Re: Why work before energy in texts

[Robert Cohen <Robert.Cohen@PO-BOX.ESU.EDU>]

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 introducing
energy 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 separate
equations 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 total
initial 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              |
----------------------------------------------------------