Physics 131
11/26/12
November 26, 2013
Physics 131
Prof. E. F. Redish
  Theme
Music:
Earth, Wind, & Fire
Energy
  Cartoon:
DaveCoverley
Speed Bump
11/26/13
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Physics 131
Lets look at electrical force
moving an object
“Initial”: t1
Potential
energy U
q
m
Electrical
Where does the potential energy go
when the charges move apart?
11/26/13
Prof. E. F. Redish
q
m
33
Physics 131
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Physics 131
11/26/12
Now lets make one object
1000 times heavier
“Initial”: t1
M=1000m
qM
Electrical
q
m
How does the momentum of the two objects change?
How does the KE of the two objects change?
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Physics 131
Momentum vs. energy
If we are changing the motion of two interacting
objects so the momentum of each change in the
same way, it might be useful to look at the KE
in terms of
!
!
!
!
p
=
!
p
=
"!
p
=
"
p
A
A
B
B
that momentum.
2 2
m A vA
  Suppose each starts
2
1
1
KE
=
m
v
=
=
2
2
A
A A
with 0 momentum
mA
and they move as
mB2 vB2
a result of
2
1
1
KEB = 2 mB vB = 2
=
each other’s forces.
m
 
(
)
(
)
B
11/26/13
Prof. E. F. Redish
Physics 131
pA2
2mA
pB2
2mB
5
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Physics 131
11/26/12
Energy Conservation
Total energy of object of interest is conserved
unless external forces move the object of interest
(i.e. do work on the object)
Kinetic
Energy
Earth
vi
Gra
tatio
Child
nal
All Interactions Crossing the
6
Boundary do WORK
11/26/13
Physics 131
Energy Conservation for SYSTEM
Total energy of system is conserved unless
external forces move object(s) within the system
(i.e. do work on the object(s))
Kinetic
Energy
Earth
11/26/13
Prof. E. F. Redish
Child
l
ona
i
t
a
t
avi
Gr
Physics 131
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3
Physics 131
11/26/12
Foothold ideas:
Potential Energy
 
For some forces work only depends
on the change in position. Then the work done
! !
can be written
F ! "r = #"U
U is called a potential energy.
 
For gravity,
Ugravity = mgh
For a spring,
Uspring = ½ kx2
For electric force,
Uelectric = kCQ1Q2/r12
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Physics 131
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Foothold ideas:
Conservation of Mechanical Energy
  Mechanical
energy
–  The mechanical energy of a system of objects
is conserved if resistive forces can be ignored.
! ( KE + PE ) = 0
KEinitial + PEinitial = KE final + PE final
  Thermal
energy
–  Resistive forces transform coherent energy
of motion (energy associated with a net
momentum) into thermal energy (energy
associated with internal chaotic motions and
no net momentum)
11/26/13
Prof. E. F. Redish
Physics 131
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