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Ball and rod, finding when compression force=0

  • Thread starter jromega3
  • Start date
  • #1
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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 moreso 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.
 

Answers and Replies

  • #2
rl.bhat
Homework Helper
4,433
7
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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