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Thus,
a
gm m
mm
com
2
2
m/s
g
g
g
=
−
+
=
−
+
=×
−
21
2
12
2
2
2
2
9 8
520
480
480
520 g
16 10
b
g
bg
c
h
.
..
The acceleration is downward.
105. (a) We place the origin of a coordinate system at the center of the pulley, with the
x
axis horizontal and to the right and with the
y
axis downward. The center of mass is
halfway between the containers, at
x
= 0 and
y
=
A
, where
A
is the vertical distance from
the pulley center to either of the containers. Since the diameter of the pulley is 50 mm,
the center of mass is at a horizontal distance of 25 mm from each container.
(b) Suppose 20 g is transferred from the container on the left to the container on the right.
The container on the left has mass
m
1
= 480 g and is at
x
1
= –25 mm. The container on
the right has mass
m
2
= 520 g and is at
x
2
= +25 mm. The
x
coordinate of the center of
mass is then
x
mx
com
g
g
g 520 g
mm.
=
+
+
=
−+
+
=
11
2 2
480
25
520
25
480
10
b
g
b
g
.
The
y
coordinate is still
A
. The center of mass is 26 mm from the lighter container, along
the line that joins the bodies.
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 Spring '08
 Any
 Physics, Center Of Mass, Mass

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