Conservation of Energy & circular motion

[nrahim]

The problem is stated on the sheet i have attached along with my attempt to the possible solution. This is a proof and i am very bad at working with proofs. This seems to be a classical problem so I'm sure some of you guys might have seen it, please guide me!

http://img22.imageshack.us/img22/1405/53811275.th.jpg

I have posted the problem with what i have tried... as you can see i was stuck, please guide me if my logic or math is wrong

 

[LowlyPion]

Welcome to PF.

Consider the conditions imposed.

Total energy in the system is m*g*L

To complete a circle then with Vt the velocity at the top of the circle about x

m*Vt²/(L-x) = m*g

m*Vt² = m*g*(L-x)

So ... at the top of that loop

1/2*m*Vt² + m*g*(2*(L-x)) = m*g*L

Substituting ...

1/2*m*g*(L-x) + m*g*(2*(L-x)) = m*g*L

 

[nrahim]

thanks a lot my friend.. you saved me a lot of hassle:D