Figure 14.2 Potential energy vs. displacement graph for a spring.You can get a general feel for how the mass on a spring moves by imagining that Chris is riding a
skateboard on a ramp shaped like the graph. A ramp shaped like this looks like a half-pipe. If he starts
from some height above the bottom, Chris will oscillate back and forth, going fastest in the middle, and
turning around when he runs out of energy at the right or left end. Although this is not precisely how a
mass on a spring moves—the mass only moves back and forth, for example—the long-term properties of
Chris’s motion and the motion of the mass on a spring are the same. The mass oscillates back and forth,
with its fastest speed in the middle, just like Chris does.
Thinking about Chris on a skateboard works for all U vs. x graphs. Consider a model of the energy
between two atoms that looks like the graph in Figure 14.3 .
Figure 14.3 Potential energy vs. displacement graph for two atoms.If Chris on his skateboard released himself from rest near position x 1 , he’d just oscillate back and forth,
much like in the mass on a spring problem. But if he were to let go near the position labeled x 2 , he’d
have enough energy to keep going to the right as far as he wants; in fact, he’d make it off the page, never
coming back. This is what happens to the atoms in molecules, too. If a second atom is placed pretty close
to a distance x 1 from the first atom, it will just oscillate back and forth about that position. However, if
the second atom is placed very close to the first atom, it will gain enough energy to escape to a faraway
place.
Practice Problems
Multiple Choice:
Questions 1 and 2