Re: work done by friction

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Thu, 28 Oct 1999, Robert Carlson wrote:

> Leigh,
>
> ... You write:
>
>                    1           2      2
>               WA = - MA * ( VAf  - VAi  )
>                    2
> and:
>                    1           2      2
>               WB = - MB * ( VBf  - VBi  )
>                    2
>
> Where I would have written:
>
>                    1           2      2
>               WA = - MA * ( VAf  - VAi  ) + CA*(TA - Ti)
>                    2
> and:
>                    1           2      2
>               WB = - MB * ( VBf  - VBi  ) + CB*(TB - Ti)
>                    2

This is because Bob is using a different definition of work.  As I pointed
out in a message that crossed in the mail, Leigh was using what is often
called "pseudowork." Pseudowork can be shown to be equal to the change in
the bulk translational kinetic energy of the system.  On the other hand,
Bob is (implicitly) using the one that Harvey Leff and I call the
"frame-specific external work."  This work is defined as the sum of the
integrals of each individual external force over the parallel component of
the motion with respect to some inertial reference frame of its point of
application.  It can be shown to be equal to the change in the total
energy of the system. Once again, hard to say carefully enough in words!
See the paper.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm