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7-6 Potential energy is energy related to reversible changes in a system’s configuration 317

of motion), so the total amount of work you did to return the book to its initial
position would be zero. This looks like it might satisfy our statement that “if a force AP ® Exam Tip
exerted on an object does no net work during any closed loop then the force is said to Remember, a force is a way to
be conservative,” but it really points out something we need to be careful about when describe an interaction. Only
we see this common statement. As a system with internal energy (a human being), we forces exerted by something
decide where we push the book and when to stop it. We could have just as easily done external to a system may do
the same zero net work on the book in the case with no friction but not returned it work on (change the total
to its original position, either stopping it sooner or letting it go farther. So there is no energy of) a system. While it
special relationship between where the book is and the force you are exerting on it. As may seem handy to think of
you do this zero net work in either case, you have to convert your own internal energy interactions inside a system in
to do so, and not just count on your body returning to the shape it prefers! terms of forces, remember that
Even for nonconservative forces, kinetic friction is weird. You may have noticed internal interactions cannot
the quotes around “work” when we were talking about friction above. You can cal- change the total energy of the
culate Fd for a kinetic friction force, but sometimes it doesn’t meet our definition of system, but only allow energy
an energy transfer into or out of a system. When you push on an object or a system, to be converted from one type
the force you exert on the object times the displacement of the point you are pushing into another. Always carefully
on tells you how much energy you transferred to the system. This is not the case for define your system for any
problem or pay attention to how
kinetic friction because the “point of contact” is not simply a point, but the entire con- a system is defined for you in
tact area. As we discussed in Chapter 4, the two surfaces in contact stretch and break. the problem. If a system consists
What you end up with is some warming up of the object and some of the surface, of only one object (rather than,
and some damage (maybe microscopic) to both. So you cannot say how much of that say, the object and Earth), it can
energy is going into the system. You can say only that much energy is being removed have only kinetic energy and no
from the potential and kinetic energy in the system and cannot be recovered into those potential energy.
types (the energy is dissipated). So for kinetic friction, while you can call it work you
must remember that it is the friction force times the total distance traveled, because
the kinetic friction force always opposes the direction of motion, no matter how you
change that direction, and that you cannot account for exactly where it went, just that
it is dissipated. We will look at this more in Chapter 8.
We saw in Section 5-6 that the force exerted by a human tendon is also nonconser-
vative. The tendon exerts more force on its end while it is being stretched than when it is
relaxing to its original length, so it does more negative work on the muscle attached to its
end as it stretches than it does positive work as it relaxes. So the tendon does a nonzero
(and negative) amount of work on this “round trip.” To make the tendon go through a
complete cycle, the muscle has to do a nonzero amount of positive work on the tendon,
just like the positive work you must do to push the book around the path in Figure 7-15b.
There are many examples of potential energy in your environment. The spring in a
mousetrap has the potential to do very destructive work on any mouse unlucky enough
to release the trap. There are also many other sources of energy that drive the world
around you. For now we will just consider these sources of internal energy and we will
learn how to include them in our solutions in the next chapter. If you study physics
further, you will learn more about them. For example, in Chapter 1, we saw Einstein’s
famous equation relating mass to energy, =E mc 2 . The positively charged protons in a
uranium nucleus exert an electric force on each other, pushing each other apart, but are
prevented from doing so by the strong force between the constituents of the nucleus.
If the nucleus is broken apart, the resultant pieces have less mass than the uranium
nucleus; that missing mass is converted to energy. This is the process that provides the
energy released in a nuclear reactor.

Quantifying Potential Energy Paul Bradbury/Getty Images
An object near Earth’s surface gains kinetic energy when it is dropped. An example is
the barbell in Figure 7-16. When held at rest above the weight lifter’s head, the barbell
has no kinetic energy. If the weight lifter should drop the barbell, however, it will fall
to the ground gaining kinetic energy as it does. It can also leave a dent in the floor Figure 7-16 Potential energy The
as it comes to rest on the floor, because it does work on the floor by exerting a large barbell in this photo is at rest and
downward force on the floor over a very small distance. If we treat the barbell as an so has zero kinetic energy. It would
acquire kinetic energy if the weight
object, then Earth exerts an external force of gravity that does work on the barbell as it lifter should drop it. How we describe
falls to the floor, increasing the barbell’s kinetic energy. Because the force of gravity is that gain in kinetic energy depends on
conservative, we can instead think of a change in potential energy associated with this our definition of the system.

Uncorrected proofs have been used in this sample. Copyright © Bedford, Freeman & Worth Publishers.
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