Page 90 - 9780077418427.pdf

/Users/user-f465/Desktop
tiL12214_ch03_061-084.indd Page Sec3:67 9/1/10 9:33 PM user-f465
tiL12214_ch03_061-084.indd Page Sec3:67 9/1/10 9:33 PM user-f465 /Users/user-f465/Desktop

The higher the shelf, the greater the potential for the book
3.2 MOTION, POSITION, AND ENERGY
to do work. The ability to do work is defined as energy. The
Closely related to the concept of work is the concept of energy. energy that an object has because of its position is called
Energy can be defined as the ability to do work. This definition potential energy (PE). Potential energy is defined as energy
of energy seems consistent with everyday ideas about energy due to position. This is called gravitational potential energy,
and physical work. After all, it takes a lot of energy to do a lot of since it is a result of gravitational attraction. There are other
work. In fact, one way of measuring the energy of something is types of potential energy, such as that in a compressed or
to see how much work it can do. Likewise, when work is done stretched spring.
on something, a change occurs in its energy level. The following Note the relationship between work and energy in the ex-
examples will help clarify this close relationship between work ample. You did 10 J of work to raise the book to a higher shelf. In
and energy. so doing, you increased the potential energy of the book by 10 J.
The book now has the potential of doing 10 J of additional work
on something else; therefore,
POTENTIAL ENERGY
work done on increase in
Consider a book on the floor next to a bookcase. You can do increase in
an object to = = work the object
work on the book by vertically raising it to a shelf. You can mea- potential energy
change position can do
sure this work by multiplying the vertical upward force applied
by the distance that the book is moved. You might find, for ex- work on book = potential energy = work by book
ample, that you did an amount of work equal to 10 J on the book of book
(see example 3.1). (10 J) (10 J) (10 J)
Suppose that the book has a string attached to it, as shown
As you can see, a joule is a measure of work accomplished on an
in Figure 3.6. The string is threaded over a frictionless pulley
object. A joule is also a measure of potential energy. And a joule
and attached to an object on the floor. If the book is caused to
is a measure of how much work an object can do. Both work and
fall from the shelf, the object on the floor will be vertically lifted
energy are measured in joules (or ft·lb).
through some distance by the string. The falling book exerts a
The gravitational potential energy of an object can be cal-
force on the object through the string, and the object is moved
culated, as described previously, from the work done on the ob-
through a distance. In other words, the book did work on the
ject to change its position. You exert a force equal to its weight
object through the string, W = Fd.
as you lift it some height above the floor, and the work you do
The book can do more work on the object if it falls from
is the product of the weight and height. Likewise, the amount of
a higher shelf, since it will move the object a greater distance.
work the object could do because of its position is the product of
its weight and height. For the metric unit of mass, weight is the
product of the mass of an object times g, the acceleration due to
gravity, so
gravitational potential energy = weight × height
PE = mgh
equation 3.3
For English units, the pound is the gravitational unit of force, or
weight, so equation 3.3 becomes PE = (w)(h).
Under what conditions does an object have zero poten-
tial energy? Considering the book in the bookcase, you could
say that the book has zero potential energy when it is flat on
the floor. It can do no work when it is on the floor. But what
W = mgh
W = 10 J if that floor happens to be the third floor of a building? You
could, after all, drop the book out of a window. The answer
F = mg
W = mgh is that it makes no difference. The same results would be ob-
F = mg W = 10 J tained in either case since it is the change of position that is
important in potential energy. The zero reference position for
potential energy is therefore arbitrary. A zero reference point
is chosen as a matter of convenience. Note that if the third
floor of a building is chosen as the zero reference position, a
book on ground level would have negative potential energy.
This means that you would have to do work on the book to
bring it back to the zero potential energy position (Figure 3.7).
FIGURE 3.6 If moving a book from the floor to a high shelf
requires 10 J of work, then the book will do 10 J of work on an You will learn more about negative energy levels later in the
object of the same mass when the book falls from the shelf. chapters on chemistry.

3-7 CHAPTER 3 Energy 67