How Can Friction and Spring Dynamics Affect Velocity on a Circular Track?

[Ravnus9]

Alright so my physics teacher assigns this problem, its a take home test problem and we are allowed to use any resource available to us including the internet, he says you won't find the answer anywhere on the web and even if you did it wouldn't look like you did it. Anyway, i am pretty decent at physics and i have a week to complete this problem but its day 2 and i am stuck, i have spent the past 4 hours trying to do it and it seems impossible. I am new here so i don't know exactly how to attach the form so i will try to describe it to you and you can i guess advise me on how to do it? i don't want you to do it for me, i just need some help, anything will be apreciated. Ok so what you have is a circular track hanging vertically in the air. Oh this track is a collar that weighs 1.2 kg. The track has a radius of .18 meters. at the top of the track there is a point labled C. Point C is where the collar started, and at t=0, V-initial equals 0. at 90 degrees from C, in other words theta=0 on a unit circle, there is a point A. You are looking for the Velocity of the collar when it reaches A. So far not too difficult of a problem, a typical work kinetic energy problem. However, attached to the collar is a spring. the spring has its origin .075 meters higher than the center of the circle... or in other words .105 meters down from point C. The springs uncompressed/unstretched length is .105 meters... so it is unstretched when it is at C. And its spring constant equal 300N/M. Now for the part that i can't figure out... the track and the collar have a coefficient of kenetic friction between them of .2. so basically, as the spring stretches farther the normal force from the track increases, thus increasing the amount of friction force. So the frictional force is a function of the spring stretching while also taking into acount the fact that there is normal and tangential acceleration due to the collar traveling about a circular path, but even that seems strange because the radius of curvature could be about either the springs origin or the tracks origin... and the accelaration due to the weight of the collar... i don't know if you can figure out what i am trying to say here... but i think i am trying to incorporate too many different ideas into solving this... i have tried several approaches... mostly Newton's second law and kinematics, or kinetic energy and potential energy. But it seems impossible, if you could just point me in the right direction for how to start... and possibly help with the equation of how to find the normal force versus the stretch of the spring, i would really apreciate it. Thank you for your time... and if you would like a diagram i can scan you what i am using and email it to you. thanks again
Nathan

 

[vsage]

Doesn't seem particularly hard just LONG :). I could probably show you in the right direction if I knew what the heck a collar was. Dog collar? I don't get it :(

 

[Ravnus9]

alright

ok the collar is just a metal piece that fits onto the track and can't come off of it... so the track is a circular metal tube and the collar is just a slightly larger in diameter piece of tubing that's only a couple inches long, that is fitted around the track. And you know i said the same thing about the problem... i just can't figure out an integral that works for the friction. and so then i try to do it different ways... and then, well then i get all messed up... hah.
Nathan

 

[Clausius2]

An advice

An advice:

I have one principle:

when I spend more than two minutes reading a dynamics problem, automatically it means it is very long and hard for making it with Newton's 2nd Law. Therefore the solution is to employ the Lagrange equations.