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Re: third law forces cancel?



Larry Smith 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?

I would hope that they are the answers to two different
questions, so neither one is wrong, and there is no
discrepancy. (One would need to provide more context
to convert this hope to a certainty.)

> 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?

The 3rd law force statement means the same thing as conservation
of momentum. Whenever I'm confused about a 3rd-law force issue,
I reformulate it as a conservation of momentum issue. (Of course
the formulation in terms of forces remains useful also.)

The law of conservation of mometum applies region-by-region.
The change in momentum in any given region equals the flow
of momentum across the boundary of that region. If you
choose a region that includes only object k, the law tells
you something useful. If you choose a region that includes
both object k and object j, the law tells you something else,
also useful.

The force equation
F_{k on j} + F_{j on k} = 0
expresses the global conservation of momentum, which is a
good thing (but not the only good thing).

Global conservation doesn't tell the whole story; we also
need local conservation. Local conservation implies global
conservation but not vice versa.

Telling kids to pay attention to the _local_ balance of
forces is a useful recommendation, especially as a starting
point, but it does not exclude paying attention to the
global balance of forces also.

A good exercise is to consider the forces in a static
weightless chain under tension.
-- There is a local balance of forces for each link.
-- You can parlay this (by induction) into a global
balance of forces, involving just the force on the
two points of attachment.