- #1

Lambdalove

picture: https://ibb.co/k5P0GG

Two objects slide without friction on a circular ring of radius R, oriented in a vertical plane. The heavier object (of mass 3m) is attached to a spring with an unstretched length of zero (admittedly an unphysical assumption) and spring constant k. The fixed end of the spring is attached to a point a horizontal distance 2R from the center of the circle.

1. What is the kinetic and potential energy of the heavy particle in the initial state, when it passes the left most position, horizontal with respect to the center of the circle, and when it hits the light particle.

Here's what I've come up with (K_f is just before collision)

K_i + U_i + U_spring = K_f + U_f

0 + (3m)g(2R)+k/2(displacement) = 1/2(3m)(v_1)^2+k/2(displacement)

I'm having trouble with finding the displacement of the spring, as it is along a circular path, which I haven't worked with before. Should I only account for the x-axis displacement, add x- and y-axis displacement or am I completely lost?

Any help is much appreciated!