Finding angle of swinging pendulum

[the whizz]

Homework Statement

6.) A sphere of mass LaTeX Code: m hangs from a string of length LaTeX Code: l and is drawn back so that the string makes an angle of LaTeX Code: \\theta with the vertical axis. It swings down until the strings hits a peg which is LaTeX Code: l/2 directly below the point where the string is attached to the ceiling. When the string hits the peg, the sphere keeps moving and swings up through an angle LaTeX Code: \\alpha . Use conservation of energy to find an equation for the angle LaTeX Code: \\alpha . Show that this equation makes sense with a few, well-chosen examples for LaTeX Code: \\theta .

doesnt exacly show the diagram.

Homework Equations

to find that angle theta. I set up the two equations of 1/2mv^2 = mgh. the first one for the the relationship between the ball at the top and right before it hits the peg when its straight down.

I will scan my solution on here so the diagrams will work hopefully my attachments will be viewable.

The Attempt at a Solution

 

[LowlyPion]

The mass starts at a height, gains KE, strikes the peg, thereby losing some KE, and then rises to another height that will be less than the original height by an amount that was taken from the KE of the object striking the peg. Hence α will necessarily be less than the original θ .

 

[the whizz]

The problem..http://img201.imageshack.us/img201/3900/question6ri5.th.jpg http://g.imageshack.us/thpix.php

My Solution...

http://img217.imageshack.us/img217/2244/scan0012id0.th.jpg http://g.imageshack.us/thpix.php lets see if this works...any help would be great.