Ball and rod, finding when compression force=0

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SUMMARY

The discussion focuses on determining the angle θ at which the compression force in a rod supporting a ball becomes zero. The ball, with mass M, is fixed to a rod of negligible mass and length L, released from rest at θ=0. As the ball descends, the compressional force, defined as mg*cosθ, decreases while the centripetal force increases. The critical point occurs when these forces equalize, resulting in zero normal reaction and thus no compressional force on the rod.

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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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