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!

Lagrangian equation for 5 pulley Atwood Machine.

  1. Apr 9, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider the Atwood’s pulley shown below. The masses are 4m, 3m, and m. Let x and y be the directed distances from the centers of the fixed (i.e. inertial) top pulleys for the left and right masses as indicated.
    VXEygxt.png
    http://imgur.com/VXEygxt

    a) Write down the Lagrangian for this system in terms of x and y and their time derivatives as usual. (You will need to eliminate z, the distance 3m is from the inertial pulleys using the single rope constraint).

    b) By inspection, determine transformations of the form x → x+Kxε, y→y+Kyε that leave the Lagrangian invariant (i.e. determine the generators Kx and Ky). Then use Noether’s theorem to construct the conserved momentum for the system

    2. Relevant equations

    L=T-U

    3. The attempt at a solution

    a) I'm unsure how to deal with the middle pulley. At the moment I have:

    T=1/2{4m(x')2 + m(y')2 + 3m(z-(x'))2 + 3m(z-(y'))2}

    U=4mgx-mgy+3mg(x-y-z)

    b) I don't understand what it's asking. Is there an easier way to explain what it's asking?

    Thanks!
     
  2. jcsd
  3. Apr 9, 2013 #2

    jedishrfu

    Staff: Mentor

    your image link is broken
     
  4. Apr 9, 2013 #3
    Oops! Fixed. Thanks.
     
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: Lagrangian equation for 5 pulley Atwood Machine.
  1. Atwood machines (Replies: 1)

  2. Double Atwood machine (Replies: 4)

Loading...