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318 Chapter 7 Conservation of Energy and an Introduction to Energy and Work

y change in location of the barbell. Potential energy changes depend on changes in the config-
F weight lifter
uration of the system. The shape of the barbell does not change, but the distance between
the barbell and Earth’s surface does change. If we choose our system to be the barbell and
x
Earth, we can no longer use work done by the force of gravity, because gravity is no longer
an external force! Instead we talk about the gravitational potential energy of the system.
How we choose our system completely determines whether we use work or potential
energy to describe the effects of conservative interactions.
F g
Gravitational Potential Energy
There are two ways to quantify the amount of potential energy stored in the Earth–
barbell system in Figure 7-16. First, we compare the potential energy due to a reversible
change in the configuration of a system to the work that would be done if the object were
isolated. If the system is just the barbell, and it has mass m and is initially a height h above
the floor (we are going to consider the floor as = 0h ), as it falls, Earth (because Earth is
not in the system, the gravitational force on the barbell in its direction of motion is an
y = 0
external force) would do an amount of work W grav = g F d cos θ = g F h cos 0°= g F h = mgh
Figure 7-17 Adding potential on the barbell. From the work-energy theorem this is equal to the kinetic energy that
energy The change in the kinetic the dropped barbell has just before it hits the floor. We’re ignoring any effects of air
energy of the barbell as it is raised by resistance. We could instead say that the gravitational potential energy (symbol U ) of
the weight lifter is zero. The work that grav
the weight lifter does to lift the barbell the Earth–barbell system before the barbell was dropped was U grav = mgh, and that this
goes into increasing the potential potential energy was converted to kinetic energy as the barbell fell, so the change in grav-
energy of the Earth–barbell system. itational potential energy is the negative of the change in kinetic energy ∆U grav = −mgh .
Note that potential energy has units of joules, the same as work and kinetic energy.
This is one of the reasons we like to focus on changes in energy. Notice that if we
had decided to call =h 0 the height from which the weight lifter dropped the barbell, then
the final position of the barbell would be –h. The displacement would still be h f − h i =
0 − h = −h, and so the changes in energy would be exactly the same, as they must be.
WATCH OUT ! the initial potential energy came from for the Earth–barbell system. To see this, con-
A second way to quantify the amount of potential energy is to consider where
Objects can have only kinetic sider what happens as a weight lifter raises the barbell from the floor to a height h
energy; it takes a system to (Figure 7-17). During the lifting, the barbell begins with zero kinetic energy (sitting on
have potential energy. the floor) and ends up with zero kinetic energy (at rest above the weight lifter’s head),
and the weight lifter exerts an average force mg upward over the displacement h, to
Never be sloppy and say, keep the barbell moving upward at constant speed. The net change in its kinetic energy
“The barbell has gravitational is zero and the force of gravity does no work on the system, because it is internal to
potential energy.” The weight the system. Hence the positive work that the weight lifter did to raise the barbell must
lifter uses internal energy to provide the potential energy mgh of the Earth–barbell system when the barbell is at
increase the gravitational height h (again assuming U
grav is zero at the floor). The potential energy stored in the
potential energy of the barbell– configuration of a system because of a gravitational interaction (mgh near the surface of
Earth system by moving the
barbell away from Earth. Earth) is called gravitational potential energy. The gravitational potential energy mgh
Always be careful to define would be the same if the barbell remained at rest but Earth as a whole were pushed
your system when using work down a distance h. The weight lifter converted internal energy (that snack eaten earlier)
and energy to solve problems. into the work done on the barbell. Any time energy comes from changing the configu-
ration of chemicals in food, some of that internal energy goes into warming the weight
lifter up. We will discuss this more in the next chapter.
In general, if an object of mass m is at a vertical coordinate y above the surface of
Earth, the gravitational potential energy of the Earth–object system is

Gravitational potential energy stored in the Earth–object system Mass of the object
EQUATION IN WORDS U = mgy
Gravitational potential energy grav
stored in an Earth–object (7-14)
system near the surface Acceleration due to gravity Height of the object
of Earth above Earth, assuming
the ground is y = 0 and
positive y is upward

When the weight lifter in Figure 7-16 raises the barbell (so y increases), the grav-
itational potential energy of the Earth–barbell system increases; when she lowers or

Uncorrected proofs have been used in this sample. Copyright © Bedford, Freeman & Worth Publishers.
Distributed by Bedford, Freeman & Worth Publishers. For review purposes only. Not for redistribution.

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