9781118230725.pdf

This is a pretty formal definition of something that is actually familiar to you.

An example might help better than the definition: A bungee-cord jumper plunges

from a staging platform (Fig. 8-1). The system of objects consists of Earth and the

jumper. The force between the objects is the gravitational force. The configuration

of the system changes (the separation between the jumper and Earth decreases —

that is, of course, the thrill of the jump). We can account for the jumper’s motion

and increase in kinetic energy by defining a gravitational potential energyU. This

is the energy associated with the state of separation between two objects that at-

tract each other by the gravitational force, here the jumper and Earth.

When the jumper begins to stretch the bungee cord near the end of the

plunge, the system of objects consists of the cord and the jumper. The force

between the objects is an elastic (spring-like) force. The configuration of the sys-

tem changes (the cord stretches). We can account for the jumper’s decrease in

kinetic energy and the cord’s increase in length by defining an elastic potential

energyU. This is the energy associated with the state of compression or extension

of an elastic object, here the bungee cord.

Physics determines how the potential energy of a system can be calculated so

that energy might be stored or put to use. For example, before any particular

bungee-cord jumper takes the plunge, someone (probably a mechanical engi-

neer) must determine the correct cord to be used by calculating the gravitational

and elastic potential energies that can be expected. Then the jump is only thrilling

and not fatal.

Work and Potential Energy

In Chapter 7 we discussed the relation between work and a change in kinetic energy.

Here we discuss the relation between work and a change in potential energy.

Let us throw a tomato upward (Fig. 8-2). We already know that as the tomato

rises, the work Wgdone on the tomato by the gravitational force is negative

because the force transfers energy fromthe kinetic energy of the tomato. We can

now finish the story by saying that this energy is transferred by the gravitational

forcetothe gravitational potential energy of the tomato – Earth system.

The tomato slows, stops, and then begins to fall back down because of the

gravitational force. During the fall, the transfer is reversed: The work Wgdone on

the tomato by the gravitational force is now positive — that force transfers energy

fromthe gravitational potential energy of the tomato – Earth system to the

kinetic energy of the tomato.

For either rise or fall, the change Uin gravitational potential energy is

defined as being equal to the negative of the work done on the tomato by the

gravitational force. Using the general symbol Wfor work, we write this as

UW. (8-1)

178 CHAPTER 8 POTENTIAL ENERGY AND CONSERVATION OF ENERGY

Figure 8-1The kinetic energy of a bungee-
cord jumper increases during the free fall,
and then the cord begins to stretch, slow-
ing the jumper.

Rough Guides/Greg Roden/Getty Images, Inc.

Figure 8-2A tomato is thrown upward. As it rises, the

gravitational force does negative work on it, decreasing

its kinetic energy. As the tomato descends, the

gravitational force does positive work on it, increasing

its kinetic energy.

Negative

work done

by the

gravitational

force

Positive

work done

by the

gravitational

force