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M3
Procedure to determine
F
3
in section V.2 and V.3
Refer to fig.1.
We know the directions of
1
F
G
and
2
F
G
.
The vector
2
1
F
F
G
G
+
lies
somewhere within the angle
φ
defined by
1
F
G
and
2
F
G
.
Since
0
3
2
1
=
+
+
F
F
F
G
G
G
→
2
1
3
F
F
F
G
G
G
−
−
=
.
Thus
3
F
G
lies somewhere within the arc AB.
The following procedure can be followed to find both magnitude and direction of
3
F
G
Step 1.
Load the first and second hangers with m
1
and m
2
.
Leave the third hanger empty
for the time being. Pull down on the string of
the third hanger so that the ring is
approximately centered around the peg P.
Step 2
. Scan the position of the third pulley within the arc AB.
At some specific
position of the pulley within the arc AB the ring will move with respect to the peg P.
This defines the angle
θ
3
. Now load the third hanger with a test mass.
One of the
following two distinct outcomes will occur:
Outcome A
(see fig. 2a).
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 Fall '10
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