Chapter 39
443
P39.23
γ
=
−
=
−
=
1
1
1
10
9
9
5
10 0
22
2
vc
.
.
We are also given:
L
1
200
=
.
m, and
θ
=°
30 0
.
(both measured in a
reference frame moving relative to the rod).
Thus,
LL
x
11
1
2 00
0 867
1 73
==
=
cos
.
.
.
m
m
af
a
f
and
y
11 1
2 00
0 500
1 00
=
sin
.
.
.
m
a
f
L
x
2
is a proper length, related to
L
x
1
by
L
L
x
x
1
2
=
.
Therefore,
xx
21
10 0
17 3
..
m
and
yy
100
.
m
.
(Lengths perpendicular to the motion are unchanged).
FIG. P39.23
(a)
L
xy
2
2
2
=+
bg
ej
gives
L
2
17 4
=
. m
(b)
2
1
2
2
=
−
tan
L
L
y
x
gives
2
330
.
*P39.24
Einstein’s reasoning about lightning striking the ends of a train shows that the moving observer sees
the event toward which she is moving, event B , as occurring first. The
S
frame coordinates of the
events we may take as (
x
=
0,
y
=
z
=
t
=
0) and (
x
=
100 m,
y
=
z
=
t
=
0). Then the
coordinates in
′
S
are given by the Lorentz transformation. Event A is at (
′=
x
y
z
t
0).
The time of event B is
−
F
H
G
I
K
J
=
−
−
F
H
G
I
K
J
=−
×
F
H
G
I
K
J
×
−
tt
v
c
x
c
c
2
2
2
7
1
8
0
08
100
1 667
80
444 10
.
.
m
m
31
0
m
s
s
8
.
The time elapsing before A occurs is
444 ns .
P39.25
(a)
From the Lorentz transformation, the separations between the bluelight and redlight
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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

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