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The English vocabulary for describing forces is unfortunately rooted in
Aristotelianism, and often implies incorrectly that forces are one-way
relationships. It is unfortunate that a half-truth such as “the table exerts an
upward force on the book” is so easily expressed, while a more complete and
correct description ends up sounding awkward or strange: “the table and the
book interact via a force,” or “the table and book participate in a force.”
To students, it often sounds as though Newton’s third law implies
nothing could ever change its motion, since the two equal and opposite
forces would always cancel. The two forces, however, are always on two
different objects, so it doesn’t make sense to add them in the first place —
we only add forces that are acting on the same object. If two objects are
interacting via a force and no other forces are involved, then both objects
will accelerate — in opposite directions!
Excuse me, ma'am, but it
appears that the money in your
purse would exactly cancel
out my bar tab.
It doesn’t make sense for the man to
talk about the woman’s money can-
celing out his bar tab, because there
is no good reason to combine his
debts and her assets. Similarly, it
doesn’t make sense to refer to the
equal and opposite forces of Newton’s
third law as canceling. It only makes
sense to add up forces that are acting
on the same object, whereas two
forces related to each other by
Newton’s third law are always acting
on two different objects.
Newton’s third law does not mean that
forces always cancel out so that noth-
ing can ever move. If these two figure
skaters, initially at rest, push against
each other, they will both move.
Section 5.1Newton’s Third Law
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