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13a)
L
=
m
1
2
( ˙
x
1
)
2
+
m
2
2
( ˙
x
2
)
2

k
(
x
1

x
2
)
2
(5)
δ
x
L
=
∂L
∂x
1
δx
1
+
∂L
∂x
2
δx
2
=

2
k
(
x
1

x
2
)
δx
1
+ 2
k
(
x
1

x
2
)
δx
2
=

2
k
(
x
1

x
2
)
δx
+ 2
k
(
x
1

x
2
)
δx
= 0
(6)
where
δx
1
=
δx
2
=
δx
because both particles are being translated by the same amount.
This shows that the sum of the forces in a closed system is 0. The force particle 1 exerts on
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This note was uploaded on 11/10/2011 for the course PHY 4241 taught by Professor Berg during the Spring '11 term at University of Florida.
 Spring '11
 Berg

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