Re: Why work before energy in texts

["John S. Denker" <jsd@MONMOUTH.COM>]

At 11:54 AM 10/14/01 -0400, Robert Cohen wrote:

> 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.

Physically, it looks fine to me, subject to the provisos I posted this morning:
 -- point particle, or object with no internal degrees of freedom,
 -- undergoing uniform acceleration.

This D=2 derivation is clearly superior to taking the D=1 formula plus lots
of hand-waving to produce the D=2 formula.

The pedagogical value depends on how it is used.  It's a cute result, but I
wouldn't recommend over-selling it;  it's not one of the cornerstones of
physics.

> That is my question - why isn't this approach used in textbooks?

No comment.  I'm only responsible for what I write, not what other people
write.