126
The figures show two somewhat more practical laboratory experiments
for investigating this issue accurately and without too much interference
from extraneous forces.
In the first experiment, a large magnet and a small magnet are weighed
separately, and then one magnet is hung from the pan of the top balance so
that it is directly above the other magnet. There is an attraction between the
two magnets, causing the reading on the top scale to increase and the
reading on the bottom scale to decrease. The large magnet is more “power-
ful” in the sense that it can pick up a heavier paperclip from the same
distance, so many people have a strong expectation that one scale’s reading
will change by a far different amount than the other. Instead, we find that
the two changes are equal in magnitude but opposite in direction, so the
upward force of the top magnet on the bottom magnet is of the same
magnitude as the downward force of the bottom magnet on the top mag-
net.
In the second experiment, two people pull on two spring scales. Regard-
less of who tries to pull harder, the two forces as measured on the spring
scales are equal. Interposing the two spring scales is necessary in order to
measure the forces, but the outcome is not some artificial result of the
scales’ interactions with each other. If one person slaps another hard on the
hand, the slapper’s hand hurts just as much as the slappee’s, and it doesn’t
matter if the recipient of the slap tries to be inactive. (Punching someone in
the mouth causes just as much force on the fist as on the lips. It’s just that
the lips are more delicate. The forces are equal, but not the levels of pain
and injury.)
Newton, after observing a series of results such as these, decided that
there must be a fundamental law of nature at work:
Newton's Third Law
Forces occur in equal and opposite pairs: whenever
object A exerts a force on object B, object B must also
be exerting a force on object A. The two forces are
equal in magnitude and opposite in direction.
In one-dimensional situations, we can use plus and minus signs to indicate
the directions of forces, and Newton’s third law can be written succinctly as
F
A on B
= –F
B on A
.
There is no cause and effect relationship between the two forces. There
is no “original” force, and neither one is a response to the other. The pair of
forces is a relationship, like marriage, not a back-and-forth process like a
tennis match. Newton came up with the third law as a generalization about
all the types of forces with which he was familiar, such as frictional and
gravitational forces. When later physicists discovered a new type force, such
as the force that holds atomic nuclei together, they had to check whether it
obeyed Newton’s third law. So far, no violation of the third law has ever
been discovered, whereas the first and second laws were shown to have
limitations by Einstein and the pioneers of atomic physics.
magnet
magnet
scale
scale
(a) Two magnets exert forces on each
other.
(b) Two people’s hands exert forces
on each other.
Chapter 5Analysis of Forces