POTENTIAL ENERGY
AND
ENERGY
CONSERVATION
?
As
this diver enters
the water,
is
the force
of
gravity
doing positive
or negative work on
him?
Is
the water doing
positive or negative
work
on
him?
W
hen
a diver jumps
off
a
high
board
into a swimming pool,
he
hits
the
water moving pretty fast, with a
lot
of
kinetic energy. Where does that
energy
come
from?
The
answer
we
learned
in
Chapter 6
was
that
the
gravitational force (his weight) does
work
on
the
diver
as
he
falls.
The
diver's
kinetic
energy--energy
associated
with
his
motion-increases
by
an arnount
equal
to
the
work done.
However, there
is
a very useful alternative way
to
think:
about
work
and
kinetic energy. This
new
approach
is
based
on
the
concept
of
potential energy,
which
is
energy associated
with
the
position
of
a system rather than its motion.
In
this approach, there
is
gravitational potential energy
even while
the
diver
is
standing
on
the
high board. Energy
is
not
added
to
the
earth-diver
system
as
the
diver falls, but rather a storehouse
of
energy
is
transformed
from
one
form
(potential energy)
to
another (kinetic energy)
as
he
falls.
In
this chapter
we'll
see
how
the
work-energy
theorem explains this transfonnation.
If
the
diver bounces
on
the
end
of
the
board before
he
jwnps,
the
bent
board
stores a second kind
of
potential energy called
elastic potential energy.
We'll
dis-
cuss elastic potential energy
of
simple systems
such
as
a stretched
or
compressed
spring.
(An
important third
kind
of
potential energy
is
associated
with
the
posi-
tions
of
electrically charged particles relative
to
each
other.
We'll
encounter this
potential energy
in
Chapter 23.)
We will prove that
in
some cases
the
swn
of
a system's kinetic
and
potential
energy, called
the
total mechanical energy
of
the
system,
is
constant during
the
motion
of
the
system. This will lead
us
to
the
general statement
of
the
law
of
con-
servation
of
energy,
one
of
the
most
fundamental
and
far-reachiog principles
in
all
of
science.
7
LEARNING
GOALS
By
studying
this
duJpter.
you
willll!tlm:
How
to
use the concept
of
gravita-
tional
potential
energy
in
problems
that
involve
vertical
motion.
How
to
use the concept
of
elastic
potential
energy
in
problems
that
involve
a
moving
body
attached
to
a stretched
or
compressed
spring.
The
distinction
between
conserva-
tive
and
nonconservative
forces,
and
how
to
solve
problems
in
which
both
kinds
of
forces
act
on
a
moving
body.
How
to
calculate
the
properties
of
a
conservative
force
if
you
know
the
corresponding
potential-€nergy
function.
How
to
use energy
diagrams
to
understand
the
motion
of
an
object
moving
in
a
straight
line
under the
influence
of
a
conservative
force.
213

214
CHAPTER
7
Potential
Energy
and
Energy
Conservation
7.1
As
a basketball descends, gravitational
potential energy
is
converted
to
kinetic
energy
and
the
basketball's speed
increases.