University |
| bbq@esu.edu East Stroudsburg, PA 18301 |
| http://www.esu.edu/~bbq/ (570) 422-3428 |
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