Basic Dynamics Fc: Find Distance "L" from Point of Support

[Mr Beatnik]

Homework Statement

A ring radius R is fixed vertically to the floor. From the top of the ring and object slides down without friction. Find the distance "L" from the point of support of the ring to the point where the object hits the ground.

Homework Equations

I think the object travels tangetially from 90 degrees from the top of the circle. This is where the normal force equals the centripetal force and the net force is the weight. Is this right? If so how do I prove this?

The Attempt at a Solution

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[Mr Beatnik]

Ok so after some struggling I realized that the attempt above is completely wrong. I have broken the circle down into its components and solved for cos(O) and got 2/3 which I was able to verify so I know that part is right. So I have also found that part of the length is Rsin(O) and now I need to solve for the rest. I hope I'm making this clear because I don't think I am. Please let me know if you need more info. I think I'm at the point where the normal force is at 0 and the object goes into parabolic freefall. The problem is I don't know how to finish the problem. How do I take what I have solved for so far, Cos(0) = 2/3 and get the rest of my length from the freefall. I should probably know this but I can't seem to put the pieces together. Help please!

 

[Dweirdo]

Ok so after some struggling I realized that the attempt above is completely wrong. I have broken the circle down into its components and solved for cos(O) and got 2/3 which I was able to verify so I know that part is right. So I have also found that part of the length is Rsin(O) and now I need to solve for the rest. I hope I'm making this clear because I don't think I am. Please let me know if you need more info. I think I'm at the point where the normal force is at 0 and the object goes into parabolic freefall. The problem is I don't know how to finish the problem. How do I take what I have solved for so far, Cos(0) = 2/3 and get the rest of my length from the freefall. I should probably know this but I can't seem to put the pieces together. Help please!

Basically,You finished it...
Not much left, remember:
the ball when it disconnects has V tangential to the point it was left, you can find the V in the y direction and V in the X direction,You have initial height, get T from kinematics of the y direction, and than place it in the X direction distance.
tell me if You need more clues, good luck!

 

[Mr Beatnik]

Thanks for the help. I'll try it and see what I come up with. Either way I'll post an answer and maybe you can tell me if it's right.