Re: third law forces cancel?

[Herb Schulz <herbs@WIDEOPENWEST.COM>]

On 10/11/04 11:34 AM, "Larry Smith" <larry.smith@SNOW.EDU> wrote:

> Many authors say that N's 3rd law pair forces do not cancel because they
> are acting on different (i.e. opposite) objects.  Randy Knight, in his new
> PER-based textbook, says, in his discussion of conservation of momentum,
> that
> \vec{F}_{k on j} + \vec{F}_{j on k} = \vec{0}.  Is the discrepancy between
> these two statements real or imagined?  Would you tell your students one or
> both or neither of these statements?  I have told students that we don't
> even add forces on different objects together; should I not have?  What's
> the best pedagogical approach to this?  Further comments?
>
> Thanks in advance,
> Larry

Howdy,

\vec{F}_{k on j} + \vec{F}_{j on k} = \vec{0} is just a statement of
Newton's 3rd Law and is certainly correct.

However, I think you're mixing apples and oranges and there is no
discrepancy between the statements.

Newton's 2nd Law for object j only involves the forces acting ON object j so
it doesn't include \vec{F}_{j on k} since that acts on object k (k \ne j).
Therefore the first part of your statement is also true and they don't
conflict.

If you are trying to derive Momentum Conservation from Newton's 2nd Law for
each of the objects you will add the two 2nd Law equations and then the sum
of those ``internal'' (to the system of the two object) forces will cancel
so only the external forces acting on the system of two objects are left.

Good Luck,

Herb Schulz
(herbs@wideopenwest.com)