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Re: Why work before energy in texts




I mistakenly thought the argument was which to use first in an intro text
i.e..
HS w/ at most algebra. Many posts talk about integrals, etc. It was my
assumption that it was "bone head" physics, and that is why I suggested
what was
kinesthetic be intro'd first i.e. pushing a lawn mower and Mgh, next KE and
springs.

bc

Point well taken, Bernard. Let me mumble for a bit:

Despite what some text might do, I would never present either work or
energy first. Even though the idea of energy was not derived this way
historically and I think that a historical approach is clearly best for
novice students, this is a case where a non-historical approach does not
bend their minds. The W/E principle comes first. These two concepts are
inextricably interdependent and need to be presented together. There can
be no change in the level of energy of a system without doing work on the
system. (Now if your class is really "bone head" it may take a few lectures.)

First Day: Class here I have a wheeled fligit. If I push the fligit on a
horizontal table (an air-track would be better but alas...), it goes
fast. But if I push for a greater distance, it goes faster. If I push
harder, it goes faster still. If I push a less massive fligit, the begger
really zooms.

Let's call 0.5mv^2 the energy of the fligit and the force times the
distance the work I did on the fligit. Class after you take the calculus,
you will understand how this is derived. Greater work; greater increase in
the level of the energy. ie W==Fxd = deltaE -- always and necessarily

Next day (or maybe a few days later): Consider this book. I raise the
book. Why doesn't the book continue the way the fligit did? Yes, there
are two forces on the book: my hand and gravity. Because the forces are
equal and opposite the work done by each cancel - and I get no increase in
the level of energy. But if I let go of the book, the work done by the
single force of gravity can cause an increase in the level of energy of the
book. See!

Now if I slide the book across the table slowly, there are again two
forces acting -- my hand and friction -- and the work done by each force
cancels. See the book does not continue to move -- the level of energy is
not increased. {A little lie to be corrected later -- necessary because I
haven't introduced KE yet}

What is the difference between gravity and friction? With gravity I can
get a subsequent increase in the level of energy and with friction I can
not. Let me call such forces conservative and non-conservative.

Because the work done by conservative forces has the potential to increase
the level of energy of the system, I will call this work, deltaPE. And I
will call the first energy KE.

So Wnc + Wc== Wnc + deltaPE = deltaKE

But things look better (and will later give rise to unbelievable grief and
confusion because of the reificaton of energy) if I change signs and write

Wnc=deltaKE + deltaPE

And we have work and both PE(-Wc) and KE(E) all at the same time. And
the students understand what is going on and why much better.

Now, Bernard, there are gaps to fill in but I know that you and everyone
else can do this and all of the above much better than I.

Jim Green
mailto:JMGreen@sisna.com
http://users.sisna.com/jmgreen