This preview shows page 1. Sign up to view the full content.
456
Relativity
P39.69
(a)
At any speed, the momentum of the particle is given by
pm
u
mu
uc
==
−
γ
1
2
bg
.
Since
Fq
E
dp
dt
:
qE
d
dt
mu
u
c
=−
F
H
G
I
K
J
L
N
M
M
O
Q
P
P
−
1
2
2
12
qE
m
u
c
du
dt
mu
u
c
u
c
du
dt
F
H
G
I
K
J
+−
F
H
G
I
K
J
F
H
G
I
K
J
−−
1
1
2
1
2
2
2
2
2
32
2
.
So
qE
m
du
dt
uc uc
=
−+
−
L
N
M
M
M
O
Q
P
P
P
1
1
22 22
22
ej
and
a
du
dt
qE
m
u
c
−
F
H
G
I
K
J
1
2
2
.
(b)
For
u
small compared to
c
, the relativistic expression reduces to the classical
a
qE
m
=
. As
u
approaches
c
, the acceleration approaches zero, so that the object can never reach the speed
of light.
(c)
du
qE
m
dt
u
t
t
1
00
−
=
zz
=
u
qEct
mc
qEt
=
+
2 22
xu
d
t
q
E
c
tdt
tt
+
0
0
x
c
qE
m
c
=+
−
F
H
I
K
P39.70
(a)
An observer at rest relative to the mirror sees the light travel a distance
Dd
x
2
, where
xv
t
S
=
is the distance the ship moves toward the mirror in time
t
S
. Since this observer
agrees that the speed of light is
c
, the time for it to travel distance
D
is
t
D
c
dv
t
c
S
S
−
2
t
d
cv
S
=
+
2
.
(b)
The observer in the rocket measures a lengthcontracted initial distance to the mirror of
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .
 Fall '11
 Staff
 Physics, Momentum

Click to edit the document details