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86. From the law of cosines, with
φ
= 59.95º, we have
L
2
Invar
=
L
2
alum
+
L
2
steel
–
2
L
alum
L
steel
cos
φ
Plugging in
L
=
L
0
(1 +
Įǻ
T
), dividing by
L
0
(which is the same for all sides) and
ignoring terms of order (
ǻ
T
)
2
or higher, we obtain
1 + 2
Į
Invar
ǻ
T
=
2 + 2 (
Į
alum
+
Į
steel
)
ǻ
T–
2 (1 + (
Į
alum
+
Į
steel
)
ǻ
T
) cos
φ
.
This is rearranged to yield
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics

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