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Re: Why work before energy in texts



1) The "total work - kinetic energy" theorem as
proven by Chuck can easily be generalised to 3D.
Subdivide the entire 3D path into a sequence
od very short 1D segments and apply the theorem
to each segment. Then add the left sides to get
the total work done by the net force. A lot of
terms on the right side will cancel and you will
end up with KEf-KEi. Right?

2) I find it useful the emphasize another aspect
of the work-KE theoreme for a rigid body or particle.
It states that no matter how large a net force is
the work done by it never leads to to a change of
potential energy. It is illuminating to discuss
this in a classroom. The explanation is simple;
see item 4 below.

3)The W-KE theorem, even for a simple case of
a particle acted upon by a net force along a
straight line, is sufficient to demonstrate the
usefulness of the 0.5*m*v^2 expression and to
invent a special name for it. As emphasized by
JohnD, F is any NET force, even frictional or
electric.

4)After failing to find a simple derivation for
the PEspr=0.5*k*x^2 I am giving up the idea of
introducing energy without leaning on the concept
of work. Why bother? What is wrong with the way
in which I learned the sequence? It was:

PEgrv==work done against a weight (or -work by wieght)
PEspr==work done against a spring (or -work by spring)
PEelctr==(later) is work against the electric field.
In general work done against a conservative force
BECOMES POTENTIAL ENERGY ASSOCIATED WITH THAT FORCE
(energy=ability to do work). Is this acceptable or not?
Ludwik Kowalski

----- Original Message -----
From: Robert Cohen <Robert.Cohen@PO-BOX.ESU.EDU>
Date: Sunday, October 14, 2001 11:54 am
Subject: Re: Why work before energy in texts

I always introduce energy before work but only slightly so (as
shown below).
I thought the debate was whether we should go over forces before
introducingenergy or not. However, if the debate is just whether
we should introduce
energy before work, my vote in algebra-based courses is for energy
(slightly) before work much like Chuck Britton wrote.

Still, I have a question about the technique used to get work from the
kinematic equations (and F=ma)...

On Saturday, October 13, 2001 8:52 PM, Chuck Britton wrote (sans
eq #s):

kinematics usually involves the 'Four Magic Equations' of motion.
Each one 'leaves out' one of the four 'variables', d, v, a, or t.

The one that is missing t is usually written

Vf^2 = Vi^2 + 2ad

but can also be written:

1/2 Vf^2 - 1/2 Vi^2 = a d [eq 1]

multiplying through by mass gives us

delta KE = F d [eq 2]

which is a 'pretty good' intro of the Work Energy Thm.

While the above derivation works for 1-D motion, it seems many
algebra-based
textbooks then apply it to 2-D motion without really addressing
why we can
now use the magnitudes of V, a and d whereas before we had to have
separateequations for each component.

For example, in an equation like
Xf = Xi + Vi*t + 1/2 a*t^2
we do not use the magnitude of the total displacement (Xf-Xi), the
totalinitial velocity (Vi) and the total acceleration, without
regard for
direction.

Do people find that this confuses students? It confuses me. So,
in my
algebra-based course, I derive [eq 2] by combining the two component
equations:

Vf_x^2 = Vi_x^2 + 2a_x d_x
and
Vf_y^2 = Vi_y^2 + 2a_y d_y

to give

(Vf_x^2 + Vf_y^2) = (Vi_x^2 + Vi_y^2) + 2 (a_x d_x + a_y d_y)

which can then be written as

Vf^2 = Vi^2 + 2 (a dot d)

To me, this makes more sense since now it is more clear why work
is defined
as the dot product (i.e., with the cosine of the angle). Since I
don't see
this approach in the textbooks, I wonder if this is pedagogically or
physically correct. That is my question - why isn't this approach
used in
textbooks?

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