Ball and rod, finding when compression force=0

AI Thread Summary
The discussion focuses on determining the angle theta at which the compression force in a rod, supporting a ball of mass M, becomes zero as the ball is released from rest. The analysis involves understanding the dynamics of the system, particularly the forces acting on the ball, including gravitational force and centripetal force. As the angle theta increases from the vertical, the compressional force decreases due to the relationship between gravitational force and the centripetal force required to keep the ball on the rod. The key point is that the compressional force becomes zero when the normal reaction force on the ball equals the centripetal force. The solution involves drawing a diagram and establishing a relationship between the variables involved, including the height and angle.
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Homework Statement


the ball has a mass M and is fixed to a rod having a negligible mass and length L. If it's released from rest when theta=0, determine the angle theta at which the compression force in the rod becomes zero.


Homework Equations



A(tangent) = dv/dt = vdv/ds
A (normal) = v^2p ...where p is radius of curvature, or L.




The Attempt at a Solution


well, I'm stumped. This is dynamics problem more so than physics, but still.
I have a FBD with mg down and the C force.
I used tangent-normal coordinates, and have the Compression force in the normal direction.
So I get A=V^2 / L
I guess I just don't get conceptually why the force would ever need to become zero?

PS...so theta is from the vertical axis down.

So it starts completely vertical and makes its way down clockwise.
 
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As the rod falls, the compressional force is mg*cosθ. This force provides the necessary centripetal force for the ball to remain on the rod. As θ increases this force decreases, the normal reaction on the ball decreases and centripetal force on the ball increases. When theses two forces are equal normal reaction is zero and there is no compressional froce on the rod.
Since the ball is falling freely v^2 = 2gh.
Now draw the diagram, and find the relation between Ρ, h and cosθ.
 
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