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22 High energy
10 by a string or wire from a support. If the bob is moved to
one side and then released, it will swing back and forth in
10 21
Gamma rays an arc. At the moment that the bob reaches the top of its swing,
10 20 it stops for an instant, then begins another swing. At the instant
19 of stopping, the bob has 100 percent potential energy and no
10
kinetic energy. As the bob starts back down through the swing, it
10 18 X rays
is gaining kinetic energy and losing potential energy. At the instant
10 17 the bob is at the bottom of the swing, it has 100 percent kinetic en-
Ultraviolet ergy and no potential energy. As the bob now climbs through the
16
10
Visible other half of the arc, it is gaining potential energy and losing kinetic
10 15 energy until it again reaches an instantaneous stop at the top, and
10 14 the process starts over. The kinetic energy of the bob at the bottom
Frequency, Hz 10 12 Infrared (Figure 3.15). Disregarding friction, the sum of the potential ene rgy
of the arc is equal to the potential energy it had at the top of the arc
13
and the kinetic energy remains constant throughout the swing.
10
The potential energy lost during a fall equals the kinetic
11
10
energy gained (Figure 3.16). In other words,
10 Microwave
10
PE = KE gained
lost
10 9
Substituting the values from equations 3.3 and 3.4,
10 8 FM, TV
1 _ 2
7

10 mgh = mv
2
10 6
AM broadcast Canceling the m and solving for v f ,
10 5 Low energy
v = √
2

gh
4 f
10
Long radio equation 3.5
10 3 waves
Equation 3.5 tells you the final speed of a falling object after
its potential energy is converted to kinetic energy. This assumes,
FIGURE 3.13 The frequency spectrum of electromagnetic however, that the object is in free fall, since the effect of air resis-
waves. The amount of radiant energy carried by these waves
tance is ignored. Note that the m’s cancel, showing again that the
increases with frequency. Note that visible light occupies only a
small part of the complete spectrum. mass of an object has no effect on its final speed.
FIGURE 3.14 The blades of a steam turbine.
In a power plant, chemical or nuclear energy is used
to heat water to steam, which is directed against the
turbine blades. The mechanical energy of the turbine
turns an electric generator. Thus, a power plant
converts chemical or nuclear energy to mechanical
energy, which is then converted to electrical energy.

72 CHAPTER 3 Energy 3-12