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!

Pendulum motion

  1. Mar 10, 2009 #1
    1. The problem statement, all variables and given/known data
    My teacher gave us a problem to work, but it's not assigned. He will probably give extra credit or something if we can do it... But anyway, I kind of want to solve it on my own, but I need a little help getting started.

    Ok, so let's say there is a cart of mass 'M' that can move horizontally on frictionless rails, and there is a pendulum of mass 'm' and length 'a' attached to the cart. (either hanging underneath it, or hanging down a rod coming up off the cart, it shouldn't matter.) The pendulum and cart are initially at rest, then suddenly an impulse is applied to the pendulum giving it a momentum of p, and an angular velocity of w. The motion of the pendulum will cause the cart to begin moving.
    I need to find a way to describe the motion of the pendulum and cart as functions of time. (I think for the pendulum a function of motion relative to the cart will be fine, or not... either way.)
    The actual problem involves two pendulums, but if I can do this I'd like to try and extend it to the two pendulum problem myself.


    2. Relevant equations
    [itex]\omega = \frac{p}{m*r}[/itex]
    [itex]a_{centripetal} = \frac{v^{2}}{r}[/itex]
    F = ma
    and possibly:
    KE = (1/2)mv^2
    PE = mgh

    3. The attempt at a solution
    I have tried several different approaches, I think that my problem is that I can't figure out exactly how to relate the motion of the pendulum to the resulting motion of the cart.
    I tried finding the centripetal force on the pendulum bob, which should be equal in magnitude to the force that will "pull" the cart. There should also be a gravitational force acting parallel to the string (between cart and pendulum). I then add those forces together to find the force on the cart:
    [tex]F_{cart} = -mg*sin^{2}(\theta) + \omega^{2}am*sin(\theta)[/tex]
    But theta, is a function of time (I think), so I'm not sure how to proceed.
    I also tried a few differential equations that didn't work out so well. I won't list all of my attempts as it will probably just get messy and won't help anyone help me anyway.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted