A spring is attatched to a single position with a 1.2 kg collar at the end. The collar is attatched to a circular fixed body so it can rotate around it. The radius of the circle is 180 mm and the position of where the spring is attatched is 75mm directrly above the center of circle. The springs constant is 300 n/m and its undeformed length is 105mm. It starts out at rest at the top of the circle and is given a slight push to get it moving. It passes through point A on the circle, which is located halfway down on the circle. Using energy methods, find the velocity of collar as it passes through point A.
Vs=1/2kX^2=potential spring energy, Vg=(distance)x(weight)=gravitational potential energy
The Attempt at a Solution
the distance of point A to the attatched spring is sqrt(75^2+180^2)=195mm
The elongation of the spring is therefore 195-105=90mm then the potential energy would be 1/2kX^2=1/2(300N/m)(.09mm)^2=1.215 J
and the gravitational potential energy would be (.18mm)(1.2 kg)(9.8m/s^2)=2.1
This is where I don't know what to do after calculating the potential energy at point A. How am I supposed to get velocity out of all this mess?
I understand this is a lengthy problem so any help will be GREATLY appreciated.