Tricky track/friction problem (again)

[Ravnus9]

Ok, so i posted this problem last night and got a couple of replies, but sadly no real help. I already have tried to use lagrange equations to solve the problem, and F=ma... i just need help setting up an integral i mean with the lagrange equations i can't figure out how to incorporate the friction correctly... i mess it all up basically... so i am gunna copy and paste the problem again... please help if you can

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.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.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.

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 is fitted around the track.

 

[ehild]

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.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.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.

I think you should use just Newton's second law. Decompose all force components tangential and normal to the track, and express them with the angle alpha. The resultant of all the normal components should give up the centripetal force, mv^2/R inward. The sum of all tangential components is m*dv/dt. The spring is a bit tricky, but you can express its length with alpha, and from that you get the magnitude of the force exerted by the spring. See the picture attached. Show what equations you got and we try to do it further.
Try to use tex when writing in formulas. It is quite easy!

 

[Clausius2]

Ok, so i posted this problem last night and got a couple of replies, but sadly no real help. I already have tried to use lagrange equations to solve the problem, and F=ma... i just need help setting up an integral i mean with the lagrange equations i can't figure out how to incorporate the friction correctly... i mess it all up basically... so i am gunna copy and paste the problem again... please help if you can

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.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.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.

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 is fitted around the track.

You should post a drawing or scheme of your problem. Sure the employing of Lagrange equations is easy for that problem, because it's an energetic method. But please, post a figure of it.