29&30-1 (SJP, phys1120)
Electric Potentials:
We've been talking about electric forces, and the related quantity
E
=
F
/q, the E field, or "force per unit charge". In 1110, after talking about
forces, we moved on to work and energy
Quick Review of work and energy:
The work done by a constant force, F, moving
something through a displacement "d", is
W
=
r
F
"
r
d
=
F
||
d
=
Fd
cos
#
More formally, if
F
varies as you follow some path:
W
=
r
F
"
d
r
r
#
.
E.g. if you (an "external force") lift a book (at constant speed) up a distance d,
Newton II says
F
_net = m
a
,
i.e.
F
_ext -
F
_g = 0
(because, remember, if speed is constant =>
a
=0)
or
F
_ext = mg.
You
do work W_ext = F_ext*d = +mgd
(The + sign is because
θ
is 0 degrees, your force is UP, and so
is the displacement vector)
The gravity field does W_field = -F_g*d = -mgd
(The minus sign is because
θ
is 180 degrees, the force of gravity points DOWN
while the displacement vector is UP)
The NET work (done by all forces) is W_ext+W_field = 0, that's just the
work-
energy principle
, which says W_net =
Δ
KE (=0, here)
You did work. Where did it go? NOT into KE: it got "stored up", it turned into
potential energy (PE).
In other words, F_ext did work, which went into
increased
gravitational potential energy.
For gravity, we defined this potential energy to be PE = mgy, so
!
PE = mg(y_final - y_initial) = + mgd
(=W_ext)
(The change in PE is all we ever cared about in real problems)
Summary: If you do work on an object in a "conservative" force field:
!
PE = W_"by you" = -W_"by the field"=
"
r
F
field
#
d
r
r
$
Knight generally uses the symbol "U" for "Potential Energy", by the way.
!
d
F
F
_ext
F
_g
= mg