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bendezium
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Homework Statement
Problem statement: Please see the attached picture. A rigid rod rotates with constant angular velocity w. A rigid bar with length A is attached perpendicular to the rotating rod. A second rigid bar with length B is attached to the other end of bar A by a hinge. The hinge allows bar B to swing up and out, but not side to side (from a top view, bar A and bar B will be perfectly aligned). An object with mass m is attached to the far end of bar B. The angle of bar B with respect to the y-axis, theta, is unknown.
Known: length A, length B, angular velocity w, mass m
Assume: The rod and both bars are rigid; the object is a point mass; friction can be neglected;
Find: theta in terms of the known variables
Homework Equations
F = m * a
vt = w * r (angular velocity)
ar = w^2 * r (radial acceleration)
The Attempt at a Solution
Since w is constant, the system is not accelerating, so theta will be constant. My attached picture shows a free-body diagram of the mass. Its weight pulls it down, and centrifugal force pushes the mass outwards. The tension 'T' from bar B holds the mass in place. Here's what I've got:
Sum of all forces in the x direction = 0 = m * r * w^2 - T * sin(theta)
Sum of all forces in the y direction = 0 = T * cos(theta) - m * g
which implies
T * cos(theta) = m * g
T * sin(theta) = m * r * w^2
Here's where I'm stuck. Is r with respect to the point at the hinge, or the rotating rod? Which of the following is true:
r = B * sin(theta)
OR
r = B * sin(theta) + A
If I can get past this step, I can solve the problem. Thanks so much,
Eryk
EDIT: since the picture isn't approved yet, here it is on ImageShack: http://img189.imageshack.us/img189/4717/problemeqs.jpg
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