1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Circular motion with friction differential equation

  1. Sep 24, 2015 #1
    1. The problem statement, all variables and given/known data
    Capture.PNG

    2. Relevant equations

    F=ma
    ac=v^2/r
    f=uN
    v=v0+at
    w=v/r
    3. The attempt at a solution

    v=v0+at
    v=vo+umv^2/r
    v^2(u/r)-v+vo=0


    I don't see what differential equation i could use since the speed is dependent on the friction (equal to friction coeff times centripetal force) which in it's turn is also dependent on the speed
     
  2. jcsd
  3. Sep 24, 2015 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Your v=v0+at equation only applies for constant acceleration. It will not be.
     
  4. Sep 24, 2015 #3
    As i understand this problem, the centripetal force, which points towards the center of the ring, equals the normal force. In that case, the friction would be equal to a coefficient times the centripetal force. When the speed changes (due to friction), the centripetal force will change (mv^2/r) and so will the normal. However since the speed is dependent on the friction which in turn is dependent on the speed, I seem to be stuck in a circular situation. Would any one have advice to help me find the relation that will allow me to express v? Thanks!
     
  5. Sep 24, 2015 #4
    image.jpg
    my solution gives me v instead of v0 in the denominator. Is there a typo in the statement? Thanks
     
  6. Sep 24, 2015 #5

    TSny

    User Avatar
    Homework Helper
    Gold Member

    You used the expression v = vo - atant which is not applicable, as haruspex pointed out.

    You found atan = μv2/R. Express the acceleration on the left side in terms of the rate of change of the speed.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Circular motion with friction differential equation
Loading...