101
The idea of a numerical scale of force and the newton unit were intro-
duced in chapter 0. To recapitulate briefly, a force is when a pair of objects
push or pull on each other, and one newton is the force required to acceler-
ate a 1-kg object from rest to a speed of 1 m/s in 1 second.
More than one force on an object
As if we hadn’t kicked poor Aristotle around sufficiently, his theory has
another important flaw, which is important to discuss because it corre-
sponds to an extremely common student misconception. Aristotle con-
ceived of forced motion as a relationship in which one object was the boss
and the other “followed orders.” It therefore would only make sense for an
object to experience one force at a time, because an object couldn’t follow
orders from two sources at once. In the Newtonian theory, forces are
numbers, not orders, and if more than one force acts on an object at once,
the result is found by adding up all the forces. It is unfortunate that the use
the English word “force” has become standard, because to many people it
suggests that you are “forcing” an object to do something. The force of the
earth’s gravity cannot “force” a boat to sink, because there are other forces
acting on the boat. Adding them up gives a total of zero, so the boat
accelerates neither up nor down.
Objects can exert forces on each other at a distance
Aristotle declared that forces could only act between objects that were
touching, probably because he wished to avoid the type of occult specula-
tion that attributed physical phenomena to the influence of a distant and
invisible pantheon of gods. He was wrong, however, as you can observe
when a magnet leaps onto your refrigerator or when the planet earth exerts
gravitational forces on objects that are in the air. Some types of forces, such
as friction, only operate between objects in contact, and are called contact
forces. Magnetism, on the other hand, is an example of a noncontact force.
Although the magnetic force gets stronger when the magnet is closer to
your refrigerator, touching is not required.
Weight
In physics, an object’s weight , F
W
, is defined as the earth’s gravitational
force on it. The SI unit of weight is therefore the Newton. People com-
monly refer to the kilogram as a unit of weight, but the kilogram is a unit of
mass, not weight. Note that an object’s weight is not a fixed property of that
object. Objects weigh more in some places than in others, depending on the
local strength of gravity. It is their mass that always stays the same. A
baseball pitcher who can throw a 90-mile-per-hour fastball on earth would
not be able to throw any faster on the moon, because the ball’s inertia
would still be the same.
Positive and negative signs of force
We’ll start by considering only cases of one-dimensional center-of-mass
motion in which all the forces are parallel to the direction of motion, i.e.
either directly forward or backward. In one dimension, plus and minus
signs can be used to indicate directions of forces, as shown in the figure. We
can then refer generically to addition of forces, rather than having to speak
sometimes of addition and sometimes of subtraction. We add the forces
shown in the figure and get 11 N. In general, we should choose a one-
In this example, positive signs have
been used consistently for forces to
the right, and negative signs for forces
to the left. The numerical value of a
force carries no information about the
place on the saxophone where the
force is applied.
+8 N
+4 N
+2 N
-3 N
Section 4.1Force