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45. (a) The links are numbered from bottom to top. The forces on the bottom link are the
force of gravity
mg
G
, downward, and the force
G
F
21
on
of link 2, upward. Take the positive
direction to be upward. Then Newton’s second law for this link is
F
2on1
–
mg
=
ma
. Thus,
F
2on1
=
m
(
a
+
g
) = (0.100 kg) (2.50 m/s
2
+ 9.80 m/s
2
) = 1.23 N.
(b) The forces on the second link are the force of gravity
mg
G
, downward, the force
G
F
12
on
of link 1, downward, and the force
G
F
32
on
of link 3, upward. According to Newton’s third
law
1on2
F
G
has the same magnitude as
G
F
on
. Newton’s second law for the second link is
F
3on2
–
F
1on2
–
mg
=
ma
, so
F
3on2
=
m
(
a
+
g
) +
F
1on2
= (0.100 kg) (2.50 m/s
2
+ 9.80 m/s
2
) + 1.23 N = 2.46 N.
(c) Newton’s second for link 3 is
F
4on3
–
F
2on3
–
mg
=
ma
, so
F
4on3
=
m
(
a
+
g
) +
F
2on3
= (0.100 N) (2.50 m/s
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 Spring '08
 Any
 Physics, Force, Gravity

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