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PHY2061
R. D. Field
Department of Physics
relativity_8b.doc
University of Florida
Relativistic Kinetic Energy (
derivation
)
Relativistic Force:
The force is equal to the rate of chance of the (relativistic) momentum as
follows:
v
dt
dm
dt
v
d
m
dt
v
m
d
dt
p
d
F
!
!
!
!
+
=
=
=
)
(
where
0
m
m
γ
=
is the relativistic mass.
Relativistic Kinetic Energy:
The
kinetic energy of a particle is (as
classical) the total work done in
moving particle from rest to the
speed v as follows:
RME
E
c
m
mc
dm
c
dm
v
dm
v
c
dm
v
mvdv
mv
vd
dx
dt
mv
d
Fdx
KE
m
m
m
m
−
=
−
=
=
+
−
=
+
=
=
=
=
∫
∫
∫
∫
∫
∫
2
0
2
2
2
2
2
2
0
0
)
)
((
)
(
)
(
)
(
where I used
)
/
1
(
2
2
0
2
2
m
m
c
v
−
=
and
dm
v
c
mvdv
)
(
2
2
−
=
.
Energy Momentum Connection:
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This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.
 Spring '08
 FRY
 Physics, Energy, Force, Kinetic Energy, Momentum

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