Physics 53
Energy 2
Things are more like they are now than they ever were before.
— Dwight D. Eisenhower
Conservative forces
In general the work done by a force depends on the
path
taken from the initial position
to the Fnal one, as well as on the location of those points. But, as we have seen, there are
some forces for which the work depends only on the endpoints,
not
on the path. These
are called
conservative forces
.
Consider a trajectory which ends where it began, forming a closed curve. The work
done by a conservative force for such a path must be zero. We therefore have two
equivalent ways to deFne a conservative force:
Conservative force: two deFnitions
F
⋅
d
r
1
2
∫
is independent of path
F
⋅
d
r
∫
=
0
In the second case, the small circle around the integral sign denotes a line integral following a
closed curve
,
one that ends where it began.
Potential energy
Suppose a conservative (net) force moves a particle from point 1 to point 2, during
which time it does positive work, so the kinetic energy increases. Now suppose the
same force then moves the particle back to point 1. The work done in this part must be
exactly the negative of the other, because the
total
work done by a conservative force in
a round trip is zero. The particle's kinetic energy thus decreases back to its original
value. Is kinetic energy “created” by the force in the trip from 1 to 2 and then
“destroyed” in the return trip? It seems more useful, since this process could be
repeated indeFnitely, to imagine that the “lost” kinetic energy during the trip from 2 to
1 is
stored
somewhere and can be returned to the particle during its next trip from 1 to 2.
PHY 53
1
Energy 2
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View Full DocumentThe idea of storing energy is the basis of
potential energy
. It is one of the most
important concepts in physics. It is called “potential” because it has the possibility of
being converted back into kinetic energy.
Where is the energy stored? That turns out to be a very deep question, to which we will return when we
discuss the gravitational Feld.
Potential energy, denoted by
U
, is associated with the conservative force, i.e., with the
interaction between the particle and its environment.
It is a property of the system of
interacting objects
. It is not (like kinetic energy) a property of any single particle.
To make the idea quantitative, we introduce a deFnition:
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 Spring '07
 Mueller
 Physics, Energy, Force, Potential Energy, Work, Conservative force

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