9781118230725.pdf

What Is Physics?

One job of physics is to identify the different types of energy in the world,
especially those that are of common importance. One general type of energy is
potential energyU. Technically, potential energy is energy that can be associated
with the configuration (arrangement) of a system of objects that exert forces on
one another.

CHAPTER 8

Potential Energy and

Conservation of Energy

8-1POTENTIAL ENERGY

After reading this module, you should be able to...
8.01Distinguish a conservative force from a nonconservative
force.
8.02For a particle moving between two points, identify that
the work done by a conservative force does not depend on
which path the particle takes.

8.03Calculate the gravitational potential energy of a particle

(or, more properly, a particle–Earth system).

8.04Calculate the elastic potential energy of a block–spring

system.

●A force is a conservative force if the net work it does on
a particle moving around any closed path, from an initial
point and then back to that point, is zero. Equivalently, a force
is conservative if the net work it does on a particle moving
between two points does not depend on the path taken by
the particle. The gravitational force and the spring force are
conservative forces; the kinetic frictional force is a noncon-
servative force.

●Potential energy is energy that is associated with the con-
figuration of a system in which a conservative force acts.
When the conservative force does work Won a particle
within the system, the change Uin the potential energy of
the system is

UW.

If the particle moves from point xito point xf, the change in
the potential energy of the system is

U

xf

xi

F(x)dx.

●The potential energy associated with a system consisting of

Earth and a nearby particle is gravitational potential energy. If

the particle moves from height yito height yf, the change in the

gravitational potential energy of the particle–Earth system is

Umg(yfyi)mgy.

●If the reference point of the particle is set as yi 0 and the

corresponding gravitational potential energy of the system is

set as Ui 0 , then the gravitational potential energy Uwhen

the particle is at any height yis

U(y)mgy.

●Elastic potential energy is the energy associated with the

state of compression or extension of an elastic object. For a

spring that exerts a spring force Fkxwhen its free end

has displacement x, the elastic potential energy is

●The reference configuration has the spring at its relaxed

length, at which x 0 andU 0.

U(x)^12 kx^2.

Key Ideas

Learning Objectives

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