ME 562 Advanced Dynamics
Summer 2010
HOMEWORK # 5
Due: July 16, 2010
Q1.
(
see
Problem 61 in the text for the figure).
A fixed smooth rod makes an angle of 30
with the
floor.
A small (negligible radius) ring (say P
1
) of mass
m
can slide on the rod and supports a string which
has one end connected to a point on the floor; the other end is attached to a particle (say P
2
) of mass 2
m
.
Assume that the string and the rod lie in the same vertical plane
.
Since there are two objects with mass,
one can use their Cartesian coordinates with respect to a (x,y) system with origin at the lower left corner.
Let
l
be the length of the string.
Since the ring is constrained to move along the rod, and
l
is constant, the
four coordinates (x
1
,y
1
) and (x
2
,y
2
) are constrained.
Also, let
a
be the coordinate of the point on the floor
where the string is attached, and
b
be the height of the point where the rod is attached to the vertical wall.
Then,
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 Fall '10
 BAJAJ
 Geometry, Cartesian Coordinate System, Polar coordinate system

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