Announcements
•
Reading for Friday: 3.73.12
•
First Midterm is next week (Feb. 9
th
,
7:30pm). It will cover Chapters 1&2.
Room:
MUEN E050
. Allowed
materials: see course syllabus.
Review: Relativistic mechanics
u
r
p
m
dt
d
m
propper
γ
=
≡
Relativistic momentum:
(
29
u
p
F
m
dt
d
dt
d
γ
=
≡
Relativistic force:
E
tot
=
γ
mc
2
= K + mc
2
Total energy of a
particle with mass ‘m’:
We found that these definitions fulfill the momentum and
energy conservation laws. And for u<<c the definitions
for p, F, and K match the classical definitions. But we
found that funny stuff happens to the proper mass ‘m’.
E
tot
=
γ
2mc
2
= 2K + 2mc
2
Equivalence of Mass and Energy
m
v
v
m
Conservation of the total energy requires that the final
energy E
tot,final
is the same as the energy E
tot,
before
E
tot,final
= Mc
2
= 2K + 2mc
2
= E
tot,initial
We find that the total mass M of the final system is bigger
than the sum of the masses of the two parts! M>2m.
Potential energy inside an object contributes to its mass!!!
the collision. Therefore:
E=mc
2
Convert mass to energy?
Atomic cores are built from neutrons and protons. There
are very strong attractive forces between them. The
potential energy associated with the force keeping them
together in the core is called the binding energy E
B.
We now know that the total rest energy of the particle
equals the sum of the rest energy of all constituents minus
the total binding energy E
B
:
Mc
2
=
Σ
(
m
i
c
2
)
–
E
B
Or in terms of Mass per nucleon
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 Spring '08
 staff
 Physics, Electron, Energy, Momentum, Photon, Special Relativity

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