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42. (a) Squaring Eq. 3844 gives
E
2
=
(
mc
2
)
2
+2
mc
2
K
+
K
2
which we set equal to Eq. 3852. Thus,
(
mc
2
)
2
+2
mc
2
K
+
K
2
=(
pc
)
2
+
(
mc
2
)
2
=
⇒
m
=
(
pc
)
2
−
K
2
2
Kc
2
.
(b) At low speeds, the preEinsteinian expressions
p
=
mv
and
K
=
1
2
mv
2
apply. We note that
pc
À
K
at low speeds since
c
À
v
in this regime. Thus,
m
→
(
mvc
)
2
−
(
1
2
mv
2
)
2
2
(
1
2
mv
2
)
c
2
≈
(
mvc
)
2
2
(
1
2
mv
2
)
c
2
=
m.
(c) Here,
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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