# Homework Help: Circular motion problem. Help appreciated.

1. Nov 7, 2004

### KnowledgeIsPower

I have around 15 pages of the book to go and unfortunately came across an annoying problem where i am getting a slightly different answer to the book. Any help is appreciated. The question is as follows:

A particle of mass m is suspended from a fixed point A by a light inextensible string of length l. The particle moves in a horizontal circle, whose centre is vertically below A, with constant angular speed w and with the string taut and inclined at an angle theta to the downward vertical through A.
a) Show (w^2)lcos(theta) = g. [Done this part. Part (b) is the problem]:

The string is replaced by a light elastic string of natural length a and modulus of elasticity lamda. The particle now moves in a horizontal circle, whose centre is vertically below A, with constant angular speed 2w. The elastic string makes the same angle theta to the downward vertical:
b) Show that 1/(4a) - 1/(4l) = (mw^2)/(lamda) [This is the problem. I am getting a slightly different answer. My working is attached. Have i gone wrong somewhere or is there a typo in the book?
http://img129.exs.cx/img129/1708/Q16B-P1.jpg
http://img129.exs.cx/img129/1452/Q16B-P2.jpg

Thanks for any help.