1. Not finding help here? Sign up for a free 30min 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!

Equilibrium - Particle in Bowl, looking for guidance

  1. Dec 6, 2007 #1
    Equilibrium - Particle in Bowl, looking for guidance!!

    1. The problem statement, all variables and given/known data
    A point particle of mass m is confines to the frictionless surface of a sphere cal bowl. There are 2 degrees of freedom. Prove that the equilibrium point is the bottom of the bowl. Near the bottom of the bowl, what is the most general form possible for the shape of the bowl in order to maintain the stability of the equilibrium point at the bottom?


    2. Relevant equations
    spherical coordinates: rsin[tex]\thetacos\varphi + rsin\thetasin\varphi + rcos\theta[/tex]
    Lagrange = Kinetic Energy(T)- Potential (V)

    3. The attempt at a solution
    I started off by getting the Lagrange and got:
    [tex]\stackrel{1}{2}[/tex]r^2 (theta)'^2 - mgrcos(theta)
    Then I got the E.O.M
    (mr^2 (theta)'')/2 - mgsin(theta)


    I have to prove that it is at equilibrium at [tex]\theta[/tex]=0
    But when I plug in 0 I am still left with (mr^2 (theta)'')/2
    What am I doing wrong

    [NOTATION::(theta)' is theta dot or velocity and (theta)'' is theta double dot or acceleration]

    Any help is appreciated!!
    Thanks
     
  2. jcsd
  3. Dec 7, 2007 #2
    i guess it´s not useful to go with the lagrangian just build up your potential in terms of spherical coordinates.
    I guess it is V=m*g*r*sin(theta) as you said. And as in your case theta is between 0 and Pi/2
    the minimum is at theta =0 because this is the lowest value sine take on [0,Pi/2]
    how about that ?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Equilibrium - Particle in Bowl, looking for guidance
  1. Fish in a Fish bowl? (Replies: 1)

  2. Parabolic Bowl (Replies: 2)

Loading...