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?